An exactly curl-free finite-volume scheme for a hyperbolic compressible barotropic two-phase model
CoRR(2024)
摘要
We present a new second order accurate structure-preserving finite volume
scheme for the solution of the compressible barotropic two-phase model of
Romenski et. al in multiple space dimensions. The governing equations fall into
the wider class of symmetric hyperbolic and thermodynamically compatible (SHTC)
systems and consist of a set of first-order hyperbolic partial differential
equations (PDE). In the absence of algebraic source terms, the model is subject
to a curl-free constraint for the relative velocity between the two phases. The
main objective of this paper is, therefore, to preserve this structural
property exactly also at the discrete level. The new numerical method is based
on a staggered grid arrangement where the relative velocity field is stored in
the cell vertexes while all the remaining variables are stored in the cell
centers. This allows the definition of discretely compatible gradient and curl
operators, which ensure that the discrete curl errors of the relative velocity
field remain zero up to machine precision. A set of numerical results confirms
this property also experimentally.
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