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

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 compressible components. Our work is two-fold: 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 pressure equilibrium closure law is used to complete this new model. The resulting model is demonstrated to be hyperbolic under simple assumptions and consistent. 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 consistency and stability properties but also 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 discretization preserves Riemann invariants like pressure and velocity at the interfaces. 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 with the upwind Lagrange-Remap scheme.

Development of numerical methods to simulate the melting of a thermal protection system

“…This anti-diffusive approach has been extended to the five-equation model (without dissipative effects) by Kokh and Lagoutière [KL10] using a fully explicit Lagrange-Projection scheme. An extension to multi-phase flow has also been done by [FK14]. To completely avoid numerical diffusion of the material interface, another approach is to use Glimm's scheme [Gli65].…”

Sharpening Methods for Finite Volume Schemes

“…This technique was incorporated in FV algorithms for the simulation of twocomponent fluid flows, for the mass fraction, volume fraction, or color function of components, in, e.g., [DL07], [KL10], and extended to multi-component in [JL07] and [BFK14].…”

“…This technique was incorporated in FV algorithms for the simulation of twocomponent fluid flows, for the mass fraction, volume fraction, or color function of components, in, e.g., [DL07], [KL10], and extended to multi-component in [JL07] and [BFK14]. This was also modified to apply to non-linear discontinuities such as classical shocks, in [AC16], and non-classical shocks in the scalar context, [BCLL08], and in the context of systems in [Agu16].…”

“…It is not possible to give an exhaustive list of all possible sharpening techniques implementation, we will try to give hereafter an overview of the works that have been achieved the past years that is inevitably incomplete. The approach of section 3.1 has been successfully extended to other systems like the five-equation model of [MSNA02,ACK02] in [KL10] and also for compressibles flows involving an arbitrary number of components separated by interfaces [JL07,BFK14]. Other techniques may be used to sharpen front in systems with interface.…”