Approximate Riemann solvers, parameter vectors, and difference schemes. Roe, P., L. Journal of Computational Physics, 43(2):357-372, Academic Press, 10, 1981.
Approximate Riemann solvers, parameter vectors, and difference schemes [pdf]Paper  doi  abstract   bibtex   
Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution are worth striving for. It is shown that these features can be obtained by constructing a matrix with a certain "Property U." Matrices having this property are exhibited for the equations of steady and unsteady gasdynamics. In order to construct thems it is found helpful to introduce "parameter vectors" which notably simplify the structure of the conservation laws. © 1981.

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