
Highorder accurate entropy stable adaptive moving mesh finite difference schemes for special relativistic (magneto)hydrodynamics
This paper develops highorder accurate entropy stable (ES) adaptive mov...
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On the Geometric Conservation Law for the Non Linear Frequency Domain and TimeSpectral Methods
The aim of this paper is to present and validate two new procedures to e...
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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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Efficient computation of Jacobian matrices for entropy stable summationbyparts schemes
Entropy stable schemes replicate an entropy inequality at the semidiscr...
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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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Entropy Stable pNonconforming Discretizations with the SummationbyParts Property for the Compressible NavierStokes Equations
The entropy conservative, curvilinear, nonconforming, prefinement algor...
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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 adaptive moving mesh schemes for 2D and 3D special relativistic hydrodynamics
This paper develops entropy stable (ES) adaptive moving mesh schemes for the 2D and 3D special relativistic hydrodynamic (RHD) equations. They are built on the ES finite volume approximation of the RHD equations in curvilinear coordinates, the discrete geometric conservation laws, and the mesh adaptation implemented by iteratively solving the EulerLagrange equations of the mesh adaption functional in the computational domain with suitably chosen monitor functions. First, a sufficient condition is proved for the twopoint entropy conservative (EC) flux, by mimicking the derivation of the continuous entropy identity in curvilinear coordinates and using the discrete geometric conservation laws given by the conservative metrics method. Based on such sufficient condition, the EC fluxes for the RHD equations in curvilinear coordinates are derived and the secondorder accurate semidiscrete EC schemes are developed to satisfy the entropy identity for the given convex entropy pair. Next, the semidiscrete ES schemes satisfying the entropy inequality are proposed by adding a suitable dissipation term to the EC scheme and utilizing linear reconstruction with the minmod limiter in the scaled entropy variables in order to suppress the numerical oscillations of the above EC scheme. Then, the semidiscrete ES schemes are integrated in time by using the secondorder strong stability preserving explicit RungeKutta schemes. Finally, several numerical results show that our 2D and 3D ES adaptive moving mesh schemes effectively capture the localized structures, such as sharp transitions or discontinuities, and are more efficient than their counterparts on uniform mesh.
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