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The monolayer metamaterial that consists of graphene arrangement squares and four L-shaped graphene blocks is designed to achieve quintuple plasmon-induced transparency (quintuple-PIT). First, the accuracy of the results has been validated through finite difference time domain simulations and coupled mode theory, which show good agreement. Second, a quadruple-frequency asynchronous switch with amplitude modulation degree (AMD) values of 94.7%, 91.1%, 96.6%, and 77.4% and a sextuple-frequency synchronous switch with AMD values of 95.0%, 96.8%, 88.0%, 93.3%, 58.6%, and 71.5% have been proposed by dynamic control, respectively. It is worth noting that the number of PIT windows in the transmission curve can be freely adjusted from a quintuple-PIT to single-PIT mode by manipulating the Fermi level states of different parts of the structure. Finally, further investigations have demonstrated that the proposed structure exhibits excellent slow-light properties and is insensitive to polarized light, which indicates that the metamaterial structure possesses good stability and anti-interference capabilities under various polarization conditions. The metamaterial and results provide valuable insights and ideas for the design of optoelectronic devices. [ABSTRACT FROM AUTHOR]

In this work, the Hellmann–Feynman theorem is extended within the doubly occupied configuration interaction space to enable practical calculations of reduced density matrices and expected values. This approach is straightforward, employing finite energy differences, yet remains reliable and accurate even with approximate energies from successive approximation methods. The method's validity is rigorously tested against the Richardson–Gaudin–Kitaev and reduced Bardeen–Cooper–Schrieffer models using approximate excitation energies procured from the Hermitian operator method within the same space, effectively proving the approach's reliability with median error rates for reduced density matrix calculations around 0.1%. These results highlight the procedure's potential as a practical tool for computing reduced density matrices and expected values, particularly valuable as an ad hoc method in scenarios where only system energies are easily available. [ABSTRACT FROM AUTHOR]

Ge1−xSnx thin films with a Sn content of x ≥ 0.1 present a direct bandgap, which is very interesting for the fabrication of efficient photonic devices. The monostanogermanide phase, Ni(GeSn), is promising to form ohmic contact in GeSn-based Si photonic devices. However, the formation kinetics of Ni stanogermanides and the incorporation of Sn in Ni–GeSn phases are not fully understood. In this work, Ni thin films were deposited on Ge and Ge0.9Sn0.1 layers grown in epitaxy on an Si(100) substrate using magnetron sputtering technique. In situ x-ray diffraction measurements were performed during the solid-state reaction of Ni/Ge and Ni/Ge0.9Sn0.1. 1D finite difference simulations based on the linear parabolic model were performed to determine the kinetics parameters for phase growth. The nucleation and growth kinetics of Ni germanides are modified by the addition of Sn. A delay in the formation of Ni(GeSn) was observed and is probably due to the stress relaxation in the Ni-rich phase. In addition, the thermal stability of the Ni(GeSn) phase is highly affected by Sn segregation. A model was developed to determine the kinetic parameters of Sn segregation in Ni(GeSn). [ABSTRACT FROM AUTHOR]

The high-order finite difference real-space pseudopotential density functional theory (DFT) approach is a valuable method for large-scale, massively parallel DFT calculations. A significant challenge in the approach is the oscillating "egg-box" error introduced by aliasing associated with a coarse grid spacing. To address this issue while minimizing computational cost, we developed a finite difference interpolation (FDI) scheme [Roller et al., J. Chem. Theory Comput. 19, 3889 (2023)] as a means of exploiting the high resolution of the pseudopotential to reduce egg-box effects systematically. Here, we show an implementation of this method in the PARSEC code and examine the practical utility of the combination of FDI with additional methods for improving force precision and/or reducing its computational cost, including orbital-based forces, compensating charges (namely, adding and subtracting a judiciously chosen charge density such that the total density is unaltered), and a modified spatial domain in which the real-space grid is defined. Using selected small molecules, as well as metallic Li, as test cases, we show that a combination of all four aspects leads to a significant reduction in computational cost while retaining a high level of precision that supports accurate structures and vibrational spectra, as well as stable and accurate molecular dynamics runs. [ABSTRACT FROM AUTHOR]

We have used surface plasmon resonant metal gratings to induce and probe the dielectric response (i.e., electro-optic modulation) of ionic liquids (ILs) at electrode interfaces. Here, the cross-plane electric field at the electrode surface modulates the refractive index of the IL due to the Pockels effect. This is observed as a shift in the resonant angle of the grating (i.e., Δϕ), which can be related to the change in the local index of refraction of the electrolyte (i.e., Δnlocal). The reflection modulation of the IL is compared against a polar (D2O) and a non-polar solvent (benzene) to confirm the electro-optic origin of resonance shift. The electrostatic accumulation of ions from the IL induces local index changes to the gratings over the extent of electrical double layer (EDL) thickness. Finite difference time domain simulations are used to relate the observed shifts in the plasmon resonance and change in reflection to the change in the local index of refraction of the electrolyte and the thickness of the EDL. Simultaneously using the wavelength and intensity shift of the resonance enables us to determine both the effective thickness and Δn of the double layer. We believe that this technique can be used more broadly, allowing the dynamics associated with the potential-induced ordering and rearrangement of ionic species in electrode–solution interfaces. [ABSTRACT FROM AUTHOR]

A consideration of the point group symmetry of molecules is often advantageous from a computational efficiency standpoint and sometimes necessary for the correct treatment of chemical physics problems. Many modern electronic structure software packages include a treatment of symmetry, but these are sometimes incomplete or unusable outside of that program's environment. Therefore, we have developed the MolSym package for handling molecular symmetry and its associated functionalities to provide a platform for including symmetry in the implementation and development of other methods. Features include point group detection, molecule symmetrization, arbitrary generation of symmetry element sets and character tables, and symmetry adapted linear combinations of real spherical harmonic basis functions, Cartesian displacement coordinates, and internal coordinates. We present some of the advantages of using molecular symmetry as achieved by MolSym, particularly with respect to Hartree–Fock theory, and the reduction of finite difference displacements in gradient/Hessian computations. This package is designed to be easily integrated into other software development efforts and may be extended to further symmetry applications. [ABSTRACT FROM AUTHOR]

We report the implementation of the analytical Hessian for the mechanochemical extended hydrostatic compression force field method in the Q-Chem program package. To verify the implementation, the analytical Hessian was compared with finite difference calculations. In addition, we calculated the pressure dependency of the Raman active vibrational modes of methane, ethane, and hydrogen, as well as all IR and Raman active modes of Buckminsterfullerene, and compared the results with experimental and theoretical data. Our implementation paves the way for the analysis of geometric points on a pressure-deformed potential energy surface and provides a straightforward model to calculate the vibrational properties of molecules under high pressure. [ABSTRACT FROM AUTHOR]

The investigation of charge carrier transport in state-of-the-art nanoelectronic devices based on III/V semiconductors proves to be challenging, even more so when the highly non-parabolic energy dispersion exhibited by these materials is taken into account. Unlike the common approach of neglecting this behavior by the use of the parabolic band approximation, a novel combination of a tight-binding approach with a quantum Liouville-type equation is introduced here, where any arbitrary energy dispersion can effectively be included. This leads to a discretization based on the atomic structure without the need for finite difference approximations of the Hamiltonian. Because this allows for the stationary as well as the transient simulation of quantum charge carrier transport, it is well suited for the analysis of ultrathin FETs such as dual-gate FETs when it is combined with a mode-space approach. We demonstrate that the parabolic approximation not only vastly underestimates the current densities when compared to the non-parabolic case but also fails to capture transient effects such as gain compression when amplifier operation is considered. [ABSTRACT FROM AUTHOR]

Scanning x-ray microbeam topography and fluorescence experiments were conducted in situ to study the electromigration behavior of a 0.5 μm thick, 10 μm wide, and 200 μm long Al(0.25 at. % Cu) conductor line with 1.5 μm-thick SiO2 passivation on a single crystal Si substrate. The strain sensitivity of x-ray topography measurement allowed detailed examination of the electromigration-induced stress distribution and evolution in the conductor line in response to the depletion of Cu solute early in the electromigration process. Upon electromigration at 0.4 MA/cm2 and 303 °C, a short-range stress gradient was quickly induced by Al migration in the Cu-depleted cathode region to counteract further Al flow. The stress gradient was fully developed during the 5.3 h incubation time, extending over the critical Blech length of about 66 μm from the cathode end. Plastic deformation then occurred at the downstream end of the Cu-depleted region. The preferential electromigration of Cu did not cause detectable stress change outside the Cu-depleted region, except for the significant stress development from the Al2Cu precipitation at the anode end which appeared to initiate the fracture in the passivation. Preliminary finite difference modeling was undertaken to simulate the experimental observations, from which important parameters dictating electromigration in Al(Cu) line were extracted: an apparent effective valence of −5.6 and −1.9 for Cu and Al in Al(Cu), respectively, and a critical Cu concentration of 0.16 at. % above which Al grain boundary diffusion is effectively blocked. [ABSTRACT FROM AUTHOR]

Thermodynamics shows that the open-circuit voltage (V o c) of a solar cell is dependent on the external radiative efficiency at V o c . In planar solar cells with low photon recycling probability, this efficiency is limited to 2% due to total internal reflection of the emitted light, providing a penalty of 101 mV to the V o c . Tapered nanowire solar cells allow for an adiabatic expansion of the guided optical mode into air, allowing to reduce this loss. For this purpose, we first perform simulations of the photon escape probability in tapered nanowires with both finite difference time domain simulations as well as with rigorous coupled-wave analysis, showing photon escape probabilities up to 47.2% for normally tapered nanowires and up to 92% for inversely tapered nanowires. We subsequently show that by fine tuning the recipe for reactive ion etching of the tapered InP nanowires, we can decrease the nanowire tapering angle from 4.5° down to 1.8°, allowing to significantly increase the measured external radiative efficiency. We finally observe an open-circuit voltage of 0.746 V at a tapering angle of 2.46°. [ABSTRACT FROM AUTHOR]

Microring resonators (MRRs), typically comprising straight and ring waveguides, have played pivotal importance in recent years as far as integrated on-chip systems are concerned. The evanescent coupling in such MRR or solid microdisk resonators is very sensitive to the coupling gap between two waveguides, which affects the resonator's performance. To overcome the stringent requirement of the gap between two waveguides, we propose a coupling-gap-free, on-chip ellipsoid microresonator. The theoretical framework has been deduced to attain the modal properties of such integrated microresonator geometry, which shows an excellent agreement with the finite difference time domain simulations and experimental results. The absence of a coupling region makes the device uniquely compact and robust, with an insertion loss of ∼ 5 dB. The resonator's geometrical dimensions can also be conveniently scaled within certain constraints. The proposed device can be a potential alternative to MRRs and could help in applications such as optical filters, delay lines, on-chip sensing, and many more. [ABSTRACT FROM AUTHOR]

Slow and very slow landslides can cause severe economic damage to structures. Due to their velocity of propagation, it is possible to take action such as programmed maintenance or evacuation of affected zones. Modeling is an important tool that allows scientists, engineers, and geologists to better understand their causes and predict their propagation. There are many available models of different complexities which can be used for this purpose, ranging from very simple infinite landslide models which can be implemented in spreadsheets to fully coupled 3D models. This approach is expensive because of the time span in which the problems are studied (sometimes years), simpler methods such as depth‐integrated models could provide a good compromise between accuracy and cost. However, there, the time step limitation due to CFL condition (which states that the time step has to be slower than the ratio between the node spacing Δx$\Delta x$ and the physical velocity of the waves results in time increments which are of the order of one‐10th of a second on many occasions. This paper extends a technique that has been used in the past to glacier evolution problems using finite differences or elements to SPH depth‐integrated models for landslide propagation. The approach is based on assuming that (i) the flow is shallow, (ii) the rheological behavior determining the velocity of propagation is viscoplastic, and (iii) accelerations can be neglected. In this case, the model changes from hyperbolic to parabolic, with a time increment much larger than that of classic hyperbolic formulations. [ABSTRACT FROM AUTHOR]

In our research laboratory, we have developed an absorber composed of various materials and structures. This absorber comprised the following layers arranged from top to bottom: a cubic array layer of titanium and silicon dioxide (SiO2), a magnesium fluoride dielectric layer (MgF2), and an aluminum substrate. Previously, we employed finite difference time domain (FDTD) simulations to identify optimal parameters for this structure and subsequently applied them to COMSOL simulations. The optimal parameters determined through FDTD simulations resulted in an average absorptivity of 95.2% within the wavelength range from 400 to 1500 nm. However, when these parameters were applied to COMSOL simulations, the average absorptivity within the same wavelength range decreased to 93.7%. Subsequently, we utilized COMSOL to adjust various parameters in order to identify the optimal ones. Our investigation focused on exploring the impact of different parameters such as material thicknesses, absorber structures, electromagnetic field distributions, and incident angles on the absorptivity. Through this comprehensive analysis, we aimed to refine our understanding of how these parameters affect the absorptivity performance of the structure. This research not only contributes to the optimization of absorber design but also enhances our knowledge of the underlying physical mechanisms governing light absorption in such structures. [ABSTRACT FROM AUTHOR]

This paper addresses the valuation of European options, which involves the complex and unpredictable dynamics of fractal market fluctuations. These are modeled using the α -order time-fractional Black–Scholes equation, where the Caputo fractional derivative is applied with the parameter α ranging from 0 to 1. We introduce a novel, high-order numerical scheme specifically crafted to efficiently tackle the time-fractional Black–Scholes equation. The spatial discretization is handled by a tailored finite point scheme that leverages exponential basis functions, complemented by an L1-discretization technique for temporal progression. We have conducted a thorough investigation into the stability and convergence of our approach, confirming its unconditional stability and fourth-order spatial accuracy, along with (2 − α) -order temporal accuracy. To substantiate our theoretical results and showcase the precision of our method, we present numerical examples that include solutions with known exact values. We then apply our methodology to price three types of European options within the framework of the time-fractional Black–Scholes model: (i) a European double barrier knock-out call option; (ii) a standard European call option; and (iii) a European put option. These case studies not only enhance our comprehension of the fractional derivative's order on option pricing but also stimulate discussion on how different model parameters affect option values within the fractional framework. [ABSTRACT FROM AUTHOR]

This paper presents a study of the hydraulic response of an infinite unsaturated slope exposed to a perturbation of the ordinary seasonal climatic cycle. The ground flow is modelled via a simplified one-dimensional finite difference scheme by decomposing the two-dimensional slope seepage into antisymmetric and symmetric parts. The numerical scheme incorporates two distinct hysteretic and non-hysteretic soil water retention laws, whose parameters have been selected after a preliminary sensitivity analysis. Results indicate that, in the hysteretic case, the "memory" of the perturbation takes a long time to fade, and the ordinary soil saturation cycle is only restored after several years of normal weather. Instead, in the non-hysteretic case, the recovery of the ordinary saturation regime is almost immediate after the perturbation. In contrast with the markedly different predictions of degree of saturation, both hysteretic and non-hysteretic slope models predict virtually identical evolutions of negative pore water pressures, with an almost immediate restoration of the ordinary cycle after the perturbation. [ABSTRACT FROM AUTHOR]

This paper is devoted to the theoretical and numerical investigation of the initial boundary value problem for a system of equations used for the description of waves in coastal areas, namely, the Boussinesq–Abbott system in the presence of topography. We propose a procedure that allows one to handle very general linear or nonlinear boundary conditions. It consists in reducing the problem to a system of conservation laws with nonlocal fluxes and coupled to an ordinary differential equation. This reformulation is used to propose two hybrid finite volumes/finite differences schemes of first and second order, respectively. The possibility to use many kinds of boundary conditions is used to investigate numerically the asymptotic stability of the boundary conditions, which is an issue of practical relevance in coastal oceanography since asymptotically stable boundary conditions would allow one to reconstruct a wave field from the knowledge of the boundary data only, even if the initial data are not known. [ABSTRACT FROM AUTHOR]

Control of nonlinear systems in the presence of model mismatch and system constraints is quite challenging. To address the issue, this work proposes an adaptive Gaussian process-based real-time optimisation (AGP-RTO) control framework. Specifically, the control law consists of two components, a feedforward tracking control law and an uncertainty compensation control law. Because GP has high flexibility to capture complex unknown functions by using very few parameters and it inherently handles measurement noise, this work utilises the GP as an alternative to estimate the mismatch between the real plant and the approximated model. During every RTO execution, the GPs adaptively update the predictions of the model mismatch, then the predictions are embedded into a nonlinear optimisation problem for the correction of the model cost and constraint functions, which yields the uncertainty compensation control law. The proposed AGP-RTO framework ensures that the Karush-Kuhn-Tucker (KKT) conditions determined by the model match those of the plant upon convergence. Compared to many direct adaptive control methods, AGP-RTO does not rely on a high gain for fast adaptation and hence it improves the robustness of the closed-loop system. Compared to the modifier adaptation (MA) method, AGP-RTO avoids the plant-gradient estimation by using the finite difference scheme, besides it trains the GP models offline, which speeds up online evaluation and improves the applicability and efficacy of real-time control. Comparisons are carried out to illustrate the superiority of the AGP-RTO. [ABSTRACT FROM AUTHOR]

This study introduces an alternative method to the Takagi–Taupin equations for investigating the dark‐field X‐ray microscopy (DFXM) of deformed crystals. In scenarios where dynamical diffraction cannot be disregarded, it is essential to assess the potential inaccuracies of data interpretation based on the kinematic diffraction theory. Unlike the Takagi–Taupin equations, this new method utilizes an exact dispersion relation, and a previously developed finite difference scheme with minor modifications is used for the numerical implementation. The numerical implementation has been validated by calculating the diffraction of a diamond crystal with three components, wherein dynamical diffraction is applicable to the first component and kinematic diffraction pertains to the remaining two. The numerical convergence is tested using diffraction intensities. In addition, the DFXM image of a diamond crystal containing a stacking fault is calculated using the new method and compared with the experimental result. The new method is also applied to calculate the DFXM image of a twisted diamond crystal, which clearly shows a result different from those obtained using the Takagi–Taupin equations. [ABSTRACT FROM AUTHOR]

In this paper, a finite difference (FD) scheme based on time two-grid algorithm is proposed for solving the two-dimensional time-fractional Fisher equation (2D-TFFE). Firstly, the Caputo fractional derivative and the spatial derivative are discretized by the $ L2-1_\sigma $ L 2 − 1 σ formula and the central difference formula, respectively. In order to improve the efficiency of computation, the time two-grid algorithm is then constructed. Secondly, based on the cut-off function technic, stability and convergence of the time two-grid FD scheme are obtained by the energy method, and the global convergence order is $ O(\tau _{F}^2 +\tau _{C}^4 +h_x^2 +h_y^2) $ O (τ F 2 + τ C 4 + h x 2 + h y 2) , where $ \tau _{F} $ τ F and $ \tau _{C} $ τ C represent time-step sizes on the fine and coarse grid, respectively, while $ h_x $ h x and $ h_y $ h y represent the space-step sizes. Finally, numerical experiments are presented to show the feasibility and efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a generalized diffusion–advection–reaction equation (GDARE) is considered and by using the solitary wave solution two new class of exact finite difference (EFD) schemes are proposed under certain functional relationship between the temporal and space step sizes. Suitable denominator functions are identified from these EFD schemes and a new non-standard finite difference (NSFD) scheme is developed. This NSFD scheme preserves positivity and boundedness properties of the solution of GDARE. The $ L_2 $ L 2 , $ L_\infty $ L ∞ errors and CPU times are obtained for the proposed NSFD and EFD schemes to show the proficiency and accuracy of the schemes. [ABSTRACT FROM AUTHOR]

Time domain finite difference methods have been widely used for wave‐equation modelling in exploration geophysics over many decades. When using time domain finite difference methods, it is desirable to use a larger time step so as to save numerical simulation time. The Lax–Wendroff method is one of the well‐known methods to allow larger time step without increasing the time grid dispersion. However, the Lax–Wendroff method suffers from more time consumption because there are more spatial derivatives required to be approximated by the finite difference operators. We propose a new finite difference scheme for the Lax–Wendroff method so as to reduce the numerical simulation time. Then we determine the finite difference operator coefficients and analyse the dispersion error of the proposed finite difference scheme for the Lax–Wendroff method. At last, we apply the proposed finite difference scheme for the Lax–Wendroff method to different velocity models. The numerical simulation results indicate that the proposed finite difference scheme for the Lax–Wendroff method can effectively suppress time grid dispersion and is more efficient compared to the traditional finite difference scheme for the Lax–Wendroff method. [ABSTRACT FROM AUTHOR]

The current study explores the transient magnetohydrodynamic (MHD) flow with the interaction of quadratic convection, slip of second‐order momentum, viscous dissipation, and Newtonian heating. In this setup, the governing equations become highly nonlinear. The numerical solutions are attained by utilizing an implicit type of the Crank–Nicolson technique. The primary aim of the exploration is to figure out the consequence of MHD nonlinear convection and momentum slip of second‐order on the overall behavior of the system. The robust agreement is evinced by numerical computations verified against existing research. Skin friction and Nusselt number decreases for second‐order slips, δ=0,−2,−4,−8 $\delta =0,-2,-4,-8$, and −16. And for γ=1.0 $\gamma =1.0$ and δ=‐2.0 $\delta = \mbox{-} 2.0$ the temporal coefficients of friction and heat transmission attain a steady state at time t = 29.88. It is significant that nonlinear convection predominates over viscous dissipation and that nonlinear convection is influenced by magnetic fields. The results are described using plots and tables. [ABSTRACT FROM AUTHOR]

Film boiling has practical applications in the current technology including steam power plants, cooling of electronic devices and emergency cooling systems. A finite difference/front tracking method is used to simulate film boiling at high density ratios on a horizontal plate subject to a constant wall heat flux. The grid resolution is relatively high (768 grids per width of the domain). The flow is dominated by Rayleigh–Taylor instability as well as Kelvin–Helmholtz instability. The flow structure includes the roll up of the interface between the gas and liquid. This happens at high density ratio (1000) where the difference between the gas and the liquid velocities across the interface is large. The jump in tangential velocity is an order of magnitude smaller at a lower density ratio (100). Hence, there is no roll up at a lower density ratio. The flow is also influenced by vortex development as a result of the baroclinic term in the vorticity transport equation. The density gradient is large at the interface at high density ratio which tends to amplify the baroclinic term. The plot of pressure gradient and density gradient shows that they are not parallel in the roll up regions. As a result, vortices in small scales develop that shed in the gas phase. The plot of the enstrophy with time shows that it is smooth and match for two grid resolutions, however at a specific time enstrophies become spiky, and they depart from each other at two grid resolutions. The spiky behavior of enstrophy is due to vortex shedding in the roll up region. [ABSTRACT FROM AUTHOR]

In this paper, the effect of crosstalk noise in a mutually coupled multiwalled carbon nanotube (MWCNT) interconnect were investigated. The multiresolution time-domain method (MRTD) is used to analyze the crosstalk noise model. On the victim line of MWCNT interconnects, the worst-case propagation delay and peak voltage have been measured and compared to those obtained using the conventional finite difference time domain (FDTD) method, and HSPICE simulations for the 22 nm technology node have been validated. The results of the proposed method shows that the crosstalk induced propagation delays in both dynamic in-phase, out-phase, and peak voltage timing and peak voltage in functional crosstalk of the MWCNT interconnects are an average error less than 2% for the proposed model and conventional FDTD model with HSPICE simulations. It has been observed that the simulation results of the proposed model match accurately with HSPICE and dominate the conventional FDTD model. For various cases of input switching, the proposed numerical model is extremely time efficient and effective in evaluating crosstalk mediated propagation delay and peak voltages. The suggested approach could also be used to fix problems including electromagnetic interference and on-chip interconnect reliability. [ABSTRACT FROM AUTHOR]

In this article, we propose two procedures focusing on the computation of the time‐dependent convected wave equation in a free field with a uniform background flow. Both procedures are based on a framework, expended from Du et al. (SIAM J. Sci. Comput. 40 (2018), A1430–A1445.), of constructing the Dirichlet‐to‐Dirichlet (DtD)‐type discrete absorbing boundary conditions (ABCs). The first procedure is dedicated to reducing the infinite problem into a finite problem by a direct application of the framework on the finite difference discretization of the convected wave equation. However, the presence of convection terms makes the stability analysis hard to implement, which motivates us to develop the second procedure. First, the convected wave equation is transformed into a standard wave equation by using the Prandtl‐Glauert‐Lorentz transformation. After that, we obtain the DtD‐type ABC by using the above framework, and on this basis, derive an equivalent Dirichlet‐to‐Neumann‐type ABCs, which makes stability and convergence analysis easy to be obtained by the classical energy method. The effectiveness and comparison of these two procedures are investigated through numerical experiments. [ABSTRACT FROM AUTHOR]

Use of the finite difference method has produced successful solutions to the general partial differential equations due to its efficiency and effectiveness with wide applications. For example, the 2D Boussinesq paradigm equation can be numerically studied using a linear‐implicit finite difference scheme based on the Crank‐Nicolson/Adams‐Bashforth technique. First, conservative quantities are derived and preserved through numerical scheme. Then, the convergence and stability analysis is then provided to simulate a numerical solution whose existence and uniqueness are proved based on the boundedness of the numerical solution. Analysis of spatial accuracy is found to be second order on a uniform grid. Numerical results from simulations indicate that these proposed scheme provide satisfactory second‐order accuracy both in time and space with an L∞$$ {L}^{\infty } $$‐norm, and also preserve discrete invariants. Additionally, previous scientific literature review has provided little evidence of studied terms with dispersive effect in 2D Boussinesq paradigm equation. The current study explores solution behavior by applying the proposed scheme to numerically analyze initial Gaussian condition. [ABSTRACT FROM AUTHOR]

Linear viscoelasticity can be characterized by a stress relaxation function. We consider a power‐law type stress relaxation to yield a fractional order viscoelasticity model. The governing equation is a Volterra integral problem of the second kind with a weakly singular kernel. We employ spatially discontinuous Galerkin methods, symmetric interior penalty Galerkin method (SIPG) for spatial discretization, and the implicit finite difference schemes in time, Crank–Nicolson method. Further, in order to manage the weak singularity in the Volterra kernel, we use a linear interpolation technique. We present a priori stability and error analyses without relying on Grönwall's inequality, and so provide high quality bounds that do not increase exponentially in time. This indicates that our numerical scheme is well‐suited for long‐time simulations. Despite the limited regularity in time, we establish suboptimal fractional order accuracy in time as well as optimal convergence of SIPG. We carry out numerical experiments with varying regularity of exact solutions to validate our error estimates. Finally, we present numerical simulations based on real material data. [ABSTRACT FROM AUTHOR]

The current article investigates the effects of nonlinear mixed convection flow in an upright channel with asymmetric or symmetric heating and cooling conditions, considering the influence of temperature-dependent thermal conductivity. The momentum equation is approximated using the nonlinear Boussinesq approximation in the buoyancy force term. Computational solutions for the dimensionless partial differential equations are obtained through the use of an unconditionally stable and convergent implicit finite difference technique. A regular perturbation series approach is employed to ascertain steady-state solutions, facilitating the assessment of the correctness of the numerical approach. During the numerical computing process, it is observed that the nonlinearity in density variation with temperature, along with the mixed convection parameter and the symmetric or asymmetric heating and cooling of the plates, significantly influences flow generation. It is also noted that in the scenario of asymmetric heating, fluid motion is stronger at the bottom plate, whereas in the case of symmetric heating/cooling settings, the highest velocity is observed in the center of the channel. [ABSTRACT FROM AUTHOR]

Solitons of the purely cubic nonlinear Schrödinger equation in a space dimension of n ≥ 2 suffer critical and supercritical collapses. These solitons can be stabilized in a cubic-quintic nonlinear medium. In this paper, we analyze the Crank-Nicolson finite difference scheme for the (2+1)D cubic-quintic nonlinear Schrödinger equation with cubic damping. We show that both the discrete solution, in the discrete L 2 -norm, and discrete energy are bounded. By using appropriate settings and estimations, the existence and the uniqueness of the numerical solution are proved. In addition, the error estimations are established in terms of second order for both space and time in discrete L 2 -norm and H 1 -norm. Numerical simulations for the (2+1)D cubic-quintic nonlinear Schrödinger equation with cubic damping are conducted to validate the convergence. • The (2+1)D cubic-quintic NLS equation can against 2D-soliton collapses. • A Crank-Nicolson finite difference scheme for the damped (2+1)D cubic-quintic NLS equation is proposed. • The existence and uniqueness of solutions are demonstrated using the boundedness of discrete energy and mass. • The scheme converges second order in time and space. • The numerical experiments are demonstrated to verify the theoretical results. [ABSTRACT FROM AUTHOR]

We consider a subdiffusive fractional differential problem characterized by an equation that incorporates a time Riemann-Liouville fractional derivative of order 1 − α , α ∈ (0 , 1) , on its right-hand side, while the diffusive coefficient is allowed to vary with both space and time. An high order numerical method for the subdiffusion problem is derived based on the fractional splines of degree β ∈ (1 , 2 ]. The main purpose of this work is to apply fractional splines for approximating the fractional integral in the definition of the Riemann-Liouville fractional derivative, and hence explain how to solve the subdiffusion problem using this approach. It is discussed how the rate of convergence of the numerical method depends on the solution, the degree of the spline and the order of the fractional derivative. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the implementation of the finite difference method on arbitrary meshes in conjunction with a fixed-point algorithm for the lubrication problem of a journal bearing with cavitation, considering the Elrod-Adams model. We establish numerical properties of the generalized finite difference scheme and provide several illustrative examples. [ABSTRACT FROM AUTHOR]

Boundary value problems (BVPs) in ordinary differential equations (ODEs) with singularities arise in numerous mathematical models describing real-life phenomena in natural sciences and engineering. This motivates vivid research activities aiming to characterize the analytical properties of singular problems, to investigate convergence of the standard numerical methods when they are applied to simulate differential equation with singularities, and to provide software for their efficient numerical treatment. There are two well-known, high order numerical methods which we focus on in this paper, the finite difference schemes and the collocation methods. Those methods proved to be dependable and highly accurate in the context of regular differential equations, so the question arises how do they preform for singular problems. While, there is a strong evidence for the collocation schemes to be a robust method to solve singular systems in a stable and efficient way, finite difference schemes are still considered less suitable for this problem class. In this paper, we shall compare the performance of the code HOFiD_bvp based on the high order finite difference schemes and bvpsuite2.0 based on polynomial collocation, when the codes are applied to singular problems in ODEs. We are fully aware of the difficulties in a code comparison, so in this paper, we will try to only diagnose the potential improvements, we could address in the next update of the codes. [ABSTRACT FROM AUTHOR]

Hybrid nanoliquids are not underestimated for their involvement in microelectronics, transportation, coolant processes, ships, biological processes and power generation. Hence motivation for current work is to examine homogeneous-heterogeneous reactions in entropy optimized flow by curved sheet stretched with nonlinear velocity. Trihybrid nanoliquid is synthesized through 2 % of ferrous oxides (F e 3 O 4 ) , 2 % of silver (A g) and 2 % of copper (C u). Kerosene oil is employed as the base fluid. These specific kinds of nanoparticles are taken into consideration because of their numerous applications in heat dissipation, air filters, dynamic sealing, biosensors and catalysts process. Kerosene oil may have applications in many different domains such as energy storage, cleaning agent, portable heaters, fuel additive and industrial lubricants. Darcy-Forchheimer model is employed. Analysis in presence of radiation, dissipation, Ohmic heating, entropy generation and heat generation/absorption are organized. Unlike the previous considerations, the thermal expression here consists of impacts through Darcy-Forchheimer relation. Adequate transformations are implemented. Computations have been arranged by applying finite difference technique (FDM) using MATLAB. Quantities for physical interest are addressed. The presented analysis may have relevance for solar systems, chemical reacting processes, cooling towers and polymer data processes. The conclusions are also organized for important key findings. It is noticed that trihybrid nanomaterial has more entropy rate when compared with hybrid and classical nanoliquids when volume fraction is chosen as 2 % for trihybrid fluid. It is proposed that the ability to transfer heat is enhanced when nanoparticles are added to conventional fluids. Decay in concentration is noticed for both homogeneous and heterogeneous parameters. Reduction for Bejan number is noticed through homogeneous diffusion factor. Comparison with previous study is also presented and found great consensus between them. [ABSTRACT FROM AUTHOR]

To study the water management of natural rivers, two-dimensional (2D) hydrodynamic models have become essential tools. The performance of five different hydrodynamic modelling packages, SRH 2D (developed by U.S. Bureau of Reclamation), Delft 3D (developed by Deltares), FESWMS (developed by Federal Highway Administration), MIKE 21 FM (developed by DHI), and Hec Ras 2D (developed by US Army Corps of Engineers) was evaluated in this study. Numerical solutions to shallow water equations were obtained using finite elements, finite differences, and finite volumes. This work aims to provide the most accurate and objective information that can help select two-dimensional models for different annual scenarios. This study focused on comparing annual flow cases in-channel rather than flood flow. A study area on the Nile River was selected for this study. A performance assessment has been conducted based on the calibration of the model, the representation of the channel flow, and the computing efficiency of the model. The results show that Delft 3D and SRH 2D models were the most compatible with the measured data. Delft 3D model outperforms SRH 2D in computational efficiency up to 66% times faster. [ABSTRACT FROM AUTHOR]

Thermal transient problems, essential for modeling applications like welding and additive metal manufacturing, are characterized by a dynamic evolution of temperature. Accurately simulating these phenomena is often computationally expensive, thus limiting their applications, for example for model parameter estimation or online process control. Model order reduction, a solution to preserve the accuracy while reducing the computation time, is explored. This article addresses challenges in developing reduced order models using the proper generalized decomposition (PGD) for transient thermal problems with a specific treatment of the moving heat source within the reduced model. Factors affecting accuracy, convergence, and computational cost, such as discretization methods (finite element and finite difference), a dimensionless formulation, the size of the heat source, and the inclusion of material parameters as additional PGD variables are examined across progressively complex examples. The results demonstrate the influence of these factors on the PGD model's performance and emphasize the importance of their consideration when implementing such models. For thermal example, it is demonstrated that a PGD model with a finite difference discretization in time, a dimensionless representation, a mapping for a moving heat source, and a spatial domain non‐separation yields the best approximation to the full order model. [ABSTRACT FROM AUTHOR]

The continuous adjoint method for transitional flows of compressible fluids is developed and assessed, for the first time in the literature. The gradient of aerodynamic objective functions (aerodynamic forces) with respect to design variables, in problems governed by the compressible Navier–Stokes equations coupled with the Spalart–Allmaras turbulence model and the γ−R˜eθt$$ \gamma -\tilde{R}{e}_{\theta t} $$ transition model (in three, non‐smooth and smooth, variants of it), is computed based on the continuous adjoint method. The development of the adjoint to the smooth transition model variant proved to be beneficial. The accuracy of the computed sensitivity derivatives is verified against finite differences. Programming is performed in an in‐house, vertex‐centered finite‐volume code, efficiently running on GPUs. The proposed continuous adjoint method is used in 2D and 3D aerodynamic shape optimization problems, namely the constrained optimization of the NLF(1)–0416 isolated airfoil and that of the ONERA M6 wing. The impact of "frozen transition" (assumption according to which the adjoint to the transition model equations are not solved) or "frozen turbulence" (by additionally ignoring the adjoint to the turbulence model) are evaluated; it is shown that both lead to inaccurate sensitivities. [ABSTRACT FROM AUTHOR]

This study analyzes the transmission of typhoid fever caused by Salmonella typhi using a mathematical model that highlights the significance of delay in its effectiveness. Time delays can affect the nature of patterns and slow down the emergence of patterns in infected population density. The analyzed model is expanded with the equilibrium analysis, reproduction number, and stability analysis. This study aims to establish and explore the non-standard finite difference (NSFD) scheme for the typhoid fever virus transmission model with a time delay. In addition, the forward Euler method and Runge-Kutta method of order 4 (RK-4) are also applied in the present research. Some significant properties, such as convergence, positivity, boundedness, and consistency, are explored, and the proposed scheme preserves all the mentioned properties. The theoretical validation is conducted on how NSFD outperforms other methods in emulating key aspects of the continuous model, such as positive solution, stability, and equilibrium about delay. Hence, the above analysis also shows some of the limitations of the conventional finite difference methods, such as forward Euler and RK-4 in simulating such critical behaviors. This becomes more apparent when using larger steps. This indicated that NSFD is beneficial in identifying the essential characteristics of the continuous model with higher accuracy than the traditional approaches. [ABSTRACT FROM AUTHOR]

To develop a numerical method for global geophysical fluids, we usually need to choose a spherical grid and numerical approximations to represent the partial derivative equations. Some alternatives include the use of finite differences or finite volumes with latitude–longitude or reduced grids. Each of these cases has some advantages and also some limitations. This paper presents a comparison between two methods and describes a composite model using them side by side. The first is a well-known method for latitude–longitude grids and was used from 75 ∘ S until 75 ∘ N. The second is a recently developed scheme for reduced grids and was used only in the polar regions. The similarity between the two methods allows the use of small adaptations in their approximations to obtain consistency and mass conservation also in the transition between the two regions. The composite model combines advantages of the other two schemes and has a smaller computational cost. Numerical tests indicated order 2 of convergence, prevention of grid-imprinting errors, and avoidance of nonlinear instability. This model has numerical properties that may lead to efficient implementations with massive parallel computation. [ABSTRACT FROM AUTHOR]

A full‐color colorimetric humidity sensor with high brightness is proposed by using a hetero‐structured dielectric film in a metal‐insulator‐metal (MIM) resonator. A humidity‐responsive polymer is designed to graft on top of a metal‐organic frameworks (MOFs) thin film (MOFs‐Polymer) as insulator layer in the resonator. Programmable tuning of reflected color is achieved by controlling the polymer thicknesses, and finite difference time domain simulation of light‐matter interactions at subwavelength scales proves the dependence of the reflected wavelength on dielectric layer thickness of the resonator. Vivid full‐color changing is realized during tracking humidity process due to swelling of the stimuli‐responsive polymer. Ultrafast response (≈0.75 s) is achieved for tracking trace H2O from H2O/methanol mixture, which is ≈104 faster than that of the pure polymer‐based MIM resonator. Meanwhile, the study observes significant spectral redshift because the porous MOFs film facilitates the preconcentration of external stimulus and improves the detection sensitivity of the resonator. Further, double‐channel anti‐counterfeiting multiplexing imaging is devised on the MIM resonator by photomask technology. Patterned encoding for security label is achieved on the MIM resonator by engineering humidity‐tunable pixels of Au/MOFs‐Polymer/Au and humidity‐invalid pixels of Au/MOFs/Au. [ABSTRACT FROM AUTHOR]

In this research, the ongoing COVID-19 disease by considering the vaccination strategies into mathematical models is discussed. A modified and comprehensive mathematical model that captures the complex relationships between various population compartments, including susceptible (Sα), exposed (Eα), infected (Uα), quarantined (Qα), vaccinated (Vα), and recovered (Rα) individuals. Using conformable derivatives, a system of equations that precisely captures the complex interconnections inside the COVID-19 transmission. The basic reproduction number (R0), which is an essential indicator of disease transmission, is the subject of investigation calculating using the next-generation matrix approach. We also compute the R0 sensitivity indices, which offer important information about the relative influence of various factors on the overall dynamics. Local stability and global stability of R0 have been proved at a disease-free equilibrium point. By designing the finite difference approach of the conformable fractional derivative using the Taylor series. The present methodology provides us highly accurate convergence of the obtained solution. Present research fills research addresses the understanding gap between conceptual frameworks and real-world implementations, demonstrating the vaccination therapy's significant possibilities in the struggle against the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

During the oilfield development process, various factors can cause different types of reservoir damage, leading to reduced oil well production or even shutdown, and decreased water injection capacity in water wells, resulting in significant economic losses for the oilfield. However, formation damage control measures must be based on the quantitative diagnosis of the types and degrees of reservoir damage. This paper establishes a spatiotemporal evolution numerical model for 12 common types of damage during the oil and gas exploration and development process, based on the material balance theory and Fick's diffusion law in reservoir damage processes. This model achieves numerical simulation of the degree of various reservoir damage types in different spatiotemporal domains. The overall damage degree of a specific well's evolution with time and space is further simulated in simple superposition way. The sequential core flow experiment was carried out in the laboratory, and then compared with the calculation results. The accuracy is above 90%. Finally, using field test data, the simulation results show a 95% or higher degree of agreement with the actual field measurements, proving that the reservoir damage spatiotemporal evolution quantitative simulation technology established in this paper has high accuracy and practicality. [ABSTRACT FROM AUTHOR]

This paper aims to investigate some new dynamics of a new model describing the rabies virus dynamics, taking into account the effect of proper vaccination. The model's population is divided into three main compartments, namely, susceptible S(t), infected I(t), and recovered R(t) individuals. The model is formulated and then the equilibrium points of the model are found. The local and global stabilities of equilibrium points of the proposed model are investigated where conditions of stability are attained in terms of key parameters in the model. Bifurcation analysis is performed for the possible occurrence of codimension‐one bifurcations in the model. In addition, bifurcation surfaces are plotted in the space of parameters in the model. For the numerical verification, a nonstandard finite difference method is adapted for solving the model and the accurate results of numerical simulations are depicted to reveal the dynamics of the model. The method provides realistic data for the model and these data can be used to predict the spread of the virus and to provide insight into proper procedures and control measures that can be taken. [ABSTRACT FROM AUTHOR]

In recent years, an entirely new class of nanofluids has been developed, namely hybrid nanofluids. Their efficiency when it comes to heat transfer has been demonstrated to be much higher than the traditional nanofluids. In this study, the flow of hybrid nanofluid is analyzed subjected to the flow geometry of oscillatory disk that also rotates with the constant angular speed. Mainly, we investigated hybrid nanofluid flow subjected to an oscillatory disk that rotates at a constant angular speed as an incompressible, laminar and time-dependent electrically conducting flow. The implication of similarity functions normalizes the flow phenomenon. Furthermore, we solved the governing system by implementing the finite differences, and then the iterative procedure is carried out with the help of Successive Over-Relaxation (SOR) technique. In the later part of the paper, graphical representation is given to discuss dimensionless factors in both scenarios of nanofluid and hybrid nanofluid. [ABSTRACT FROM AUTHOR]

This study investigates the thermal behaviour of unsteady hybrid nanofluid flow on an infinite vertical plate. The investigation takes into account parameters such as magnetohydrodynamics and radiation effects, as well as the stratified medium. The systems of equations were solved by employing the explicit finite difference approach of Dufort-Frankel method. The main motivation of the study is to compare the performance of water, magnetic oxide, and multi-wall carbon nanotubes as working fluids. Additionally, velocity, temperature, and concentration outlines are visualized through plots, elucidating the fluid behaviour. Tables are provided for the Skin friction, Nusselt number, and Sherwood number, offering comprehensive insights crucial for optimizing performance in engineering applications ranging from thermal management systems to renewable energy technologies. The main finding of this study indicates that the quantitative result reveals that the temperature outline escalates among increasing values of radiation. In contrast, the outlines of a velocity and concentration show a decrease as the values of magnetohydrodynamics increase. In addition, multi-walled carbon nanotubes consume a larger outcome on temperature. A statistical study displays that the thermal stream rate of magnetic oxide-multi-wall carbon nanotubes-water increases from 1.7615 percentages to 7.4415 percentages, respectively, when the volume fraction of nanoparticles rises from 0.01 to 0.05. Future research is important to understanding hybrid nanofluid flows and their applications in thermal engineering systems such as energy systems, nuclear reactors, biomedical applications, electronics cooling, solar thermal systems, chemical processing, and other heat transfer applications where improved thermal performance is crucial. [ABSTRACT FROM AUTHOR]

In this paper, we established a polynomial scaling method to investigate the numerical solution of Rosenau–Korteweg De Vries‐regularized long wave (Rosenau‐KdV‐RLW) equation. We start with discretization of the time variable of the equation using a finite difference approach equipped with a linearization. After the time discretization, we have used polynomial scaling functions for the discretization of the spatial variable. These two discretizations give us the desired discrete system of equations to obtain numerical solutions. We further derive an error estimate for the proposed method. We have applied the proposed method to Rosenau‐KdV, Rosenau‐RLW, and Rosenau‐KdV‐RLW equations and used error norms to examine the accuracy and reliability of the presented method. Also, to enhance accuracy of the results, we utilize Richardson extrapolation. The comparisons with the analytical solution and earlier studies that use different methods indicate that the proposed method is accurate and reliable. [ABSTRACT FROM AUTHOR]

The article contains a numerical analysis of the effects of electromagnetic wave propagation in an area containing a non-ideal, non-uniform, and absorbing dielectric. The analysis concerned the influence of the structure of the building material and its electrical parameters on the electric field intensity. The analysis took into account the variability of the number of hollows in the brick, the width of hollows, as well as the arrangement of these hollows relative to each other using the example of two types of bricks. The article also provides the most commonly used values of electrical parameters for building materials (brick, plaster). For this reason, the article includes results for different values of conductivity (0–0.2 S/m). The FDTD (Finite Difference Time Domain) method was used for multivariate analysis. The aim was to verify the correctness of the numerical assumptions adopted. Using the example of the most commonly used wall structure in construction, the results obtained using the FDTD method were compared with values obtained using another numerical method, the finite element method (FEM). The influence of an additional layer of plaster on the considered wall on the electric field was also checked. The analysis showed that a symmetrical arrangement of bricks results in higher values of the electric field by an average of 20%. Of course, this depends on the length of the hollows and the number of holes. The highest field values occur at low conductivities (0–0.04 S/m). A brick wall with a larger number of hollows and a symmetrical brick arrangement shows the highest electric field intensity, especially for hollow sizes (0.009–0.015 m). [ABSTRACT FROM AUTHOR]

This paper presents a novel spectral algorithm for the numerical solution of multi-dimensional fractional-order telegraph equations, a critical model used to capture the combined effects of diffusion and wave propagation. The core innovation of this work is the application of Jacobi-Romanovski polynomials as the basis functions for spectral discretization. These polynomials offer unique advantages, including the ability to handle nonstandard domains and boundary conditions, making them particularly suitable for partial differential equation (PDE) applications. A comprehensive error analysis is conducted, providing deep insights into the convergence rates and factors affecting the accuracy of the numerical solutions. Extensive numerical experiments further demonstrate the superior performance of the proposed spectral algorithm in solving a wide range of multi-dimensional fractional-order telegraph equation models. The results show a significant improvement in accuracy and computational efficiency compared to traditional numerical methods, such as finite difference or finite element techniques. This research advances the field of computational science by offering a robust, efficient, and versatile numerical framework for the precise solution of complex multi-dimensional PDEs. [ABSTRACT FROM AUTHOR]

The aim of this work is to develop a numerical computation program allowing designing new contours of a supersonic axisymmetric nozzle having two expansions at the throat, named by DEN (Dual Expansion Nozzle). This new nozzle gives a uniform and parallel flow at the exit section, to improve considerably the performances compared to the conventional Minimum Length Nozzle (MLN), and the Best Performances Nozzle (BPN). The present nozzle has a two unknowns external and central body curved walls. Each of them is started by an initial expansion angle to give a uniform and horizontal flow at the exit section. Two others transition regions are calculated in parallel with the contours points to give the desired exit Mach number. The walls are determined point by point by the High Temperature Method of Characteristics (HT MOC) model. The resolution of the four compatibility and characteristics equations is done numerically by the finite difference predictor corrector algorithm. The validation of the results is controlled by the convergence of the calculated critical sections ratio to that given by the theory. The design depends on four parameters, where MLN and BPN become special cases of DEN. A comparison is made with MLN , since it is currently used in the aerospace propulsion and with BPN aiming to improve their performances. The comparison is made for the same critical mass flow rate. The results demonstrate a remarkable reduction up of 45 %, and 52 % in the mass of DEN when the exit Mach number M E = 3.00 and the stagnation temperature T 0 = 2000 K. The application is made for air and for future aerospace missiles in order to improve their trajectory parameters. The chosen example demonstrates an improvement of 13 % and 16 % on the missile range compared, respectively to MLN , and BPN. [ABSTRACT FROM AUTHOR]

Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and convergence. Multigrid is an approach with excellent applicability to elliptic problems such as the Stokes equations, and can be a solution to such challenges of scalability and efficiency. The degree of success of such methods, however, is highly contingent on the design of key components of the multigrid scheme, including the hierarchy of discretizations, and the relaxation scheme used. Additionally, in many practical cases, it may be more effective to use a multigrid scheme as a preconditioner to an iterative Krylov subspace solver, as opposed to striving for maximum efficacy of the relaxation scheme in all foreseeable settings. In this paper, we propose an efficient symmetric multigrid preconditioner for the Stokes Equations on a staggered finite difference discretization. Our contribution is focused on crafting a preconditioner that (a) is symmetric indefinite, matching the property of the Stokes system itself, (b) is appropriate for preconditioning the SQMR iterative scheme [1] , and (c) has the requisite symmetry properties to be used in this context. In addition, our design is efficient in terms of computational cost and facilitates scaling to large domains. [ABSTRACT FROM AUTHOR]

Grid-Nesting is a common method of local refinement when using structured quadrilateral grid in estuarine models. Nevertheless, various issues need to be improved, such as the Courant-Friedrichs-Lewy (CFL) limitations of external gravity wave and information exchange between two-way nesting grids. Based on the material conservation law, a novel scheme with Implicit, Grid-Nesting Elevation Solution (IGNES) and matched Nesting Boundary Flux Conservation Interpolation (NBFCI) was developed in this paper. The unstructured quadrilateral grid, finite-differencing, estuarine and coastal ocean model (UFDECOM) was update to UFDECOM-i. The gravity wave propagation experiment shows that the IGNES can relax the CFL limitations. Compared to traditional i-j two-direction strip refinement, the new scheme has higher computational efficiency. When the root-mean-square-error of elevation and current velocity increases by less than 0.05% and 0.2%, the calculation time is reduced by 40%. When simulating vortex motion, it overcomes the problem of simulation collapse caused by errors in nested boundaries. When simulating material transport, NBFCI scheme has smaller errors at the nesting boundary compared to quadratic interpolation, the high-order spatial interpolation at the middle temporal level (HSMIT) parabolic interpolation, upwind Advection-Equivalent interpolation, and HSIMT Advection-Equivalent interpolation scheme. The simulation results of the severe saltwater intrusion in the Changjiang Estuary in the late summer and early autumn of 2022 demonstrate that the UFDECOM-i with NBFCI and IGNES has higher computational efficiency and accuracy. [ABSTRACT FROM AUTHOR]