A unified consistent source term computational algorithm for the γ-based compressible multi-fluid flow model

Li Ge, Li Libin, Liu Qingquan, Feng Chun, Wang Xiaoliang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Using the criterion of one-fluid preservation, we developed a consistent algorithm for the source term to solve the γ-based compressible multi-fluid flow model with three approximate Riemann solvers, namely the Lax–Friedrichs (LxF), Kurganov, and Harten–Lax–van Leer contact (HLLC) solvers. The consistent algorithm comprises a standard Godunov solver with a high-order reconstruction and a consistent source term integration part. We prove that the present algorithm is consistent with Abgrall's criterion of the moving-material-interface property in the finite volume method framework. The cell boundary velocity for the source term discretization is found to be the same as HLLC solvers from five-equation model, but for the first time for LxF and Kurganov Riemann solvers. We develop 12 compressible multi-fluid solvers by combining four reconstruction schemes and three approximate Riemann solvers together with their consistent-source-term integration algorithms. All 12 solvers can maintain the one-fluid preservation and moving-material-interface properties numerically in several one- and two-dimensional example cases. The simulation of an underwater explosion demonstrates that a boundary-variation-diminishing reconstruction predicts an interface with width controlled within approximately three cells which is independent of the Riemann solver. The simulation of an explosion near a free surface demonstrates that the proposed model can simulate a severe compressible multi-fluid flow involving an interface across which there are large differences in density, pressure and parameters in the equation of state. In conclusion, the proposed consistent algorithm provides a unified framework for one kind of non-conservative hyperbolic system into a conservative hyperbolic system and a source term with velocity divergence, where the former can be computed by classical Godunov-type algorithms and the latter can be solved by the proposed consistent algorithm.

Original languageEnglish
Article number105899
JournalComputers and Fluids
Volume259
DOIs
Publication statusPublished - 15 Jun 2023

Keywords

  • Compressible multi-fluid flow
  • Consistent algorithm
  • Interface sharpening
  • Moving interface
  • One-fluid preservation

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Ge, L., Libin, L., Qingquan, L., Chun, F., & Xiaoliang, W. (2023). A unified consistent source term computational algorithm for the γ-based compressible multi-fluid flow model. Computers and Fluids, 259, Article 105899. https://doi.org/10.1016/j.compfluid.2023.105899