Using a Viscosity Matrix to Construct a Riemann Solver for the Equations of Special Relativistic Hydrodynamics
محفوظ في:
| الحاوية / القاعدة: | Numerical Analysis and Applications vol. 18, no. 1 (Mar 2025), p. 67 |
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| المؤلف الرئيسي: | |
| منشور في: |
Springer Nature B.V.
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| الموضوعات: | |
| الوصول للمادة أونلاين: | Citation/Abstract Full Text Full Text - PDF |
| الوسوم: |
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| 100 | 1 | |a Kulikov, I. M. |u Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia (GRID:grid.465353.2) (ISNI:0000 0000 9188 6409) | |
| 245 | 1 | |a Using a Viscosity Matrix to Construct a Riemann Solver for the Equations of Special Relativistic Hydrodynamics | |
| 260 | |b Springer Nature B.V. |c Mar 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a 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. | |
| 653 | |a Velocity | ||
| 653 | |a Relativistic effects | ||
| 653 | |a Mathematical analysis | ||
| 653 | |a Viscosity | ||
| 653 | |a Hyperbolic systems | ||
| 653 | |a Magnetohydrodynamics | ||
| 653 | |a Equations of state | ||
| 653 | |a Godunov method | ||
| 653 | |a Magnetic fields | ||
| 653 | |a Polynomials | ||
| 653 | |a Chebyshev approximation | ||
| 653 | |a Variables | ||
| 653 | |a Jacobi matrix method | ||
| 653 | |a Approximation | ||
| 653 | |a Numerical analysis | ||
| 653 | |a Hydrodynamic equations | ||
| 653 | |a Cauchy problems | ||
| 653 | |a Numerical methods | ||
| 653 | |a Fluid mechanics | ||
| 653 | |a Jacobian matrix | ||
| 653 | |a Riemann solver | ||
| 773 | 0 | |t Numerical Analysis and Applications |g vol. 18, no. 1 (Mar 2025), p. 67 | |
| 786 | 0 | |d ProQuest |t Science Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3257136011/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text |u https://www.proquest.com/docview/3257136011/fulltext/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3257136011/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |