TY - JOUR
T1 - An integral equation approach to the incompressible navier-stokes equations in two dimensions
AU - Greengard, Leslie
AU - Kropinski, Mary Catherine
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1998
Y1 - 1998
N2 - We present a collection of methods for solving the incompressible Navier-Stokes equations in the plane that are based on a pure stream function formulation. The advantages of this approach are twofold: first, the velocity is automatically divergence free, and second, complicated (nonlocal) boundary conditions for the vorticity are avoided. The disadvantage is that the solution of a nonlinear fourth-order partial differential equation is required. By recasting this partial differential equation as an integral equation, we avoid the ill-conditioning which hampers finite difference and finite element methods in this environment. By using fast algorithms for the evaluation of volume integrals, we are able to solve the equations using O(M) or O(M log M) operations, where M is the number of points in the discretization of the domain.
AB - We present a collection of methods for solving the incompressible Navier-Stokes equations in the plane that are based on a pure stream function formulation. The advantages of this approach are twofold: first, the velocity is automatically divergence free, and second, complicated (nonlocal) boundary conditions for the vorticity are avoided. The disadvantage is that the solution of a nonlinear fourth-order partial differential equation is required. By recasting this partial differential equation as an integral equation, we avoid the ill-conditioning which hampers finite difference and finite element methods in this environment. By using fast algorithms for the evaluation of volume integrals, we are able to solve the equations using O(M) or O(M log M) operations, where M is the number of points in the discretization of the domain.
KW - Integral equation methods
KW - Navier-stokes equations
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U2 - 10.1137/S1064827597317648
DO - 10.1137/S1064827597317648
M3 - Article
AN - SCOPUS:0032131283
VL - 20
SP - 318
EP - 336
JO - SIAM Journal of Scientific Computing
JF - SIAM Journal of Scientific Computing
SN - 1064-8275
IS - 1
ER -