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

• Main Authors: Friess, Marie Billaud, Kokh, Samuel
• Format: Journal Article
• Language: English
• Published: 25-03-2014
• Subjects: Mathematics - Numerical Analysis
• DOI: 10.48550/arxiv.1307.8375

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.