TY - JOUR
T1 - A fast integral equation method for the two-dimensional Navier-Stokes equations
AU - af Klinteberg, Ludvig
AU - Askham, Travis
AU - Kropinski, Mary Catherine
N1 - Funding Information:
The authors gratefully acknowledge support from the Knut and Alice Wallenberg Foundation under grant 2016.0410 (LaK), from the Air Force Office of Scientific Research under grant FA9550-17-1-0329 (TA), and from the Natural Science and Engineering Research Council of Canada under grant RGPIN-03576 (MCK). We also wish to thank Adrianna Gillman for providing us with an implementation of a fast direct solver, and Fredrik Fryklund for providing us with an implementation of PUX.
Funding Information:
The authors gratefully acknowledge support from the Knut and Alice Wallenberg Foundation under grant 2016.0410 (LaK), from the Air Force Office of Scientific Research under grant FA9550-17-1-0329 (TA), and from the Natural Science and Engineering Research Council of Canada under grant RGPIN-03576 (MCK). We also wish to thank Adrianna Gillman for providing us with an implementation of a fast direct solver, and Fredrik Fryklund for providing us with an implementation of PUX.
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/5/15
Y1 - 2020/5/15
N2 - 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.
AB - 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.
KW - Function extension
KW - Integral equations
KW - Navier-Stokes equations
KW - Quadrature
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U2 - 10.1016/j.jcp.2020.109353
DO - 10.1016/j.jcp.2020.109353
M3 - Article
AN - SCOPUS:85080100753
SN - 0021-9991
VL - 409
JO - Journal of Computational Physics
JF - Journal of Computational Physics
M1 - 109353
ER -