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On Godunov-Type Methods for Gas Dynamics
Abstract
In this paper we describe a new approximate Riemann solver for compressible gas flow. In contrast to previous Riemann solvers, where a numerical approximation for the pressure and the velocity at the contact discontinuity is computed, we derive a numerical approximation for the largest and smallest signal velocity in the Riemann problem. Having obtained the numerical signal velocities, we use theoretical results by Harten, Lax and van Leer to obtain the full approximation. A stability condition for the numerical signal velocities is derived. We also demonstrate a relation between the signal velocities and the dissipation contained in the corresponding Godunov-type method. The computation of signal velocities for a general (convex) equation of state is discussed. Numerical results for the one- and two-dimensional compressible gas dynamics equations are also given.
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A contribution to the great Riemann solver debate
Quirk, J. J. (1994) · International Journal for Numerical Methods in Fluids · doi:10.1002/fld.1650180603 · Cited by 786
Ressler, S. M., White, C. J., Quataert, E., & Stone, J. M. (2020) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ab9532 · Cited by 123
Ressler, S. M., White, C. J., & Quataert, E. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stad837 · Cited by 56
Metadata
- Authors
- Einfeldt, B.
- Venue
- SIAM Journal on Numerical Analysis
- Published
- 1988-04
- Volume
- 25
- Issue
- 2
- Pages
- 294-318
- ISSN
- 0036-1429 (ISSN-L)
- 1095-7170
- OpenAlex
- W2171431553
- Cited by
- 1,031
- References
- 0
- FWCI
- 4.57
- Type
- journal article
- Language
- en
- Open access
- closed
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- Einfeldt, B. (1988). On Godunov-Type Methods for Gas Dynamics. SIAM Journal on Numerical Analysis. https://doi.org/10.1137/0725021
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