A unified consistent source term computational algorithm for the γ-based compressible multi-fluid flow model. (15th June 2023)

• Record Type: Journal Article
• Authors: Ge, Li; Libin, Li; Qingquan, Liu; Chun, Feng; Xiaoliang, Wang
• Is Part Of: Computers & fluids. Volume 259(2023)
• Publication Date: 2023-06-15
• Subjects: Compressible multi-fluid flow -- Consistent algorithm -- One-fluid preservation -- Moving interface -- Interface sharpening; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2023.105899
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: A unified consistent algorithm proposed for γ -based compressible multi-fluid model. Equivalence prove for one-fluid preservation and moving material criteria in FVM. Demonstrations of abilities of simulating severe compressible multifluid flow. 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.