Abstract
This paper presents an all-Mach method for two-phase inviscid flow in the presence of surface tension. A modified version of the Hartens–Lax–van Leer Contact (HLLC) solver is developed and combined for the first time with a widely used volume-of-fluid (VoF) method: the compressive interface capturing scheme for arbitrary meshes (CICSAM). This novel combination yields a scheme with both HLLC shock capturing as well as accurate liquid–gas interface tracking characteristics. It is achieved by reconstructing non-conservative (primitive) variables in a consistent manner to yield both robustness and accuracy. Liquid–gas interface curvature is computed via height functions and the convolution method. We emphasize the use of VoF in the interest of interface accuracy when modelling surface tension effects. The method is validated using a range of test-cases available in the literature. The results show flow features that are in sensible agreement with previous experimental and numerical work. In particular, the use of the HLLC-VoF combination leads to a sharp volume fraction and energy field with improved accuracy.
Highlights
High-speed multi-phase compressible flow induced by blast or shock waves is of interest to both basic science and engineering [1,2,3,4,5,6,7,8]
This approach was first proposed by Garrick et al [1], where Hartens–Lax–van Leer Contact (HLLC) was re-formulated to allow for surface tension effects
Fuster et al [12] successfully extended the unified semi-implicit compressible solver proposed by Xiao et al [32] and combined their formulation with a geometric VoF method [36] to allow for the inclusion of surface tension effects
Summary
High-speed multi-phase compressible flow induced by blast or shock waves is of interest to both basic science and engineering [1,2,3,4,5,6,7,8]. Subsequent work on HLLC includes the use of a compression technique to remove numerical diffusion present at the interface This approach was first proposed by Garrick et al [1], where HLLC was re-formulated to allow for surface tension effects. Their method does not take into account the liquid availability criteria [34] when advecting the interface. Fuster et al [12] successfully extended the unified semi-implicit compressible solver proposed by Xiao et al [32] and combined their formulation with a geometric VoF method [36] to allow for the inclusion of surface tension effects. The developed solver is rigorously assessed via application to a range of benchmark test-cases from 1-D to 2-D
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