界面捕捉方法的不连续伽辽金方法的一种新表述

中文摘要 AI 辅助

在计算流体动力学中，使用界面捕捉方法（水平集、伪浓度）对自由表面流动进行数值模拟需要精确求解输运方程。在本工作中，该方程采用Lesaint--Raviart不连续伽辽金方法的一种新表述来求解，该方法特别适用于无流入边界的问题。运动由带表面张力的不可压缩Navier--Stokes方程描述，空间上采用标准$P2-P1$ Taylor--Hood有限元方法离散。表面张力效应采用所谓的连续表面力模型表示。最后，所提出的方法在多个基准测试中进行了实现和验证，包括单个上升气泡和Rayleigh--Taylor不稳定性。

英文摘要

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.

发表机构

• Ibn Zohr University（伊本·佐赫尔大学）
• Léonard de Vinci Pôle Universitaire, Research Center（莱昂纳多·达·芬奇大学研究中心）

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