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High-order energy diminishing ALE-SAV finite element methods for two-phase Navier--Stokes flow
Abstract
We develop a high-order fully discrete ALE-SAV finite element method for sharp-interface two-phase Navier--Stokes flow that satisfies a discrete energy dissipation law. We introduce an SAV reformulation to ensure the stable treatment of the surface and gravitational potential energies, together with an energy-stable ALE transfer operator that controls the density-weighted kinetic energy across moving meshes. The resulting scheme is linear and satisfies a modified energy-dissipation inequality. Numerical experiments, including rising-bubble benchmarks, demonstrate the robustness of the method and confirm second-order convergence in time and arbitrarily high-order convergence in space.
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BibTeX
@misc{ma2026highorder,
title = {{High-order energy diminishing ALE-SAV finite element methods for two-phase Navier--Stokes flow}},
author = {Shu Ma},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35590},
eprint = {2609.35590},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35590},
}
RIS
TY - UNPB
TI - High-order energy diminishing ALE-SAV finite element methods for two-phase Navier--Stokes flow
AU - Shu Ma
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35590
UR - https://arxiv.org/abs/2609.35590
AB - We develop a high-order fully discrete ALE-SAV finite element method for sharp-interface two-phase Navier--Stokes flow that satisfies a discrete energy dissipation law. We introduce an SAV reformulation to ensure the stable treatment of the surface and gravitational potential energies, together with an energy-stable ALE transfer operator that controls the density-weighted kinetic energy across moving meshes. The resulting scheme is linear and satisfies a modified energy-dissipation inequality. Numerical experiments, including rising-bubble benchmarks, demonstrate the robustness of the method and confirm second-order convergence in time and arbitrarily high-order convergence in space.
ER -