Construction of solutions for two-dimensional Riemann problems
Solutions to the scalar quasilinear equation with initial data given by a two dimensional Riemann problem are piecewise smooth if f/sub 1/ identical with f/sub 2/ identical with f, and f has at most one inflection point. We show the pieces of this solution can be classified and are expressible in terms of two dimensional non-linear waves in analogy with the non-linear 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 are constructable from these waves. An application is illustrated by calculation of the interaction of water/oil banks in two phase incompressible flow in reservoirs.
- Research Organization:
- New York Univ., NY (USA). Courant Mathematics and Computing Lab.
- DOE Contract Number:
- AC02-76ER03077
- OSTI ID:
- 6431208
- Report Number(s):
- DOE/ER/03077-228; ON: DE85003136
- Country of Publication:
- United States
- Language:
- English
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