Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Convergence study of the Chorin-Marsden formula


Author: Lung-An Ying
Journal: Math. Comp. 72 (2003), 307-333
MSC (2000): Primary 65M99; Secondary 35Q30, 76D05, 76M25
Published electronically: May 3, 2002
MathSciNet review: 1933823
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Using the fundamental solution of the heat equation, we give an expression of the solutions to two-dimensional initial-boundary value problems of the Navier-Stokes equations, where the vorticity is expressed in terms of a Poisson integral, a Newtonian potential, and a single layer potential. The density of the single layer potential is the solution to an integral equation of Volterra type along the boundary. We prove there is a unique solution to the integral equation. One fractional time step approximation is given, based on this expression. Error estimates are obtained for linear and nonlinear problems. The order of convergence is $\frac 14$ for the Navier-Stokes equations. The result is in the direction of justifying the Chorin-Marsden formula for vortex methods. It is shown that the density of the vortex sheet is twice the tangential velocity for the half plane, while in general the density differs from it by one additional term.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 65M99, 35Q30, 76D05, 76M25

Retrieve articles in all journals with MSC (2000): 65M99, 35Q30, 76D05, 76M25


Additional Information

Lung-An Ying
Affiliation: School of Mathematical Sciences, Peking University 100871, People’s Republic of China
Email: yingla@pku.edu.cn

DOI: http://dx.doi.org/10.1090/S0025-5718-02-01423-0
PII: S 0025-5718(02)01423-0
Keywords: Vortex method, Navier-Stokes equation, fractional step method
Received by editor(s): June 5, 2000
Received by editor(s) in revised form: January 3, 2001
Published electronically: May 3, 2002
Article copyright: © Copyright 2002 American Mathematical Society