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arXiv · 2609.07327

A new formulation of Discontinuous Galerkin method for interface capturing approaches

W. Herri·K. Benmoussa·R. Bouydou·D. Yakoubi
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Abstract

In computational fluid dynamics, the numerical simulation of free-surface flows using interface capturing approaches (level set, pseudo-concentration) requires accurate resolution of a transport equation. In the present work, this equation is solved using a new formulation of the Lesaint--Raviart discontinuous Galerkin method, which is particularly suitable for problems without inflow boundaries. The motion is described by the incompressible Navier--Stokes equations with surface tension, discretized using the standard $P2-P1$ Taylor--Hood finite element method in space. Surface tension effects are represented using the so-called Continuum Surface Force model. Finally, the proposed approach is implemented and tested on several benchmarks, including the single rising bubble and the Rayleigh--Taylor instability.

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W. Herri, K. Benmoussa, R. Bouydou, D. Yakoubi. 2026-09-07. A new formulation of Discontinuous Galerkin method for interface capturing approaches. https://arxiv.org/abs/2609.07327

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