Random vortex methods for the Navier--Stokes equations

Journal Article · Wed Jun 01 00:00:00 EDT 1988 · J. Comput. Phys.; (United States)

DOI:https://doi.org/10.1016/0021-9991(88)90144-1· OSTI ID:7058655

Chang, Chien-Cheng

Two random vortex methods of Runge--Kutta type are presented for solving the two-dimensional Navier--Stokes equations. We intesgitate the accuracy of these methods by considering the model problem of a rotating flow with initial 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 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 Runge--Kutta methods are derivations of similar schemes proposed by us in an earlier time for solving stochastic differential equations with constant diffusion coefficients. copyright 1988 Academic Press, Inc.

• Research Organization: Lawrence-Berkeley Laboratory and Department of Mathematics, University of California, Berkeley, California 94720
• OSTI ID: 7058655
• Journal Information: J. Comput. Phys.; (United States), Journal Name: J. Comput. Phys.; (United States) Vol. 76:2; ISSN JCTPA
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANALYTICAL SOLUTION
BROWNIAN MOVEMENT
CONVECTION
DIFFERENTIAL EQUATIONS
DIFFUSION
ENERGY TRANSFER
EQUATIONS
FLUID FLOW
HEAT TRANSFER
ITERATIVE METHODS
MASS TRANSFER
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICS
RANDOMNESS
RUNGE-KUTTA METHOD
STOCHASTIC PROCESSES
TWO-DIMENSIONAL CALCULATIONS
VORTEX FLOW