High-order accurate entropy stable finite difference schemes for the shallow water magnetohydrodynamics

High-order accurate entropy stable nodal discontinuous Galerkin schemes for the ideal special relativistic magnetohydrodynamics

(2020) Junming Duan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Entropy stable adaptive moving mesh schemes for 2D and 3D special relativistic hydrodynamics

(2020) Junming Duan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

High-Order Accurate Entropy Stable Finite Difference Schemes for One- and Two-Dimensional Special Relativistic Hydrodynamics

(2019) Junming Duan & Huazhong Tang   Advances in Applied Mathematics and Mechanics

Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations

(2018) Dominik Derigs et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws

(2017) Tianheng Chen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Runge-Kutta Discontinuous Local Evolution Galerkin Methods for the Shallow Water Equations on the Cubed-Sphere Grid

(2017) Yangyu Kuang et al.   Numerical Mathematics-Theory Methods and Applications

A Newton multigrid method for steady-state shallow water equations with topography and dry areas

(2016) Kailiang Wu et al.   APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION

Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations

(2016) Andrew R. Winters et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Entropy Stable Finite Volume Scheme for Ideal Compressible MHD on 2-D Cartesian Meshes

(2016) Praveen Chandrashekar et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Parametrized Positivity Preserving Flux Limiters for the High Order Finite Difference WENO Scheme Solving Compressible Euler Equations

(2015) Tao Xiong et al.   JOURNAL OF SCIENTIFIC COMPUTING

An Entropy Stable Finite Volume Scheme for the Equations of Shallow Water Magnetohydrodynamics

(2015) Andrew R. Winters et al.   JOURNAL OF SCIENTIFIC COMPUTING

Numerical solution of shallow water magnetohydrodynamic equations with non-flat bottom topography

(2014) Saqib Zia et al.   INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS

High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains

(2013) Travis C. Fisher et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Positivity-preserving method for high-order conservative schemes solving compressible Euler equations

(2013) Xiangyu Y. Hu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Parametrized maximum principle preserving flux limiters for high order schemes solving hyperbolic conservation laws: one-dimensional scalar problem

(2013) Zhengfu Xu   MATHEMATICS OF COMPUTATION

Entropy stable shock capturing space–time discontinuous Galerkin schemes for systems of conservation laws

(2013) Andreas Hiltebrand et al.   NUMERISCHE MATHEMATIK

ENO Reconstruction and ENO Interpolation Are Stable

(2012) Ulrik S. Fjordholm et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws

(2012) Ulrik S. Fjordholm et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography

(2011) Ulrik S. Fjordholm et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations

(2011) Fengyan Li et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics

(2009) Dinshaw S. Balsara   JOURNAL OF COMPUTATIONAL PHYSICS

An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws

(2008) Rafael Borges et al.   JOURNAL OF COMPUTATIONAL PHYSICS