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

Abstract

This work concerns the simulation of compressible multi-material fluid flows and follows the method FVCF-NIP described in the former paper [5].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.

A new algorithm for surface tension forces in the framework of the FVCF–ENIP method

“…In this section, we recall the derivation of the FVCF-ENIP numerical scheme for multimaterial compressible flows as given in [12,13]. Once again, we aim at giving a concise, nevertheless sufficient, description of its main features.…”

“…The FVCF-ENIP method is a multidimensional (2D [12,13], 3D [24]), multimaterial solver with sharp interface reconstruction.…”

“…The numerical context is the following. The Finite Volume with Characteristic fluxes-Enhanced Natural Interface Positioning method (FVCF-ENIP in the following) [12,13] was developed to simulate non-miscible multimaterial compressible flows. It hybridizes both Eulerian and Lagrangian approaches providing a very robust numerical scheme, on one hand, and on the other hand a precise and explicit treatment of material interfaces.…”

An Eulerian finite volume solver for multi-material fluid flows with cylindrical symmetry

“…3.1. Study of the precision of the scheme has already been done for the 2D version and can be found in previous articles [5,3,9].…”

“…Results are obtained with the Enhanced-NIP (ENIP) method( [9]), which cures an inconsistency in the former method NIP [4], and shows good results.…”