Slip Wall Boundary Conditions in Curved Domains for Finite Element ALE Hydrodynamics
Abstract
We present a high-order finite element arbitrary Lagrangian-Eulerian (ALE) method for hydrodynamics with slip-wall boundary conditions on analytically curved domains. The method combines distinct Lagrangian, remesh, and remap phases while preserving the geometric features of curved boundaries and allowing tangential motion of boundary nodes. In the Lagrangian phase, we use weak boundary condition enforcement to impose the slip-wall condition without freezing tangential motion. In the mesh optimization phase, we adapt TMOP (target-matrix optimization paradigm) to analytic walls by replacing selected boundary coordinate degrees of freedom with curve or surface parameters. The Newton solve then moves boundary nodes tangentially with respect to the prescribed geometry while carrying the drift introduced by the Lagrangian phase. In the remap phase, we transfer the solution from the old mesh to the optimized mesh by a conservative advection-based remap over pseudo-time. We present numerical results in two and three dimensions demonstrating the method on high-order curved meshes and showing that it preserves boundary fidelity while producing the expected hydrodynamic solution features.
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BibTeX
@misc{atallah2026slip,
title = {{Slip Wall Boundary Conditions in Curved Domains for Finite Element ALE Hydrodynamics}},
author = {Nabil Atallah and Kevin Sweet and Paul Moujaes and Jan Nikl and Ketan Mittal and Vladimir Z. Tomov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36053},
eprint = {2609.36053},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36053},
}
RIS
TY - UNPB
TI - Slip Wall Boundary Conditions in Curved Domains for Finite Element ALE Hydrodynamics
AU - Nabil Atallah
AU - Kevin Sweet
AU - Paul Moujaes
AU - Jan Nikl
AU - Ketan Mittal
AU - Vladimir Z. Tomov
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36053
UR - https://arxiv.org/abs/2609.36053
AB - We present a high-order finite element arbitrary Lagrangian-Eulerian (ALE) method for hydrodynamics with slip-wall boundary conditions on analytically curved domains. The method combines distinct Lagrangian, remesh, and remap phases while preserving the geometric features of curved boundaries and allowing tangential motion of boundary nodes. In the Lagrangian phase, we use weak boundary condition enforcement to impose the slip-wall condition without freezing tangential motion. In the mesh optimization phase, we adapt TMOP (target-matrix optimization paradigm) to analytic walls by replacing selected boundary coordinate degrees of freedom with curve or surface parameters. The Newton solve then moves boundary nodes tangentially with respect to the prescribed geometry while carrying the drift introduced by the Lagrangian phase. In the remap phase, we transfer the solution from the old mesh to the optimized mesh by a conservative advection-based remap over pseudo-time. We present numerical results in two and three dimensions demonstrating the method on high-order curved meshes and showing that it preserves boundary fidelity while producing the expected hydrodynamic solution features.
ER -