Construction of solutions for two-dimensional Riemann problems.

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It is shown that parts of the solution to the scalar quasilinear equation for the Cauchy problem can be classified and are expressible in terms of two dimensional nonlinear waves in analogy with the nonlinear rarefaction and shock waves of the Riemann problem in one spatial dimension. The two dimensional waves can be expressed in almost closed form. Explicit solutions were constructed from these waves. An application is illustrated by calculation of the interaction of water/oil banks in two phase incompressible flow in reservoirs.

Original languageEnglish
Pages (from-to)413-432
Number of pages20
Volume12 A
Issue number4-5 , Apr.-May 1986
StatePublished - 1986


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