论文标题
歧管上流量的网状拉格朗日方法
A Meshfree Lagrangian Method for Flow on Manifolds
论文作者
论文摘要
在本文中，我们提出了一个新型的无网格框架，用于任意弯曲表面上的流体流量模拟。首先，我们引入了一个新的网状拉格朗日框架，以在表面上进行模型。用于离散域的网格点或颗粒，以拉格朗日的意义沿给定表面移动。这是在不离散表面周围的大块的情况下完成的，而无需参数表面，而没有背景网格。引入的关键新颖性是处理流动，并在弯曲表面上不断发展的自由边界。还介绍了该框架在移动和变形表面上模拟流程的使用。然后，我们介绍该框架的应用来解决在数值上定义的流体流问题。结合无网状的一般有限差异方法（GFDM），我们引入了强烈的网格搭配方案，以求解在歧管上构成的Navier-Stokes方程。提出了基准示例来验证Lagrangian框架和具有自由边界的表面Navier-Stokes方程。
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.
