A meshfree Lagrangian method for flow on manifolds,International Journal for Numerical Methods in Fluids

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A meshfree Lagrangian method for flow on manifolds
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-01-12 , DOI: 10.1002/fld.4957
Pratik Suchde ₁

Affiliation

In this article, we present a novel meshfree framework for fluid flow simulations on arbitrarily curved surfaces. First, we introduce a new meshfree Lagrangian framework to model flow on surfaces. Meshfree points or particles, which are used to discretize the domain, move in a Lagrangian sense along the given surface. This is done without discretizing the bulk around the surface, without parametrizing the surface, and without a background mesh. A key novelty that is introduced is the handling of flow with evolving free boundaries on a curved surface. The use of this framework to model flow on moving and deforming surfaces is also introduced. Then, we present the application of this framework to solve fluid flow problems defined on surfaces numerically. In combination with a meshfree generalized finite difference method (GFDM), we introduce a strong form meshfree collocation scheme to solve the Navier–Stokes equations posed on manifolds. Benchmark examples are proposed to validate the Lagrangian framework and the surface Navier–Stokes equations with the presence of free boundaries.

中文翻译：

歧管上流动的无网格拉格朗日方法

在本文中，我们提出了一种新颖的无网格框架，用于任意弯曲表面上的流体流动模拟。首先，我们引入一个新的无网格拉格朗日框架来模拟表面上的流动。用于使域离散化的无网格点或粒子沿拉格朗日意义沿给定表面移动。这样做时不会使表面周围的体积离散，不使表面参数化并且没有背景网格。引入的一个关键新颖之处是处理曲面上自由边界不断变化的流。还介绍了使用此框架对移动和变形表面上的流动进行建模的方法。然后，我们介绍该框架的应用，以解决数值上定义的流体流动问题。结合无网格广义有限差分法（GFDM），我们引入了一种强形式的无网格搭配方案来求解流形上的Navier-Stokes方程。提出了基准示例，以验证存在自由边界的Lagrangian框架和表面Navier-Stokes方程。

更新日期：2021-01-12

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