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Xiangxiong Zhang
Researcher at Purdue University
Publications - 54
Citations - 3208
Xiangxiong Zhang is an academic researcher from Purdue University. The author has contributed to research in topics: Discontinuous Galerkin method & Finite volume method. The author has an hindex of 20, co-authored 46 publications receiving 2437 citations. Previous affiliations of Xiangxiong Zhang include Massachusetts Institute of Technology & Brown University.
Papers
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On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes
Xiangxiong Zhang,Chi-Wang Shu +1 more
TL;DR: High order accurate discontinuous Galerkin (DG) schemes which preserve positivity of density and pressure for Euler equations of compressible gas dynamics are constructed and extended to higher dimensions on rectangular meshes.
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On maximum-principle-satisfying high order schemes for scalar conservation laws
Xiangxiong Zhang,Chi-Wang Shu +1 more
TL;DR: It is shown that the same limiter can preserve the maximum principle for DG or finite volume schemes solving two-dimensional incompressible Euler equations in the vorticity stream-function formulation, or any passive convection equation with an incompressibles velocity field.
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Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
Xiangxiong Zhang,Chi-Wang Shu +1 more
TL;DR: This paper presents a simpler implementation of genuinely high-order accurate finite volume and discontinuous Galerkin schemes satisfying a strict maximum principle for scalar conservation laws, which will result in a significant reduction of computational cost especially for weighted essentially non-oscillatory finite-volume schemes.
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Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations
TL;DR: A high order discontinuous Galerkin method is proposed which can maintain the still water steady state exactly, and at the same time can preserve the non-negativity of the water height without loss of mass conservation.
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Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for Conservation Laws on Triangular Meshes
TL;DR: This paper introduces a special quadrature rule which is exact for two-variable polynomials over a triangle of a given degree and satisfies a few other conditions, by which it can construct high order maximum principle satisfying finite volume schemes.