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Using a Viscosity Matrix to Construct a Riemann Solver for the Equations of Special Relativistic Hydrodynamics

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Publicado en:Numerical Analysis and Applications vol. 18, no. 1 (Mar 2025), p. 67
Autor principal: Kulikov, I. M.
Publicado:
Springer Nature B.V.
Materias:
Velocity
Relativistic effects
Mathematical analysis
Viscosity
Hyperbolic systems
Magnetohydrodynamics
Equations of state
Godunov method
Magnetic fields
Polynomials
Chebyshev approximation
Variables
Jacobi matrix method
Approximation
Numerical analysis
Hydrodynamic equations
Cauchy problems
Numerical methods
Fluid mechanics
Jacobian matrix
Riemann solver
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Resumen:Traditionally, to solve the hydrodynamic equations a Godunov method is used whose main stage is the solution of a Riemann problem to compute the fluxes of conservative variables through the interfaces of adjacent cells. Most numerical Riemann solvers are based on partial or full spectral decompositions of the Jacobian matrix with respect to the spatial derivatives. However, when using complex hyperbolic models and various types of equations of state, even partial spectral decompositions are quite difficult to find analytically. Such hyperbolic systems include the equations of special relativistic magnetohydrodynamics. In this paper, a numerical Riemann solver is constructed by means of a viscosity matrix based on Chebyshev polynomials. This scheme does not require any information about the spectral decomposition of the Jacobian matrix, while considering all types of waves in its design. To reduce the dissipation of the numerical solution, a piecewise parabolic reconstruction of the physical variables is used. The behavior of the numerical method is studied by using some classical test problems.
ISSN:1995-4239
1995-4247
DOI:10.1134/S1995423925010069
Fuente:Science Database