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In this study, a new cell‐centered Lagrangian discontinuous Galerkin (DG) scheme is presented to simulate gas‐water compressible flows. The two‐phase flows are governed by the compressible Euler equation with ideal and stiffened gas equations of state. We integrate the Lagrangian DG scheme with the exact gas‐water Riemann solver for calculating the numerical fluxes so that the inherent stiff features of gas‐water compressible flows are well addressed. Furthermore, in order to guarantee the positivity of the density and internal energy during the high Mach number calculation, the positivity‐preserving limiter and strong stability preserving temporal integral are incorporated to ensure the numerical stability. Six numerical examples are tested to show the accuracy, robustness and positivity‐preserving property of the present scheme. It can be found that the present scheme can handle challenging numerical cases involving large density ratio (up to 1000) and strong shock. The results obtained with the typical HLLC flux are also given for comparison and the present scheme with the exact Riemann solver shows higher accuracy, particularly in the presence of large density ratio at the gas‐water interface. [ABSTRACT FROM AUTHOR]

Elliptical particles settling in Bingham fluids in a confined, the vertical channel is studied using the immersed boundary-lattice Boltzmann method to understand their sedimentation characteristics. The present elliptical particles-Bingham fluids two-phase systems involve a single particle, a pair of particles, a chain of particles, and a cluster of particles. The graphics processing unit (GPU) is used to improve computational efficiency. Special attention is placed on the influence of yield stress on sedimentation behavior. For a pair of elliptic particles, alongside the drafting–kissing–tumbling (DKT) mode or non-DKT sedimentation mode, a periodic sedimentation mode is found. The results indicate that two elliptic particles keep a kissing state and their trajectories and orientations periodically change during settling in the confined channel. For the elliptic particles chain, the first kissing occurs between the middle and lower particles regarding any Bingham number. Moreover, particles form the cluster for different inclination angles of the particle chain at the Bingham number Bn = 0.02. For the cluster of particles (15 × 15) , the effect of vortex interaction around particles in Newtonian fluids is revealed, and the rheological property of the fluid–particle interaction in Bingham fluids is displayed. Overall, the role of yield stress on the sedimentation of elliptic particles is significant. With the acceleration of GPU, the present method has great potential for modeling large numbers of particles settling in non-Newtonian fluids. [ABSTRACT FROM AUTHOR]

In this article, three novel algorithms are developed and successfully applied to investigate the stable solutions of time‐fractional nonlinear telegraph equations. Firstly, we presented the shifted Gegenbauer polynomials through appropriate transformations. The approximation of a function u(||x||, t) is defined via shifted Gegenbauer polynomials (SGPs) and then developed the operational matrices of a positive integer and non‐integer derivatives assisted by multi‐dimensional shifted Gegenbauer polynomials vectors. Linearized fully spectral method (LFSM) is proposed by means of function approximations and developed operational matrices whilst Picard iterative scheme is used to linearize the discussed problem. To introduce a semi‐discrete method (SDM), the temporal derivative is approximated through a central difference scheme whereas spatial derivatives are approximated assisted by novel operational matrices. A fully numerical method (FNM) is proposed by introducing the central difference for temporal and spatial variables. Proposed computational methods transform the time‐fractional nonlinear telegraph equation into a system of linear algebraic equations that are easier to tackle. An inclusive comparative study is witnesses that suggested schemes are effective, accurate and well‐matched to investigate the approximate solutions of the problems udnerstudy. Convergence and error bound of the suggested methods are investigated theoretically whereas stability analysis is performed numerically. Moreover, the developed methods can be used conveniently to examine the numerical solution of other multi‐dimensional highly nonlinear fractional or variable order problems of physical nature. [ABSTRACT FROM AUTHOR]

The drafting, kissing, and tumbling (DKT) of a pair of particles in Newtonian fluids are frequently observed in particle sedimentations and have been well studied. However, sedimentation shows distinct behaviors when the particle pair is released in non-Newtonian fluids, and dynamics of the DKT have still not been completely understood. In this paper, the immersed boundary-lattice Boltzmann method with a hybrid multiple-relaxation-time scheme is used to examine the dynamics of the DKT of a pair of particles settling in non-Newtonian fluids. The particle pair is released in a confined channel filled with non-Newtonian fluids, in which the non-Newtonian behaviors of shear-thinning/shear-thickening and yield stress are considered. The results demonstrate that the horizontal migration direction at the initial stage of the separation state in a shear-thinning fluid is totally different from that happening in a Newtonian fluid. It is attributed to the asymmetrical fluid viscosity on both sides of the pair of particles. Our findings also show that yield stress plays a dominant role in the sedimentation velocity and separation distance between the particles forming this pair. Under the effect of yield stress, three sedimentation structures, which correspond to different dynamic behaviors of the pair of particles, are also identified during the sedimentation. Furthermore, some critical conditions, regarding horizontal migration toward the right or left side, DKT/non-DKT and kissing/non-kissing states are established through the Bingham number (B n)-power-law index (n) diagrams and tables. Also, the effect of the diameter ratio between two particles on the DKT is studied. [ABSTRACT FROM AUTHOR]

Conductive particles greatly impair the insulation integrity of a gas insulated switchgear (GIS). Factors including applied voltage, frequency of the alternating current, size and coefficient of restitution of the metallic particle, pressurized gas, and sizes of the GIS dramatically influence the particle dynamics. Previous investigations basically focused on certain scenarios, seldom considered the effects from coefficient of restitution, and did not provide universal laws for the particle dynamics. This paper proposes a dimensionless number that considers all the above-mentioned factors, and presents the scaling law between dimensionless mean/maximum lifting height of a charged particle in GIS and the proposed dimensionless number. It is believed that the scaling law together with the dimensionless number can provide guidance and shrink the parameter window for relevant investigations on the GIS with sparsely distributed conductive particles. [ABSTRACT FROM AUTHOR]

Understanding the connection between physiology and kinematics of natural swimmers is of great importance to design efficient bio-inspired underwater vehicles. This study looks at high-fidelity three-dimensional numerical simulations for flows over an undulating American eel with prescribed anguilliform kinematics. Particularly, our work focuses on why natural anguilliform swimmers employ wavelengths shorter than their bodylengths while performing wavy kinematics. For this purpose, we vary the undulatory wavelength for a range of values generally observed in different aquatic animals at Strouhal numbers 0.30 and 0.40. We observe that our anguilliform swimmer is able to demonstrate more suitable hydrodynamic performance for wavelengths of 0.65 and 0.80. For longer wavelengths, the swimmer experiences large frictional drag, which deteriorates its performance. The wake topology was dominated by hairpin-like structures, which are closely linked with the underlying physics of anguilliform swimming found in nature. [ABSTRACT FROM AUTHOR]