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RESEARCH PRODUCT
Riemann solvers in relativistic astrophysics
J. Ma. IbáñezJ. Ma. Martísubject
Conservation lawPartial differential equationApplied MathematicsRiemann solverLorentz factorsymbols.namesakeTheoretical physicsRiemann hypothesisComputational MathematicsRiemann problemFlow (mathematics)Shock capturing methodsymbolsMathematicsMathematical physicsdescription
AbstractOur contribution reviews High Resolution Shock Capturing methods (HRSC) in the field of relativistic hydrodynamics with special emphasis on Riemann solvers. HRSC techniques achieve highly accurate numerical approximations (formally second order or better) in smooth regions of the flow, and capture the motion of unresolved steep gradients without creating spurious oscillations. One objective of our contribution is to show how these techniques have been extended to relativistic hydrodynamics, making it possible to explore some challenging astrophysical scenarios. We will review recent literature concerning the main properties of different special relativistic Riemann solvers, and discuss several 1D and 2D test problems which are commonly used to evaluate the performance of numerical methods in relativistic hydrodynamics. Finally, we will illustrate the use of HRSC methods in several applications in special and general relativistic hydrodynamics.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1999-09-01 | Journal of Computational and Applied Mathematics |