An integral equation approach to the incompressible Navier-Stokes equations in two dimensions

Journal Article · Sat Aug 01 04:00:00 EDT 1998 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/S1064827597317648· OSTI ID:328394

Greengard, L ^[1]; Kropinski, M C ^[2]

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1. New York Univ., NY (United States). Courant Inst. of Mathematical Sciences
2. Simon Fraser Univ., Burnaby, British Columbia (Canada). Dept. of Mathematics and Statistics

The authors 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, they 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, they 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.

• Sponsoring Organization: USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States); Packard Foundation, Los Altos, CA (United States)
• DOE Contract Number: FG02-88ER25053
• OSTI ID: 328394
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 1 Vol. 20; ISSN 1064-8275; ISSN SJOCE3
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
CALCULATION METHODS
FLUID MECHANICS
INCOMPRESSIBLE FLOW
INTEGRAL EQUATIONS
NAVIER-STOKES EQUATIONS
TWO-DIMENSIONAL CALCULATIONS