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

Peer reviewed: 
Yes, item is peer reviewed.
Scholarly level: 
Final version 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.

Date created: 
Navier-Stokes equations
Integral equations
Function extension

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.


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.

Document type: