SIAM Journal on Scientific Computing · 1998 · 584 citations · 11 references
Natural SciencesMathematicsPhysicsComputational Fluid DynamicsDynamical SystemsFluid DynamicsBoundary ConditionsContinuity EquationHyperbolic DynamicsPartial Differential EquationsConservation LawsGas DynamicsHyperbolic Partial Differential EquationsRiemann - Hilbert ProblemsRiemann ProblemsRiemann SolversRiemann-hilbert Problems
The positivity principle and positive schemes to solve multidimensional hyperbolic systems of conservation laws have been introduced in [X.-D. Liu and P. D. Lax, J. Fluid Dynam., 5 (1996), pp. 133--156]. Some numerical experiments presented there show how well the method works. In this paper we use positive schemes to solve Riemann problems for two-dimensional gas dynamics.
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