An Energy Stable Nonlinear Incompressible Multi-Phase Flow Formulation
Analysis of PDEs
2024-12-31 v2 Numerical Analysis
Numerical Analysis
Abstract
We show that a reformulation of the governing equations for incompressible multi-phase flow in the volume of fluid setting leads to a well defined energy rate. Weak nonlinear inflow-outflow and solid wall boundary conditions complement the development and lead to an energy estimate in terms of external data. The new formulation combined with summation-by-parts operators lead to provably nonlinear energy stability.
Cite
@article{arxiv.2406.19525,
title = {An Energy Stable Nonlinear Incompressible Multi-Phase Flow Formulation},
author = {Jan Nordström and Arnaud. G. Malan},
journal= {arXiv preprint arXiv:2406.19525},
year = {2024}
}