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Author: search.filters.author.Bhoriya, DeepakSubject: search.filters.subject.Entropy-stable schemes

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    Entropy-stable schemes for relativistic hydrodynamics equations
    (Springer, 2020-01) Bhoriya, Deepak
    In this article, we propose high-order finite difference schemes for the equations of relativistic hydrodynamics, which are entropy stable. The crucial components of these schemes are a computationally efficient entropy conservative flux and suitable high-order entropy dissipative operators. We first design a higher-order entropy conservative flux. For the construction of appropriate entropy dissipative operators, we derive entropy scaled right eigenvectors. This is then used with ENO-based sign-preserving reconstruction of scaled entropy variables, which results in higher-order entropy-stable schemes. Several numerical results are presented up to fourth order to demonstrate entropy stability and performance of these schemes.
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    Second order divergence constraint preserving schemes for two-fluid relativistic plasma flow equations
    (2025-03) Bhoriya, Deepak
    Two-fluid relativistic plasma flow equations combine the equations of relativistic hydrodynamics with Maxwell's equations for electromagnetic fields, which involve divergence constraints for the magnetic and electric fields. When developing numerical schemes for the model, the divergence constraints are ignored, or Maxwell's equations are reformulated as Perfectly Hyperbolic Maxwell's (PHM) equations by introducing additional equations for correction potentials. In the latter case, the divergence constraints are preserved only as the limiting case. In this article, we present second-order numerical schemes that preserve the divergence constraint for electric and magnetic fields at the discrete level. The schemes are based on using a multidimensional Riemann solver at the vertices of the cells to define the numerical fluxes on the edges. The second-order accuracy is obtained by reconstructing the electromagnetic fields at the corners using a MinMod limiter. The discretization of Maxwell's equations can be combined with any consistent and stable discretization of the fluid parts. In particular, we consider entropy-stable schemes for the fluid part. The resulting schemes are second-order accurate, entropy stable, and preserve the divergence constraints of the electromagnetic fields. We use explicit and IMEX-based time discretizations. We then test these schemes using several one- and two-dimensional test cases. We also compare the divergence constraint errors of the proposed schemes with schemes having no divergence constraints treatment and schemes based on the PHM-based divergence cleaning.