An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model

• Published in: Journal of computational physics Vol. 229; no. 8; pp. 2773 - 2809
• Main Authors: Kokh, S., Lagoutière, F.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 20-04-2010; Elsevier
• Subjects: Compressible flows; Compressible fluids; Computational techniques; Computer simulation; Discretization; Exact sciences and technology; Interface problems; Invariants; Laws; Mathematical methods in physics; Mathematical models; Mathematics; Multi-component flows; Numerical Analysis; Numerical diffusion; Physics; Real fluids; Reconstruction; Solvers; Numerical diffusion; Multi-component flows; Real fluids; Compressible flows; Interface problems; Invariant; Total energy; Consistency; Numerical method; Discretization method; Calculation methods; Equations of state; Models; Calculation; Diffusion; Approximate solution; Compressible flow; anti-diffusive scheme Contents; interface problems; two-phase flows
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2009.12.003

We propose a discretization method of a five-equation model with isobaric closure for the simulation of interfaces between compressible fluids. This numerical solver is a Lagrange–Remap scheme that aims at controlling the numerical diffusion of the interface between both fluids. This method does not involve any interface reconstruction procedure. The solver is equipped with built-in stability and consistency properties and is conservative with respect to mass, momentum, total energy and partial masses. This numerical scheme works with a very broad range of equations of state, including tabulated laws. Properties that ensure a good treatment of the Riemann invariants across the interface are proven. As a consequence, the numerical method does not create spurious pressure oscillations at the interface. We show one-dimensional and two-dimensional classic numerical tests. The results are compared with the approximate solutions obtained with the classic upwind Lagrange–Remap approach, and with experimental and previously published results of a reference test case.