
Entropy Symmetrization and HighOrder Accurate Entropy Stable Numerical Schemes for Relativistic MHD Equations
This paper presents entropy symmetrization and highorder accurate entro...
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Highorder accurate entropy stable finite difference schemes for the shallow water magnetohydrodynamics
This paper develops the highorder accurate entropy stable (ES) finite d...
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Entropy stable nonoscillatory fluxes: An optimized wedding of entropy conservative flux with nonoscillatory flux
This work settles the problem of constructing entropy stable nonoscilla...
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Entropy stable discontinuous Galerkin approximation for the Relativistic Hydrodynamic Equations
This paper presents the higherorder discontinuous Galerkin entropy stab...
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An Entropy Stable Nodal Discontinuous Galerkin Method for the resistive MHD Equations. Part II: Subcell Finite Volume Shock Capturing
The second paper of this series presents two robust entropy stable shock...
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Minimum Principle on Specific Entropy and HighOrder Accurate Invariant Region Preserving Numerical Methods for Relativistic Hydrodynamics
This paper explores Tadmor's minimum entropy principle for the relativis...
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Explicit Jacobian matrix formulas for entropy stable summationbyparts schemes
Entropy stable schemes replicate an entropy inequality at the semidiscr...
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Highorder accurate entropy stable nodal discontinuous Galerkin schemes for the ideal special relativistic magnetohydrodynamics
This paper studies highorder accurate entropy stable nodal discontinuous Galerkin (DG) schemes for the ideal special relativistic magnetohydrodynamics (RMHD). It is built on the modified RMHD equations with a particular source term, which is analogous to the Powell's eightwave formulation and can be symmetrized so that an entropy pair is obtained. We design an affordable fully consistent twopoint entropy conservative flux, which is not only consistent with the physical flux, but also maintains the zero parallel magnetic component, and then construct highorder accurate semidiscrete entropy stable DG schemes based on the quadrature rules and the entropy conservative and stable fluxes. They satisfy the semidiscrete entropy inequality for the given entropy pair and are integrated in time by using the highorder explicit strong stability preserving RungeKutta schemes to get further the fullydiscrete nodal DG schemes. Extensive numerical tests are conducted to validate the accuracy and the ability to capture discontinuities of our schemes. Moreover, our entropy conservative flux is compared to an existing flux through some numerical tests. The results show that the zero parallel magnetic component in the numerical flux can help to decrease the error in the parallel magnetic component in onedimensional tests, but two entropy conservative fluxes give similar results since the error in the magnetic field divergence seems dominated in the twodimensional tests.
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