Relaxation of the Navier-Stokes-Korteweg equations for compressible two-phase flow with phase transition. (English) Zbl 1455.65176
Summary: The Navier-Stokes-Korteweg (NSK) system is a classical diffuse-interface model for compressible two-phase flow. However, the direct numerical simulation based on the NSK system is quite expensive and in some cases even not possible. We propose a lower-order relaxation of the NSK system with hyperbolic first-order part. This allows applying numerical methods for hyperbolic conservation laws and removing some of the difficulties of the original NSK system. To illustrate the new ansatz, we first present a local discontinuous Galerkin method in one and two spatial dimensions. It is shown that we can compute initial boundary value problems with realistic density ratios and perform stable computations for small interfacial widths. Second, we show that it is possible to construct a semi-discrete finite-volume scheme that satisfies a discrete entropy inequality.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
Keywords:
diffuse-interface model; compressible flow with phase transition; discrete thermodynamical consistencyReferences:
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