On numerical instabilities of Godunov-type schemes for strong shocks

Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes

Philip L. Roe · Journal of Computational Physics · 1997 · 6.3K citations

Natural Sciences, Mathematics, Physics +15

High resolution schemes for hyperbolic conservation laws

Ami Harten · Journal of Computational Physics · 1983 · 4.1K citations · Full text

Natural Sciences, Mathematics, Physics +14

On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws

Amiram Harten, Peter D. Lax, Bram van Leer · SIAM Review · 1983 · 3.3K citations

Natural Sciences, Mechanical Engineering, Physics +12

The numerical simulation of two-dimensional fluid flow with strong shocks

Paul R. Woodward, Phillip Colella · Journal of Computational Physics · 1984 · 2.9K citations

Natural Sciences, Mathematics, Physics +14

Restoration of the contact surface in the HLL-Riemann solver

Eleuterio F. Toro, M. Spruce, W. Speares · Shock Waves · 1994 · 2.4K citations

Engineering, Computational Engineering, Mathematics +10