A Lagrangian-Eulerian Volume-Tracking with Linearity-Preserving Interface Reconstruction

Abstract

This article presents a linearity-preserving volume-tracking algorithm for two-phase flow based on volume fraction remapping. The approach followed here does not deal with edge flux and corner flux computation or with corner flux correction typical of unsplit Eulerian advection. The method discussed is a Lagrangian-Eulerian advection scheme (LEAS) which is CFL condition-independent, in contrast to most of the unsplit Eulerian advection algorithms. Also, the scheme is equally applicable on general polygonal grids. The method works on the assumption that fluid content remains constant inside a stream tube generated between a Eulerian cell and a Lagrangian precell. The Lagrangian precell is obtained by back tracking of cell vertices in time. Volume fraction remapping is performed by a series of polygon intersections between a Lagrangian precell and vertex-connected neighbor cell fluid polygons. The fluid polygons are obtained from interface reconstruction. The volume fraction inconsistencies are removed by a conservative volume-fraction repair algorithm. Since interface reconstruction is also an integral part of the overall volume tracking algorithm, details of the same are presented for the sake of completeness. Overall volume tracking error is due solely to approximate interface reconstruction, while the scheme is derived naturally from the fact that volume inside a stream tube remains constant. LEAS performs better compared to the existing unsplit algorithms for the same interface reconstruction.