A universal solver for hyperbolic equations by cubic-polynomial interpolation I. One-dimensional solver

Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method

Bram van Leer · Journal of Computational Physics · 1979 · 7K citations

Natural Sciences, Computational Engineering, Mathematics +11

Physics of shock waves and high-temperature hydrodynamic phenomena

Journal of Molecular Structure · 1970 · 4.2K citations

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The Piecewise Parabolic Method (PPM) for gas-dynamical simulations

Phillip Colella, Paul R. Woodward · Journal of Computational Physics · 1984 · 4K citations

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A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws

Gary A. Sod · Journal of Computational Physics · 1978 · 2.6K citations · Full text

Natural Sciences, Mathematics, Physics +14

On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes

Ami Harten · SIAM Journal on Numerical Analysis · 1984 · 718 citations

Natural Sciences, Computational Engineering, Physics +17