A sharp-interface discontinuous Galerkin method for simulation of two-phase flow of real gases based on implicit shock tracking

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Hauptverfasser: Naudet, Charles, Taylor, Brian, Zahr, Matthew J.
Format: Preprint
Veröffentlicht: 2025
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author Naudet, Charles
Taylor, Brian
Zahr, Matthew J.
author_facet Naudet, Charles
Taylor, Brian
Zahr, Matthew J.
contents We present a high-order, sharp-interface method for simulation of two-phase flow of real gases using implicit shock tracking. The method is based on a phase-field formulation of two-phase, compressible, inviscid flow with a trivial mixture model. Implicit shock tracking is a high-order, optimization-based discontinuous Galerkin method that automatically aligns mesh faces with non-smooth flow features to represent them perfectly with inter-element jumps. It is used to accurately approximate shocks and rarefactions without stabilization and converge the phase-field solution to a sharp interface one by aligning mesh faces with the material interface. Time-dependent problems are formulated as steady problems in a space-time domain where complex wave interactions (e.g., intersections and reflections) manifest as space-time triplet points. The space-time formulation avoids complex re-meshing and solution transfer that would be required to track moving waves with mesh faces using the method of lines. The approach is applied to several two-phase flow Riemann problems involving gases with ideal, stiffened gas, and Becker-Kistiakowsky-Wilson (BKW) equations of state, including a spherically symmetric underwater explosion problem. In all cases, the method aligns element faces with all shocks (including secondary shocks that form at time t > 0), rarefactions, and material interfaces, and accurately resolves the flow field on coarse space-time grids.
format Preprint
id arxiv_https___arxiv_org_abs_2503_05557
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A sharp-interface discontinuous Galerkin method for simulation of two-phase flow of real gases based on implicit shock tracking
Naudet, Charles
Taylor, Brian
Zahr, Matthew J.
Fluid Dynamics
Numerical Analysis
Computational Physics
We present a high-order, sharp-interface method for simulation of two-phase flow of real gases using implicit shock tracking. The method is based on a phase-field formulation of two-phase, compressible, inviscid flow with a trivial mixture model. Implicit shock tracking is a high-order, optimization-based discontinuous Galerkin method that automatically aligns mesh faces with non-smooth flow features to represent them perfectly with inter-element jumps. It is used to accurately approximate shocks and rarefactions without stabilization and converge the phase-field solution to a sharp interface one by aligning mesh faces with the material interface. Time-dependent problems are formulated as steady problems in a space-time domain where complex wave interactions (e.g., intersections and reflections) manifest as space-time triplet points. The space-time formulation avoids complex re-meshing and solution transfer that would be required to track moving waves with mesh faces using the method of lines. The approach is applied to several two-phase flow Riemann problems involving gases with ideal, stiffened gas, and Becker-Kistiakowsky-Wilson (BKW) equations of state, including a spherically symmetric underwater explosion problem. In all cases, the method aligns element faces with all shocks (including secondary shocks that form at time t > 0), rarefactions, and material interfaces, and accurately resolves the flow field on coarse space-time grids.
title A sharp-interface discontinuous Galerkin method for simulation of two-phase flow of real gases based on implicit shock tracking
topic Fluid Dynamics
Numerical Analysis
Computational Physics
url https://arxiv.org/abs/2503.05557