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

TL;DR

This paper introduces a generalized multi-material flow model and an anti-diffusive numerical scheme for simulating complex interface flows involving multiple components on Cartesian grids, ensuring accuracy and stability.

Contribution

It presents a novel hyperbolic multi-component flow model and a stable, anti-dissipative discretization strategy that maintains interface sharpness and physical invariants.

Findings

Model is hyperbolic and consistent under simple assumptions.

The scheme preserves the sum of color functions and Riemann invariants.

Validation shows improved interface sharpness compared to traditional methods.

Abstract

In this paper, we present an anti-diffusive method dedicated to the simulation of interface flows on Cartesian grids involving an arbitrary number m of compress- ible components. Our work is two folds. First, we introduce a m-component flow model that generalizes a classic two material five-equation model. In that way, interfaces are localized thanks to color function discontinuities and a pres- sure equilibrium closure law is used to complete this new model. The resulting model is demonstrated to be hyperbolic under simple assumptions and consis- tent. Second, we present a discretization strategy for this model relying on an Lagrange-Remap scheme. Here, the projection step involves an anti-dissipative mechanism allowing to prevent numerical diffusion of the material interfaces. The proposed solver is built ensuring in one hand consistency and stability properties and in other hand that the sum of the color functions remains equal to one. The resulting scheme is first order accurate and conservative for the mass, momentum, energy and partial masses. Furthermore, the obtained dis- cretization preserves Riemann invariants as pressure and velocity at the inter- faces. Finally, validation computations of this numerical method are performed on several tests in one and two dimensions. The accuracy of the method is also compared to results obtained by the upwind Lagrange-Remap scheme.