An energy stable incompressible multi-phase flow formulation

Jan Nordström; Arnaud G. Malan

doi:10.1016/j.jcp.2024.113685

An energy stable incompressible multi-phase flow formulation

Jan Nordström, Arnaud G. Malan

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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. New nonlinear inflow-outflow and solid wall boundary conditions bound the energy rate and lead to an energy estimate in terms of only external data. The new formulation combines perfectly with summation-by-parts operators and leads to provable energy stability.

Original language	English
Article number	113685
Journal	Journal of Computational Physics
Volume	523
DOIs	https://doi.org/10.1016/j.jcp.2024.113685
Publication status	Published - 15 Feb 2025

Keywords

Boundary conditions
Energy stability
Multi-phase flow
Summation-by-parts
Volume of fluid

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2024.113685

Cite this

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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. New nonlinear inflow-outflow and solid wall boundary conditions bound the energy rate and lead to an energy estimate in terms of only external data. The new formulation combines perfectly with summation-by-parts operators and leads to provable energy stability.",

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AU - Malan, Arnaud G.

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AB - 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. New nonlinear inflow-outflow and solid wall boundary conditions bound the energy rate and lead to an energy estimate in terms of only external data. The new formulation combines perfectly with summation-by-parts operators and leads to provable energy stability.

KW - Boundary conditions

KW - Energy stability

KW - Multi-phase flow

KW - Summation-by-parts

KW - Volume of fluid

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JO - Journal of Computational Physics

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ER -

An energy stable incompressible multi-phase flow formulation

Abstract

Keywords

ASJC Scopus subject areas

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