Primitive upwind numerical methods for hyperbolic partial differential equations
This paper is about the construction of numerical methods based on non-conservative formulations of hyperbolic PDEs. The methods are explicit and Riemann-problem based upwind. Schemes of first, second and higher order of accuracy are constructed. A modified grp approach leads to arbitrarily high order schemes, in which sequences of Riemann problems for high-order spatial gradients are solved. Other approaches and related issues are presented in detail in [Toro (97)], [Toro (98)].
Key WordsHyperbolic PDEs Primitive Schemes Riemann Solvers Godunov Method
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