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Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study

Communications in Computational Physics 2021年第1期29卷 80-110页

作者： Xucheng Meng Thi-Thao-Phuong Hoang Zhu Wang Lili Ju Department of Mathematics University of South CarolinaColumbiaSC 29208USA Department of Mathematics and Statistics Auburn UniversityAuburnAL 36849USA SUSTech International Center for Mathematics Southern University of Science and TechnologyShenzhenGuangdong 518055China Center for Mathematical studies Advanced Institute of Natural SciencesBeijing Normal University at ZhuhaiZhuhaiGuangdong 519087China

In this paper,we investigate the performance of the exponential time differencing(ETD)method applied to the rotating shallow water *** with explicit time stepping of the same order accuracy in time,the ETD algorithms could reduce the computational time in many cases by allowing the use of large time step sizes while still maintaining numerical *** accelerate the ETD simulations,we propose a localized approach that synthesizes the ETD method and overlapping domain *** dividing the original problem into many subdomain problems of smaller sizes and solving them locally,the proposed approach could speed up the calculation of matrix exponential vector *** standard test cases for shallow water equations of one or multiple layers are *** results show great potential of the localized ETD method for high-performance computing because each subdomain problem can be naturally solved in parallel at every time step.

关键词： Exponential time differencing domain decomposition rotating shallow water equa-tions finite volume discretization

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Accuracy analysis of gradient reconstruction on isotropic unstructured meshes and its effects on inviscid flow simulation

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Advances in Aerodynamics 2019年第1期1卷 348-378页

作者： Nianhua Wang Ming Li Rong Ma Laiping Zhang State Key Laboratory of Aerodynamics China Aerodynamics Research and Development CenterMianyang 621000China Computational Aerodynamics Institute China Aerodynamics Research and Development CenterMianyang 621000China

The accuracy of gradient reconstruction methods on unstructured meshes is analyzed both mathematically and *** derivations reveal that,for gradient reconstruction based on the Green-Gauss theorem(the GG methods),if the summation of first-and-lower-order terms does not counterbalance in the discretized integral process,which rarely occurs,second-order accurate approximation of face midpoint value is necessary to produce at least first-order accurate ***,gradient reconstruction based on the least-squares approach(the LSQ methods)is at least first-order on arbitrary unstructured *** are performed on typical isotropic grid stencils by analyzing the relationship between the discretization error of gradient reconstruction and the discretization error of the face midpoint value approximation of a given analytic ***,the numerical accuracy of gradient reconstruction methods is examined with grid convergence study on typical isotropic *** verify the phenomenon of accuracy degradation for the GG methods when the face midpoint value condition is not *** LSQ methods are proved to be at least first-order on all tested isotropic *** study gradient accuracy effects on inviscid flow simulation,solution errors are quantified using the Method of Manufactured Solutions(MMS)which was validated before adoption by comparing with an exact solution case,i.e.,the 2-dimensional(2D)inviscid isentropic *** results demonstrate that the order of accuracy(OOA)of gradient reconstruction is crucial in determining the OOA of numerical *** accuracy deteriorates seriously if gradient reconstruction does not reach first-order.

关键词： finite volume discretization Unstructured grids Gradient reconstruction Accuracy analysis The method of manufactured solutions Grid convergence study

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