A mass‐fraction‐based interface‐capturing method for multi‐component flow

Abstract

SUMMARYAn interface‐capturing method based on mass fraction is developed to solve the Riemann problem in multi‐component compressible flow. Equations of mass fraction with modified form, which is derived from conservative equations of mass, are employed here to capture the interface. By introducing mass fraction into Euler equations system, as well as other conservative coefficients, a quasi‐conservative numerical model is created. Numerical examples show that the mass fraction model performs well not only in multi‐component fluids modeled by simple stiffened gas equation of state (EOS) but also in that modeled by complex Mie–Grüneisen EOS. Moreover, the mass fraction model is applied to Riemann problem with piecewise EOS; the expression of which depends on density. It is found that the mass fraction model can well adapt to the analytic change in piecewise EOS and produce accuracy solutions with fewer unknown quantities, and the model can be easily extended to m‐component fluid mixture by using only m + 4 equations with no additional conditions. Copyright © 2013 John Wiley & Sons, Ltd.

Simulation of sharp interface multi-material flows involving an arbitrary number of components through an extended five-equation model

“…In this framework, although the diffused interfaces remain a priori not physically relevant, they are consistent (up to a numerical truncation error) with the target sharp discontinuities. This approach belong to a family of methods that was popularized through several publications in the past years in [1,2,3,4,38,39,46,53,54,59,60,61,63,68]. Concerning the control of the numerical diffusion produced at the material fronts, a special Lagrange-Remap method was proposed in [41] that spares the difficulty of interfaces reconstruction.…”