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Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes by P.L. Roe is a Engineering article available to read on EtoBox.

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u(x, 0) ε u L (x Ͻ 0), u(x, 0) ε u R (x Ͼ 0). (3) Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by That is, we study the breakup of a single discontinuity. considering a sequence of Riemann problems. It is argued that in Those cases where F(u) is linear are well known and essenexisting schemes much of this information is degraded and that only certain features of the exact solution are worth striving for. It tially trivial (see [1] for a brief discussion). Those cases is shown that these features can be obtained by constructing a where u is scalar and F is nonlinear can be surprisingly matrix with a certain ''Property U.'' Matrices having this property are intricate, but have been thoroughly investigated [2]. If u exhibited for the equations of steady and unsteady gasdynamics. In is a vector and F is nonlinear, then the problem involves order to construct them, it is found helpful to introduce ''parameter nonlinear algebraic equations together with, usually, logivectors'' which notably simplify the structure of the conservation laws. ᮊ 1981 Academic Press. cal conditions which express the fact that a give

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Author

P.L. Roe

Publisher

Elsevier BV

Published

1997

Language

EN

Field

Engineering (Physical Sciences)