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03/13/2023
High-order accurate well-balanced energy stable adaptive moving mesh finite difference schemes for the shallow water equations with non-flat bottom topography
This paper proposes high-order accurate well-balanced (WB) energy stable...
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03/05/2023
Genuinely multidimensional physical-constraints-preserving finite volume schemes for the special relativistic hydrodynamics
This paper develops the genuinely multidimensional HLL Riemann solver fo...
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02/06/2023
A general class of linear unconditionally energy stable schemes for the gradient flows, II
This paper continues to study linear and unconditionally modified-energy...
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07/19/2022
Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Schemes for the Euler Equations under Gravitational Fields
This paper designs and analyzes positivity-preserving well-balanced (WB)...
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03/04/2022
A general class of linear unconditionally energy stable schemes for the gradient flows
This paper studies a class of linear unconditionally energy stable schem...
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02/16/2022
High-order accurate entropy stable adaptive moving mesh finite difference schemes for (multi-component) compressible Euler equations with the stiffened equation of state
This paper extends the high-order entropy stable (ES) adaptive moving me...
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07/26/2021
High-order accurate entropy stable adaptive moving mesh finite difference schemes for special relativistic (magneto)hydrodynamics
This paper develops high-order accurate entropy stable (ES) adaptive mov...
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07/05/2021
An analytical solution of the isentropic vortex problem in the special relativistic magnetohydrodynamics
The isentropic vortex problem is frequently solved to test the accuracy ...
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11/02/2020
Three discontinuous Galerkin methods for one- and two-dimensional nonlinear Dirac equations with a scalar self-interaction
This paper develops three high-order accurate discontinuous Galerkin (DG...
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11/02/2020
A physical-constraints-preserving genuinely multidimensional HLL scheme for the special relativistic hydrodynamics
This paper develops the genuinely multidimensional HLL Riemann solver an...
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11/02/2020
Second-order accurate BGK schemes for the special relativistic hydrodynamics with the Synge equation of state
This paper extends the second-order accurate BGK finite volume schemes f...
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07/25/2020
Entropy stable adaptive moving mesh schemes for 2D and 3D special relativistic hydrodynamics
This paper develops entropy stable (ES) adaptive moving mesh schemes for...
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07/06/2020
On the explicit two-stage fourth-order accurate time discretizations
This paper continues to study the explicit two-stage fourth-order accura...
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03/23/2020
High-order accurate entropy stable finite difference schemes for the shallow water magnetohydrodynamics
This paper develops the high-order accurate entropy stable (ES) finite d...
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11/10/2019