A totally Eulerian Finite Volume solver for multi-material fluid flows: Enhanced Natural Interface Positioning (ENIP)

TL;DR

This paper introduces the Enhanced-NIP method, improving the accuracy and stability of multi-material fluid flow simulations by refining interface reconstruction in a totally Eulerian finite volume framework.

Contribution

The paper presents a novel Enhanced-NIP method that corrects inconsistencies in previous interface reconstruction techniques, leading to better shape conservation and stability.

Findings

Improved interface shape conservation in multi-material flows.

Enhanced stability and accuracy in linear advection tests.

Successful application to compressible Euler equations.

Abstract

This work concerns the simulation of compressible multi-material fluid flows and follows the method FVCF-NIP described in the former paper Braeunig et al (Eur. J. Mech. B/Fluids, 2009). This Cell-centered Finite Volume method is totally Eulerian since the mesh is not moving and a sharp interface, separating two materials, evolves through the grid. A sliding boundary condition is enforced at the interface and mass, momentum and total energy are conserved. Although this former method performs well on 1D test cases, the interface reconstruction suffers of poor accuracy in conserving shapes for instance in linear advection. This situation leads to spurious instabilities of the interface. The method Enhanced-NIP presented in the present paper cures an inconsistency in the former NIP method that improves strikingly the results. It takes advantage of a more consistent description of the interface in the numerical scheme. Results for linear advection and compressible Euler equations for inviscid fluids are presented to assess the benefits of this new method.