Random Vortex Methods for the NavierStokes Equations
Abstract
Two random vortex methods of RungeKutta type are presented for solving the twodimensional NavierStokes equations. We investigate the accuracy of these methods by considering the model problem of a rotating flow with intitial vorticity concentrated uniformly on a disk of finite radius. Functionals of the numerical solution are computed by Monte Carlo estimates with efficient variance reduction, and the results are compared to those obtained from Euler's method. The numerical results show that both of the methods produce errors smaller by one power of the time step size than Euler's method, one seemingly even better than the other. These RungeKutta methods are derivations of similar schemes proposed by us in an earlier time for solving stochastic differential equations with constant diffusion coefficients.
 Publication:

Journal of Computational Physics
 Pub Date:
 June 1988
 DOI:
 10.1016/00219991(88)901441
 Bibcode:
 1988JCoPh..76..281C
 Keywords:

 Computational Fluid Dynamics;
 Diffusion Theory;
 NavierStokes Equation;
 RungeKutta Method;
 Two Dimensional Flow;
 Vortices;
 Monte Carlo Method;
 Random Errors;
 Rotating Disks;
 Rotating Fluids;
 Stochastic Processes;
 Vorticity Equations;
 Fluid Mechanics and Heat Transfer