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

Resource type
Date created
2020-02-24
Authors/Contributors
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.
Description
The full text of this paper will be available in February 2022 due to the embargo policies of Journal of Computational Physics. Contact summit@sfu.ca to enquire if the full text of the accepted manuscript can be made available to you.
Published as
L. af Klinteberg, T. Askham, M.C. Kropinski, A fast integral equation method for the two-dimensional Navier-Stokes equations, J. Comput. Phys. (2020), DOI: 10.1016/j.jcp.2020.109353.
Publication details
Publication title
J. Comput. Phys.
Document title
A Fast Integral Equation Method for the Two-dimensional Navier-Stokes Equations
Date
2020
Copyright statement
Copyright is held by the author(s).
Scholarly level
Peer reviewed?
Yes
Language
Member of collection