流形上流动的无网格Lagrange方法
A Meshfree Lagrangian Method for Flow on Manifolds
摘要：
在本文中，我们提出了一种新的无网格框架的任意曲面上的流体流动模拟。首先，我们引入了一个新的无网格拉格朗日框架来模拟表面上的流动。用于离散域的无网格点或粒子沿给定表面以拉格朗日意义移动。这是在不离散曲面周围的体积、不参数化曲面和不使用背景网格的情况下完成的。一个关键的新颖之处，介绍了不断发展的自由边界的曲面上的流动的处理。使用这个框架来模拟流动的移动和变形的表面也被介绍。然后，我们提出的应用程序，这个框架来解决流体流动问题的表面数值定义。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配置格式来求解流形上的Navier-斯托克斯方程.基准例子提出了验证拉格朗日框架和表面Navier-斯托克斯方程与存在的自由边界。
英文摘要：
In this paper, 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.
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