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Numerical simulation of high‐speed flows often needs a fine grid for capturing detailed structures of shock or contact wave, which makes high‐order discontinuous Galerkin methods (DGMs) extremely costly. In this work, a characteristic‐compression based adaptive mesh refinement (AMR, h‐adaptive) method is proposed for efficiently improving resolution of the high‐speed flows. In order to allocate computational resources to needed regions, a characteristic‐compression embedded shock wave indicator is developed on incompatible grids and employed as the criterion for AMR. This indicator applies the admissible jumps of eigenvalues to measure the local compression of homogeneous characteristic curves, and theoretically can capture regions of characteristic‐compression which contain structures of shock, contact waves and vortices. Numerical results show that the proposed h‐adaptive DGM is robust, efficient and high‐resolution, it can capture dissipative shock, contact waves of different strengths and vortices with low noise on a rather coarse grid, and can significantly improve resolution of these structures through mild increase of computational resources as compared with the residual‐based h‐adaptive method. [ABSTRACT FROM AUTHOR]

Copyright of Transactions of Nanjing University of Aeronautics & Astronautics is the property of Editorial Department of Journal of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We present an algorithm to solve the dispersive depth-averaged Serre--Green--Naghdi equations using patch-based adaptive mesh refinement. These equations require adding additional higher derivative terms to the nonlinear shallow water equations. This has been implemented as a new component of the open source GeoClaw software that is widely used for modeling tsunamis, storm surge, and related hazards, improving its accuracy on shorter wavelength phenomena. We use a formulation that requires solving an elliptic system of equations at each time step, making the method implicit. The adaptive algorithm allows different time steps on different refinement levels and solves the implicit equations level by level. Computational examples are presented to illustrate the stability and accuracy on a radially symmetric test case and two realistic tsunami modeling problems, including a hypothetical asteroid impact creating a short wavelength tsunami for which dispersive terms are necessary. [ABSTRACT FROM AUTHOR]

Summary: The fluid‐structure interaction is simulated using the boundary data immersion method. As the fluid‐structure interface is smeared in the smoothing region, deviations are incurred in fluid simulations. For compressible flow, high order difference schemes with more mesh cells for the stencils are usually employed to achieve high overall accuracy, but near interfaces it requires wider smoothing region of several mesh cells for computational stability and hence lowers its accuracy significantly. To address this issue, the proposed algorithm switches to lower order difference schemes near the interfaces and applies adaptive mesh refining there to compensate the accuracy loss. Implemented with Structured Adaptive Mesh Refinement Application Infrastructure (SAMRAI), the algorithm shows notable improvement in the overall accuracy and efficiency in cases such as channel flow and flow past a cylinder. The algorithm is used to simulate the shock wave past a fixed or free cylinder with Ma =2.67$$ =2.67 $$ and Re =1482$$ =1482 $$, which reveals the relaxation process and the temporal evolution of the drag coefficient, it goes through a valley and maintains at relatively high value for the fixed cylinder, while that of the free cylinder tends to decrease in fluctuation which is found to be caused by the interaction between the forward moving cylinder and vortexes in the unsteady wake. [ABSTRACT FROM AUTHOR]

The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit residual-based error estimator as well as a separate marking strategy based on the alternative error estimator and an optimal data approximation algorithm. This paper reviews and discusses available convergence results. In addition, all three strategies are investigated empirically for a set of benchmarks examples of second-order elliptic partial differential equations in two spatial dimensions. Particular interest is on the choice of the marking and refinement parameters and the approximation of the given data. The numerical experiments are reproducible using the author's software package octAFEM available on the platform Code Ocean. [ABSTRACT FROM AUTHOR]

Summary: The Oak Ridge Leadership Computing Facility (OLCF) has been preparing the nation's first exascale system, Frontier, for production and end users. Frontier is based on HPE Cray's new EX architecture and Slingshot interconnect and features 74 cabinets of optimized 3rd Gen AMD EPYC CPUs for HPC and AI and AMD Instinct 250X accelerators. As a part of this preparation, "real‐world" user codes have been selected to help assess the functionality, performance, and usability of the system. This article describes early experiences using the system in collaboration with the Hamburg Observatory for two selected codes, which have since been adopted in the OLCF test harness. Experiences discussed include efforts to resolve performance variability and per‐cycle slowdowns. Results are shown for a performance portable astrophysical magnetohydronamics code, AthenaPK, and a mini‐application stressing the core functionality of a performance portable block‐structured adaptive mesh refinement framework, Parthenon‐Hydro. These results show good scaling characteristics to the full system. At the largest scale, the Parthenon‐Hydro miniapp reaches a total of 1.7×1013 zone‐cycles/s on 9216 nodes (73,728 logical GPUs) at ≈92% weak scaling parallel efficiency (starting from a single node using a second‐order, finite‐volume method). [ABSTRACT FROM AUTHOR]

In this paper, a kind of immersed boundary method, the discretized force with ghost cell method, is introduced to study compressible flow. Meanwhile, an adaptive mesh refinement scheme and a wall treatment for turbulent flow are proposed. With the help of in-house code, the accuracy of the method is verified based on several classic tests. [ABSTRACT FROM AUTHOR]

We discuss refinement criteria for the Berger–Rigoutsos (block-based) refinement algorithm in our numerical relativity code GR-Athena++ in the context of binary black hole (BBH) merger simulations. We compare three different strategies: the 'box-in-box' approach, the 'sphere-in-sphere' approach and a local criterion for refinement based on the estimation of truncation error of the finite difference scheme. We extract and compare gravitational waveforms using the three different mesh refinement methods and compare their accuracy against a calibration waveform and demonstrate that the sphere-in-sphere approach provides the best strategy overall when considering computational cost and the waveform accuracy. Ultimately, we demonstrate the capability of each mesh refinement method in accurately simulating gravitational waves from BBH systems—a crucial aspect for their application in next-generation detectors. We quantify the mismatch achievable with the different strategies by extrapolating the gravitational wave mismatch to higher resolution. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Chongqing University of Technology (Natural Science) is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

As the need for handling complex geometries in computational fluid dynamics (CFD) grows, efficient and accurate mesh generation techniques become paramount. This study presents an adaptive mesh refinement (AMR) technology based on cell-based Cartesian grids, employing a distance-weighted least squares interpolation for finite difference discretization and utilizing immersed boundary methods for wall boundaries. This facilitates effective management of both transient and steady flow problems. Validation through supersonic flow over a forward-facing step, subsonic flow around a high Reynolds number NHLP airfoil, and supersonic flow past a sphere demonstrated AMR's efficacy in capturing essential flow characteristics while wisely refining and coarsening meshes, thus optimizing resource utilization without compromising accuracy. Importantly, AMR simplified the capture of complex flows, obviating manual mesh densification and significantly improving the efficiency and reliability of CFD simulations. [ABSTRACT FROM AUTHOR]

The JPEG algorithm is a defacto standard for image compression. We investigate whether adaptive mesh refinement can be used to optimize the compression ratio and propose a new adaptive image compression algorithm. We prove that it produces a quasi-optimal subdivision grid for a given error norm with high probability. This subdivision can be stored with very little overhead and thus leads to an efficient compression algorithm. We demonstrate experimentally, that the new algorithm can achieve better compression ratios than standard JPEG compression with no visible loss of quality on many images. The mathematical core of this work shows that Binev's optimal tree approximation algorithm is applicable to image compression with high probability, when we assume small additive Gaussian noise on the pixels of the image. [ABSTRACT FROM AUTHOR]

This paper deals with the efficient implementation of the finite element method with continuous piecewise linear functions (P1-FEM) in R d ( d ∈ N ). Although at present there does not seem to be a very high practical demand for finite element methods that use higher-dimensional simplicial partitions, there are some advantages in studying the efficient implementation of the method independent of the dimension. For instance, it provides additional insights into necessary data structures and the complexity of implementations. Throughout, the focus is on an efficient realization using Matlab built-in functions and vectorization. The fast and vectorized Matlab function can be easily implemented in many other vector languages and is provided in Julia, too. The complete implementation of the adaptive FEM is given, including assembling stiffness matrix, building load vector, error estimation, and adaptive mesh-refinement. Numerical experiments underline the efficiency of our freely available code which is observed to be of a slightly more than linear complexity with respect to the number of elements when memory limits are not exceeded. [ABSTRACT FROM AUTHOR]

This paper presents a feature-based adaptive mesh refinement (AMR) method for Large Eddy Simulation of propagating deflagrations, using massive-scale parallel unstructured AMR libraries. The proposed method, named turbulent flame propagation-AMR (TFP-AMR), is able to track the transient dynamics of both the turbulent flame and the vortical structures in the flow. To handle the interaction of the turbulent flame brush with the vortical structures of the flow, a vortex selection criterion is derived from flame/vortex interaction theory. The method is built with the general intent to prioritise conservatively estimated parameters, rather than to rely on user-dependent parameters. In particular, a specific mesh adaptation triggering strategy is constructed, adapted to the strongly transient physics found in deflagrations, to guarantee that the physics of interest consistently reside within a region of high accuracy throughout the transient process. The methodology is applied and validated on several elementary cases representing fundamental bricks of the full problem: (1) a laminar flame propagation, (2) the advection of a pair of non-reacting vortices, (3) a flame/vortex interaction. The method is then applied to three different configurations of a three-dimensional complex explosion scenario in an obstructed chamber. All cases demonstrate the TFP-AMR capability to recover accurate results at reduced computational cost without requiring any ad hoc tuning of the AMR method or its parameters, thus demonstrating its genericity and robustness. [ABSTRACT FROM AUTHOR]

A new adaptive clipping-and-redistribution method is presented which provides bounds-preservation for multidimensional interpolation in the context of high-order finite-volume discretizations with adaptive mesh refinement (AMR). The underlying finite-volume method (FVM) for the computational fluid dynamics applications is fourth-order accurate for smooth solutions and utilizes AMR for computational efficiency in solving multiscale problems involving turbulence and combustion. High-order interpolation between different AMR levels is required. However, this operation often leads to numerical issues because combustion species must have physical bounds preserved. The present study overcomes two major challenges in the development of the high-order interpolation method. First, the method needs to be bound-preserving near extrema or discontinuities to prevent the emergence of unphysical oscillations while maintaining fourth-order accuracy in smooth flows. Second, the method needs to satisfy the conservation requirement in multiple dimensions, particularly in the context of curvilinear coordinate transformations. Additionally, the method is designed to be localized and computationally inexpensive. The new interpolation scheme is demonstrated by solving reacting flows, which are extremely sensitive to unphysical overshoots in conserved quantities. The test problems are shock-induced (Formula presented.) - (Formula presented.) combustion and a (Formula presented.) -air flame in a practical bluff-body combustor. Results show the method prevents new extrema near discontinuities while maintaining high-order accuracy in smooth regions. In particular, the method is extremely beneficial for combustion with stiff chemistry. With the proposed new method, even if flame fronts cross AMR interfaces or new grids are created in the vicinity of the flame, solution stability is retained.

Reacting flow simulations for combustion applications require extensive computing capabilities. Leveraging the AMReX library, the Pele suite of combustion simulation tools targets the largest supercomputers available and future exascale machines. We introduce PeleC, the compressible solver in the Pele suite, and detail its capabilities, including complex geometry representation, chemistry integration, and discretization. We present a comparison of development efforts using both OpenACC and AMReX’s C++ performance portability framework for execution on multiple GPU architectures. We discuss relevant details that have allowed PeleC to achieve high performance and scalability. PeleC’s performance characteristics are measured through relevant simulations on multiple supercomputers. The success of PeleC’s design for exascale is exhibited through demonstration of a 160 billion cell simulation and weak scaling onto 100% of Summit, an NVIDIA-based GPU supercomputer at Oak Ridge National Laboratory. Our results provide confidence that PeleC will enable future combustion science simulations with unprecedented fidelity.

In this paper, we propose a novel staggered least squares method for elliptic equations on polygonal meshes. Our new method can be flexibly applied to rough grids and allows hanging nodes, which is of particular interest in practical applications. Moreover, it offers the advantage of not having to deal with inf-sup conditions and yielding positive definite discrete problems. Optimal a priori error estimates in energy norm are derived. In addition, a superconvergent estimates in energy norm are also developed by employing variational error expansion. The main difficulty involved here is to show the $ L^2 $ norm error estimates for the potential variable, where duality argument and the superconvergent estimates are the key ingredients. The single valued flux over the outer boundary of the dual partition enables us to construct a locally conservative flux. Numerical experiments confirm the theoretical findings and the performance of the adaptive mesh refinement guided by the least squares functional estimator are also displayed.

Detonation-based engines have a higher thermal efficiency than deflagration-based engines and are therefore widely studied. In this study, the effect of initiation conditions on the detonation wave propagation and the performance of a pulse detonation engine, one type of detonationbased engine, was numerically investigated. Hydrogen-oxygen mixtures with equivalence ratios of φ=0.8, 1.0, and 1.2 were defined as initiation conditions with constant pressure and temperature. The numerical simulations were conducted using the transient explicit density-based solver in the ANSYS Fluent commercial software. The adaptability of the adaptive mesh refinement method in detonation-based engines was explored in the numerical studies, reducing the average total cell count by a factor of 2.617, and obtaining consistent results according to validation studies. The adaptive mesh refinement method was also used in numerical simulations where different equivalence ratios were defined. It was determined that an increase in the equivalence ratio resulted in an increase in the detonation wave velocity. Also, an increase in thrust distribution at the nozzle exit was observed before the blowdown stage, and the calculated thrust values for φ=0.8, φ=1.0, and φ=1.2 were 248.28 N, 264.5 N, and 270.83 N, respectively.

Detonation-based engines have a higher thermal efficiency than deflagration-based engines and are therefore widely studied. In this study, the effect of initiation conditions on the detonation wave propagation and the performance of a pulse detonation engine, one type of detonationbased engine, was numerically investigated. Hydrogen-oxygen mixtures with equivalence ratios of φ=0.8, 1.0, and 1.2 were defined as initiation conditions with constant pressure and temperature. The numerical simulations were conducted using the transient explicit density-based solver in the ANSYS Fluent commercial software. The adaptability of the adaptive mesh refinement method in detonation-based engines was explored in the numerical studies, reducing the average total cell count by a factor of 2.617, and obtaining consistent results according to validation studies. The adaptive mesh refinement method was also used in numerical simulations where different equivalence ratios were defined. It was determined that an increase in the equivalence ratio resulted in an increase in the detonation wave velocity. Also, an increase in thrust distribution at the nozzle exit was observed before the blowdown stage, and the calculated thrust values for φ=0.8, φ=1.0, and φ=1.2 were 248.28 N, 264.5 N, and 270.83 N, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel staggered least squares method for elliptic equations on polygonal meshes. Our new method can be flexibly applied to rough grids and allows hanging nodes, which is of particular interest in practical applications. Moreover, it offers the advantage of not having to deal with inf-sup conditions and yielding positive definite discrete problems. Optimal a priori error estimates in energy norm are derived. In addition, a superconvergent estimates in energy norm are also developed by employing variational error expansion. The main difficulty involved here is to show the L 2 norm error estimates for the potential variable, where duality argument and the superconvergent estimates are the key ingredients. The single valued flux over the outer boundary of the dual partition enables us to construct a locally conservative flux. Numerical experiments confirm the theoretical findings and the performance of the adaptive mesh refinement guided by the least squares functional estimator are also displayed. In this paper, we propose a novel staggered least squares method for elliptic equations on polygonal meshes. Our new method can be flexibly applied to rough grids and allows hanging nodes, which is of particular interest in practical applications. Moreover, it offers the advantage of not having to deal with inf-sup conditions and yielding positive definite discrete problems. Optimal a priori error estimates in energy norm are derived. In addition, a superconvergent estimates in energy norm are also developed by employing variational error expansion. The main difficulty involved here is to show the norm error estimates for the potential variable, where duality argument and the superconvergent estimates are the key ingredients. The single valued flux over the outer boundary of the dual partition enables us to construct a locally conservative flux. Numerical experiments confirm the theoretical findings and the performance of the adaptive mesh refinement guided by the least squares functional estimator are also displayed. [ABSTRACT FROM AUTHOR]

A novel formulation of the vortex particle method (VPM) is developed for large-eddy simulation (LES) in a meshless scheme that is numerically stable. A new set of VPM governing equations are derived from the LES-filtered Navier-Stokes equations. The new equations reinforce the conservation of angular momentum by resizing vortex elements subject to vortex stretching. In addition to the VPM reformulation, a new anisotropic dynamic model of subfilter-scale (SFS) vortex stretching is developed. This SFS model is well suited for turbulent flows with coherent vortical structures, where the predominant cascade mechanism is vortex stretching. The mean and fluctuating components of turbulent flow and Reynolds stresses are validated through the simulation of a turbulent round jet. The computational efficiency of the scheme is showcased in the simulation of an aircraft rotor in hover, showing our meshless LES to be 100 times faster than a mesh-based LES with similar fidelity. The implementation of our meshless LES scheme is released as open-source software, called FLOWVPM. [ABSTRACT FROM AUTHOR]

To understand the actual operation of detonation engines, it is of great significance to simulate the detonation characteristics after being affected by unsteady supersonic flow. Adaptive mesh refinement method and single-step chemical reaction model were used for simulation calculations. The Navier–Stokes equations and hybrid sixth-order weighted essentially non-oscillatory centered difference scheme was adopted in this study. Three different amplitudes of disturbances (0.1, 0.2, and 0.3) and two hot jet injection times were analyzed. The results showed that a moderate disturbance can improve the stability of detonation wave under the ideal hot jet injection time. It allows detonation wave to stay in the combustion chamber for a longer time, which is beneficial for the release of thrust performance. Although the stability of detonation wave is significantly different between the low and high-amplitude disturbances, the residence time of detonation wave is close to the steady flow case under ideal initiation conditions. When the ignition time is insufficient, successful detonation can occur with low and medium-amplitude disturbances. However, the ignition delay was significantly prolonged with medium-amplitude disturbance. There was also greater instability, which is detrimental to the thrust release. When the inflow has a high-amplitude disturbance, the detonation wave fails to ignite due to insufficient energy. • This article considers the influence of unsteady inflow characteristics on detonation. • The presence of disturbances can delay the initiation of detonation waves. • Proper disturbance can enhance the stability of detonation waves under the ideal initiation conditions. • The disturbance causes a significant increase in pressure behind the wave under the non-ideal initiation conditions. [ABSTRACT FROM AUTHOR]

When a submarine encounters an emergency situation, it should take emergency-surfacing actions by moving upward with a large angle of attack in the vertical plane. Previous research has often neglected the effect of vertical plane motion on the lateral force (Fy), rolling moment (Mx), and yawing moment (Mz). To examine the flow characteristics of submarines at high angles of attack on the vertical plane, the SST-DDES method is adopted in conjunction with adaptive mesh refinement (AMR) technology, and the new Omega vortex detection method is employed as the AMR criterion for numerical calculations. The obtained results are then appropriately verified by conducting water tank experiments, and the effects of different angles of attack and heel angles on Fy, Mx, and Mz are methodically examined. The results reveal that, in the flow around the vertical plane of a submarine, the influence of Fy and Mz cannot be ignored. In addition, when the vertical velocity of the hull is greater than 0.6 m/s, the influence of Mx cannot be overlooked either. When the angle of attack on the vertical plane of the submarine is greater than 25°, the effects of Fy, Mx, and Mz cannot be neglected, and the effect of Mz is particularly prominent, with its amplitude close to or greater than the average value of the pitch moment (My). The obtained results reveal that the presence of the heel angle (θ) intensifies the forces on the hull for Fy, Mx, and Mz, and the forces caused by the vertical velocity at Fy, Mx, and Mz cannot be neglected. These findings can provide a mechanical analysis basis for the analysis of nonlinear motion phenomena during submarine surfacing. [ABSTRACT FROM AUTHOR]

In this paper, we locally construct a conservative flux for finite element solutions of elliptic interface problems with discontinuous coefficients. Since the Discontinuous Galerkin method has built-in conservative flux, we consider in this paper the conforming finite element method and a special type of nonconforming method with arbitrary orders. We also perform our analysis based on Nitsche’s method, which imposes the Dirichlet boundary condition weakly. The construction method is derived based on a mixed problem with one solution coinciding with the finite element solution and with the other solution being naturally used to obtain a conservative flux. We then apply the recovered flux to the a posteriori error estimation and prove the robust reliability and efficiency for conforming elements, under the assumption that the diffusion coefficient is quasi-monotone. Numerical experiments are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Relativistic jets are major sources of radio-frequency radiation in the Universe. Their study is complicated by the fact that the relativistic gas flows interact with interstellar space, with the formation of complex flows that are smaller than the jets but can affect the evolution of the entire jets. Adaptive grids have traditionally been used to simulate such multi-scale phenomena with high spatial resolution in the zone of complex jets and low resolution to reproduce the unperturbed gas flows. In this paper, a Patch-Block-Structured Adaptive-Mesh-Refinement technique is proposed for modeling multi-scale relativistic jets. To use this technique, mathematical tools for numerically solving the equations of special relativistic hydrodynamics are updated in a particular manner. The approach is applied to the evolution of a jet in interstellar space. [ABSTRACT FROM AUTHOR]

Based on the time-fractional Black-Scholes pricing model, the evaluation of an American-style option problem can be formulated as a free boundary problem. It is equivalent to a time-fractional parabolic variational inequality. Due to the time-fractional derivative involved in the problem, increasing the computational cost for large final times has been expected in the numerical solution for this problem. In this paper, we want to propose a new adaptive numerical method to solve this problem accurately, with low computational cost. The presented method is based on interpolating wavelets family. An adaptive scheme in time discretization with an adaptive wavelet collocation method for space discretization has been used for the given problem. We show that combination of interpolating wavelet basis and finite difference method, makes an accurate structure to design an optimal adaptive mesh for this problem. The presented computational mesh by this method can prevent growing of computational cost by time. The performance of the proposed method has been tested by means of some numerical experiments. We show that, in comparison with the full grid algorithms, the presented adaptive algorithm can capture the priori unknown free boundary and is able to find the value of American put option price with high accuracy and reasonable CPU time. [ABSTRACT FROM AUTHOR]

Aerodynamics is one of the main areas of development in vehicle design. One of the most efficient ways of testing the aerodynamic design of a vehicle is to use Computational Fluid Dynamics (CFD), which allows for faster and more accurate aerodynamic simulations, which in turn helps increase the fuel economy and electric vehicle's range. Resource optimization is one of the most important aspects of CFD, and one of its main aspects is the spatial discretization of the fluid domain. This study discusses the use of Adaptive Mesh Refinement (AMR) for the aerodynamic design of private vehicles. This paper compares the results obtained with the use of AMR based on different fluid dynamic criteria for the DrivAer model and correlates the results with experimental data and computational results provided by various authors in previous publications. Four different optimization functions are defined and compared. The results for the drag coefficient, pressure coefficient, and total pressure wake have been correlated, showing great accuracy. This study has proven that the use of AMR highly optimizes computational resources by optimizing the mesh in the desired areas, thereby reducing the number of cells needed elsewhere. The use of these criteria has proven useful for drag coefficient prediction simulations because these criteria make use of the AMR to optimize the wake region.

Hot cylinders within the cavity can find diverse thermal applications, ranging from electronic devices and heat exchangers to solar systems, nuclear reactors, and the thermal design of passive cooling systems. Consequently, considering the use of phase change materials (PCM) close to hot cylinders emerges as a viable method for both cooling and storing thermal energy. In this work, two hot cylinders are arranged vertically and horizontally in the nano-enhanced phase change material (NePCM) trapezoidal enclosure with varying angles. The novelty of the current study lies in the fact that no prior research has explored the impact of hot cylinders arrangement on the melting process of a NePCM within a trapezoidal cavity, considering various inclination angles. The fixed grid, adaptive mesh refinement, and enthalpy-porosity method are used to model the melting flow. The numerical results indicate that the trapezoidal enclosure with vertically arranged hot cylinders exhibits better thermal performance than the other configuration. It is also found that the full melting time for both arrangements is minimum when the angle of the trapezoidal enclosure is γ=+40°. The reduction in full melting times for the vertical and horizontal arrangements of this angle are 25.3% and 29.6%, respectively, compared to the trapezoidal enclosure with γ=0.0°. Moreover, the NePCM with the graphite nanoplatelets (GNPs) of φ=1.0% has the shortest melting time for 0.0%≤φ≤3.0%. As future research, further exploration into the complexities of non-Newtonian NePCM flow can be pursued. Additionally, there is potential to explore modifying the cylinders' geometry into elliptical forms, encompassing a range of aspect ratios.

We address the numerical solution of the Dirichlet problem for the two-dimensional elliptic Monge–Ampère equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators from the nonlinearities of the equation, within a splitting approach. The approximation relies on mixed low order finite element methods with regularization techniques. In order to account for data singularities in non-smooth cases, we introduce an adaptive mesh refinement technique. The error indicator is based an independent formulation of the Monge–Ampère equation under divergence form, which allows to explicit a residual term. We show that the error is bounded from above by an a posteriori error indicator plus an extra term that remains to be estimated. This indicator is then used within the existing least-squares framework. The results of numerical experiments support the convergence of our relaxation method to a convex classical solution, if such a solution exists. Otherwise they support convergence to a generalized solution in a least-squares sense. Adaptive mesh refinement proves to be efficient, robust, and accurate to tackle test cases with singularities.

In tsunami inundations or slope disasters of heavy rain, a lot of floating debris or driftwood logs are included in the flows. The damage to structures from solid body impacts is more severe than the damage from the water pressure. In order to study free-surface flows that include floating debris, developing a high-accurate simulation code of free-surface flows with high performance for large-scale computations is desired. We propose the single-phase free-surface flow model based on the cumulant lattice Boltzmann method coupled with a particle-based rigid body simulation. The discrete element method calculates the contact interaction between solids. An octree-based AMR (Adaptive Mesh Refinement) method is introduced to improve computational accuracy and time-to-solution. High-resolution grids are assigned near the free surfaces and solid boundaries. We conducted two kinds of tsunami flow experiments in the 15 and 70m water tanks at Hachinohe Institute of Technology and Kobe University to validate the accuracy of the proposed model. The simulation results have shown good agreement with the experiments for the drifting speed, the number of trapped wood pieces, and the stacked angles. [ABSTRACT FROM AUTHOR]

A large-eddy simulation (LES) of wake vortices in ground effect is conducted under the influence of airport hangar buildings to investigate the airport-specific behavior of wake vortices. We consider a landing at Tokyo/Haneda International Airport in Japan, where a wake of hangar buildings covers a landing path and touchdown zone under particular wind conditions. We combine an LES code and the Weather Research and Forecasting numerical weather prediction model to retrieve realistic wind conditions around the airport. The behavior of wake vortices is then investigated in the retrieved wind field using the adaptive mesh capability of the LES code for capturing the tiny vortex core of the wake vortex. At the crosswind on the order of a vortex descent speed, the hangar wake reduces the crosswind near the runway, enhancing the windward vortex's rebound. The effect is alleviated by doubling the crosswind to twice the vortex descent speed. On the other hand, the wind fluctuations caused by the hangar buildings only slightly affect the wake vortex decay. [ABSTRACT FROM AUTHOR]

Maintaining a reasonable balance between computational accuracy and overhead is important for neutron transport simulations of engineering problems. This paper presents a goal-oriented mesh adaptive algorithm applied to the multigroup discrete ordinates equation for fixed source and criticality problems. The dual-weighted residual (DWR) approach estimates numerical solution errors and drives local mesh refinement for specific targets, such as detector response, integral flux, and multiplication factor. We employ a reconstruction method to evaluate the spatial residuals of the fluxes obtained by the weighted difference scheme. To improve the performance of adaptive algorithms, new estimation models are proposed for adjoint fluxes needed by the DWR theory, including a regional goal model for fixed source problems and an inconsistent fission source model for k-eigenvalue problems. Additionally, we analyze the impact of the truncation of flux reconstruction and isotropic approximation of adjoint fluxes on grid error indicators and adaptive calculations. Numerical results demonstrate that for the quantities of interest, our adaptive approach saves more than 70% of computational effort and run time when obtaining a level of high accuracy comparable to that of uniform fine grids. [ABSTRACT FROM AUTHOR]

The inverse problem for radiative transfer is important in many applications, such as optical tomography and remote sensing. Major challenges include large memory requirements and computational expense, which arise from high-dimensionality and the need for iterations in solving the inverse problem. Here, to alleviate these issues, we propose adaptive-mesh inversion: a goal-oriented hp -adaptive mesh refinement method for solving inverse radiative transfer problems. One novel aspect here is that the two optimizations (one for inversion, and one for mesh adaptivity) are treated simultaneously and blended together. By exploiting the connection between duality-based mesh adaptivity and adjoint-based inversion techniques, we propose a goal-oriented error estimator, which is cheap to compute, and can efficiently guide the mesh-refinement to numerically solve the inverse problem. We use discontinuous Galerkin spectral element methods to discretize the forward and the adjoint problems. Then, based on the goal-oriented error estimator, we propose an hp -adaptive algorithm to refine the meshes. Numerical experiments are presented at the end and show convergence speed-up and reduced memory occupation by the goal-oriented mesh adaptive method. [ABSTRACT FROM AUTHOR]

The investigation of cavitating trailing vortices emerging from marine propellers is of great interest in the industry. With the help of computational fluid dynamics (CFD), studying the cavitating trailing vortices may be facilitated. However, limitations in computational power raise the necessity to execute numerical simulations as efficiently as possible. The time-efficient simulation of cavitating trailing vortices interacting with rigid bodies is especially challenging due to the continuous change of cavity locations. This study investigates the usability, capability, and practicability of automatic adaptive refinement at every calculation time step for transient Reynolds-averaged Navier–Stokes (RANS) and large eddy CFD simulations of the cavitating tip and hub vortices, utilizing the Schnerr–Sauer cavitation model, in the presence of a rudder located in the propeller slipstream and for an isolated propeller, with additional focus on the computational effort necessary for using high frequency updating adaptive mesh refinement (AMR). It is found that AMR is suitable for resolving cavities with relative motion to the propeller and in interaction with slipstream obstacles. However, the computation time is significantly increased, which renders this method useful only if a classic AMR is not possible due to geometrical limitations. Even in the cases that benefit from the automated AMR, numerical instabilities may lead to unphysical pressure fluctuations, which reduce the suitability of the method for the evaluation of underwater radiated noise. [ABSTRACT FROM AUTHOR]

Multiphase flow in porous media often occurs with the formation and coalescence of fluid ganglia. Accurate predictions of such mechanisms in complex pore geometries require simulation models with local mass conservation and with the option to improve resolution in areas of interest. In this work, we incorporate patch-based, structured adaptive mesh refinement capabilities into a method for local volume conservation that describes the behaviour of disconnected fluid ganglia during level set simulations of capillary-controlled displacement in porous media. We validate the model against analytical solutions for three-phase fluid configurations in idealized pores containing gas, oil, and water, by modelling the intermediate-wet oil layers as separate domains with their volumes preserved. Both the pressures and volumes of disconnected ganglia converge to analytical values with increased refinement levels of the adaptive mesh. Favourable results from strong and weak scaling tests emphasize that the number of patches per processor and the total number of patches are important parameters for efficient parallel simulations with adaptive mesh refinement. Simulations of two-phase imbibition and three-phase gas invasion on segmented 3D images of water-wet sandstone show that adaptive mesh refinement has the highest impact on three-phase displacements, especially concerning the behaviour of the conserved, intermediate-wet phase. [ABSTRACT FROM AUTHOR]

An adaptive mesh refinement–rotated lattice Boltzmann flux solver (AMR-RLBFS) is presented to simulate two and three-dimensional compressible flows with complex shock structures. In the method, the RLBFS, which has a strong shock-capturing capability and can effectively eliminate the shock instability phenomenon, is applied to solve the flow filed by reconstructing the fluxes at each cell interface adaptively with the mesoscopic lattice Boltzmann model. To locally and dynamically improve the resolution of intricate shock structures and optimize the required computational resources, a block-structured adaptive mesh refinement (AMR) technique is introduced. The validity and effectiveness of the proposed method are confirmed through a range of two and three-dimensional numerical cases, including the shock tube problem, the four-wave Riemann problem, explosion within a rectangular box, and the vorticity induced by a shock. The results obtained using the AMR-RLBFS exhibit excellent agreement with published data and demonstrate high accuracy in capturing complex shock structures. The computational efficiency of the AMR-RLBFS can be also improved significantly compared to the RLBFS on uniform grids. Furthermore, the numerical outcomes underscore the capability of the AMR-RLBFS to eliminate shock instability effects while efficiently capturing a broader spectrum of small-scale vertical structures. These findings highlight the ability of AMR-RLBFS to improve the computational efficiency and capture intricate shock structures effectively, making it a valuable tool for studying a wide range of compressible flows from aerodynamics to astrophysics. [ABSTRACT FROM AUTHOR]

The use of adaptive meshing strategies to perform cost-effective transient simulations of spray drying processes is evaluated. These simulations are often computationally expensive, given the large differences between the characteristic times of the central jet and those of the unsteady flow developed at its periphery. Managing the computational cost through the control of the grid resolution by regions is inadequate in many of these applications since the grid resolution requirements change dynamically within the domain. These conditions are related to the unsteady nature of the flow in both the central jet and the flow recirculation zones. Therefore, the application of adaptive mesh refinement (AMR) strategies is recommended. In this paper, general AMR criteria based on relative errors are evaluated by testing three mesh adaptation criteria: velocity gradient, pressure gradient, and vorticity. This evaluation is performed using a low-cost turbulence model with eddy resolution (DDES) in two different types of drying chambers, in which experimental measurements are available. The use of AMR exerts appreciable effects on decreasing computational costs and contributes to the capture of large eddies in critical regions. The present approach provides an appropriate balance between solution accuracy and computational cost. By using a correct AMR configuration, it is possible to obtain results similar to those obtained on a fixed grid but reducing the computational costs by 3 to 5 times. [ABSTRACT FROM AUTHOR]

We introduce several spatially adaptive model order reduction approaches tailored to non-coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz problems. The offline information is computed by means of adaptive finite elements, so that each snapshot lives in a different discrete space that resolves the local singularities of the analytical solution and is adjusted to the considered frequency value. A rational surrogate is then assembled adopting either a least-squares or an interpolatory approach, yielding a function-valued version of the the standard rational interpolation method ($ \mathcal{V} $-SRI) and the minimal rational interpolation method (MRI). In the context of building an approximation for linear or quadratic functionals of the Helmholtz solution, we perform several numerical experiments to compare the proposed methodologies. Our simulations show that, for interior resonant problems (whose singularities are encoded by poles on the real axis), the spatially adaptive $ \mathcal{V} $-SRI and MRI work comparably well. Instead, when dealing with exterior scattering problems, whose frequency response is mostly smooth, the $ \mathcal{V} $-SRI method seems to be the best-performing one.

Wavelet-based grid resolution adaptation driven by the ‘multiresolution analysis’ (MRA) of the Haar wavelet (HW) allows to devise an adaptive first-order finite volume (FV1) model (HWFV1) that can readily preserve the modelling fidelity of its reference uniform-grid FV1 counterpart. However, the MRA entails an enormous computational effort as it involves ‘encoding’ (coarsening), ‘decoding’ (refining), analysing and traversing modelled data across a deep hierarchy of nested, uniform grids. GPU-parallelisation of the MRA is needed to handle its computational effort, but its algorithmic structure (1) hinders coalesced memory access on the GPU and (2) involves an inherently sequential tree traversal problem. This work redesigns the algorithmic structure of the MRA in order to parallelise it on the GPU, addressing (1) by applying Z-order space-filling curves and (2) by adopting a parallel tree traversal algorithm. This results in a GPU-parallelised HWFV1 model (GPU-HWFV1). GPU-HWFV1 is verified against its CPU predecessor (CPU-HWFV1) and its GPU-parallelised reference uniform-grid counterpart (GPU-FV1) over five shallow water flow test cases. GPU-HWFV1 preserves the modelling fidelity of GPU-FV1 while being up to 30 times faster. Compared to CPU-HWFV1, it is up to 200 times faster, suggesting that the GPU-parallelised MRA could be used to speed up other FV1 models. HIGHLIGHTS Wavelet-based grid adaptation is parallelised on the GPU via a Z-order space-filling curve and a parallel tree traversal algorithm.; An adaptive Haar wavelet first-order finite volume shallow water model running on the GPU is developed (GPU-HWFV1).; GPU-HWFV1 is 20–300 times faster than its single-core serial CPU version 4.; GPU-HWFV1 is 1.3–30 times faster than its GPU-parallelised reference uniform-grid counterpart.;

As the need for handling complex geometries in computational fluid dynamics (CFD) grows, efficient and accurate mesh generation techniques become paramount. This study presents an adaptive mesh refinement (AMR) technology based on cell-based Cartesian grids, employing a distance-weighted least squares interpolation for finite difference discretization and utilizing immersed boundary methods for wall boundaries. This facilitates effective management of both transient and steady flow problems. Validation through supersonic flow over a forward-facing step, subsonic flow around a high Reynolds number NHLP airfoil, and supersonic flow past a sphere demonstrated AMR’s efficacy in capturing essential flow characteristics while wisely refining and coarsening meshes, thus optimizing resource utilization without compromising accuracy. Importantly, AMR simplified the capture of complex flows, obviating manual mesh densification and significantly improving the efficiency and reliability of CFD simulations.

We combine a systematic approach for deriving general a posteriori error estimates for convex minimization problems based on convex duality relations with a recently derived generalized Marini formula. The a posteriori error estimates are quasi constant-free and apply to a large class of variational problems including the p-Dirichlet problem, as well as degenerate minimization, obstacle and image de-noising problems. In addition, these a posteriori error estimates are based on a comparison to a given non-conforming finite element solution. For the p-Dirichlet problem, these a posteriori error bounds are equivalent to residual type a posteriori error bounds and, hence, reliable and efficient. [ABSTRACT FROM AUTHOR]

Highly accurate simulation of plasma transport is needed to drive the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers that are expensive to resolve. This work investigates how various mesh refinement strategies might reduce that expense to allow for more efficient simulation by comparing standard variable refinement approaches that use a field quantity to an adaptive approach that uses an error estimator. It is first verified that higher order discretization only realizes the proper rate of convergence once the mesh resolves the thin boundary layer, therefore motivating the focusing of refinement on the boundary layer. For three two-dimensional test cases that contain characteristic features of tokamak magnetic fields, an exponential refinement strategy based on the magnetic flux function, which is the standard refinement approach in the field, is compared to an adaptive strategy utilizing the established Zienwiekicz and Zhu error estimator. The adaptive mesh refinement strategy consistently achieves the same accuracy using orders of magnitude less degrees of freedom than either exponential or uniform refinement. This result makes the adaptive refinement strategy more efficient than the exponential refinement strategy while also being more generalizable to problems with complex magnetic geometries. Scaling laws are derived that quantify the improvement in cost of the adaptive refinement strategy over other refinement approaches in 2D and 3D. [ABSTRACT FROM AUTHOR]

On the path to exascale the landscape of computer device architectures and corresponding programming models has become much more diverse. While various low-level performance portable programming models are available, support at the application level lacks behind. To address this issue, we present the performance portable block-structured adaptive mesh refinement (AMR) framework P arthenon, derived from the well-tested and widely used A thena++ astrophysical magnetohydrodynamics code, but generalized to serve as the foundation for a variety of downstream multi-physics codes. P arthenon adopts the K okkos programming model, and provides various levels of abstractions from multidimensional variables, to packages defining and separating components, to launching of parallel compute kernels. P arthenon allocates all data in device memory to reduce data movement, supports the logical packing of variables and mesh blocks to reduce kernel launch overhead, and employs one-sided, asynchronous MPI calls to reduce communication overhead in multi-node simulations. Using a hydrodynamics miniapp, we demonstrate weak and strong scaling on various architectures including AMD and NVIDIA GPUs, Intel and AMD x86 CPUs, IBM Power9 CPUs, as well as Fujitsu A64FX CPUs. At the largest scale on Frontier (the first TOP500 exascale machine), the miniapp reaches a total of 1.7 × 1013 zone-cycles/s on 9216 nodes (73,728 logical GPUs) at ≈ 92 % weak scaling parallel efficiency (starting from a single node). In combination with being an open, collaborative project, this makes Parthenon an ideal framework to target exascale simulations in which the downstream developers can focus on their specific application rather than on the complexity of handling massively-parallel, device-accelerated AMR. [ABSTRACT FROM AUTHOR]