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arXiv · 1908.07392

A Fast Integral Equation Method for the Two-Dimensional Navier-Stokes Equations

Ludvig af Klinteberg·Travis Askham·Mary Catherine Kropinski
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Abstract

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.

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BibTeXRIS

Ludvig af Klinteberg, Travis Askham, Mary Catherine Kropinski. 2019-08-20. A Fast Integral Equation Method for the Two-Dimensional Navier-Stokes Equations. https://doi.org/10.1016/j.jcp.2020.109353

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