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首页> 外文期刊>Journal of Computational Physics >A fast integral equation method for the two-dimensional Navier-Stokes equations
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A fast integral equation method for the two-dimensional Navier-Stokes equations

机译：二维Navier-Stokes方程的快速积分方程方法

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摘要

The integral equation approach to partial differential equations (PDEs) provides significant advantages in the numerical solution of the incompressible Navier-Stokes equations. In particular, the divergence-free condition and boundary conditions are handled naturally, and the ill-conditioning caused by high order terms in the PDE is preconditioned analytically. Despite these advantages, the adoption of integral equation methods has been slow due to a number of difficulties in their implementation. This work describes a complete integral equation-based flow solver that builds on recently developed methods for singular quadrature and the solution of PDEs on complex domains, in combination with several more well-established numerical methods. We apply this solver to flow problems on a number of geometries, both simple and challenging, studying its convergence properties and computational performance. This serves as a demonstration that it is now relatively straightforward to develop a robust, efficient, and flexible Navier-Stokes solver, using integral equation methods. (C) 2020 Elsevier Inc. All rights reserved.
机译：部分微分方程（PDE）的整体方程方法在不可压缩的Navier-Stokes方程的数值解中提供了显着的优点。特别地，自然地处理了无分歧条件和边界条件，并且在PDE中由高阶项引起的不良调节被分析地预处理。尽管有这些优势，但由于其实施的许多困难，整体方程方法的采用缓慢。这项工作描述了一种完整的整体式基于方程式的流动求解器，其在最近开发的奇异正交和PDES在复杂结构域的溶液中构建，与几种更良好的数值方法相结合。我们将该求解器应用于许多几何形状上的问题，既简单又具有挑战性，研究其收敛性和计算性能。这是使用整体方程方法开发强大，高效和灵活的Navier-Stokes求解器的演示。 （c）2020 Elsevier Inc.保留所有权利。

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