H. Shen, C.Y. Wen, M. Parsani, C.W. Shu
Journal of Computational Physics, (2016)
Maximum-principle-satisfying scheme; Space-time conservation element and solution element (CE/SE) method; Upwind scheme; Compressible multifluids; Five-equation model
A maximum-principle-satisfying space-time conservation element and
solution element (CE/SE) scheme is constructed to solve a reduced
five-equation model coupled with the stiffened equation of state for
compressible multifluids. We first derive a sufficient condition for
CE/SE schemes to satisfy maximum-principle when solving a general
conservation law. And then we introduce a slope limiter to ensure the
sufficient condition which is applicative for both central and upwind
CE/SE schemes. Finally, we implement the upwind
maximum-principle-satisfying CE/SE scheme to solve the
volume-fraction-based five-equation model for compressible multifluids.
Several numerical examples are carried out to carefully examine the
accuracy, efficiency, conservativeness and maximum-principle-satisfying
property of the proposed approach.