Random vortex methods for the Navier-Stokes equation
type: Item
instance of: scholarly article
title: Random vortex methods for the Navier-Stokes equation
zbMATH Open document ID: 0642.76033
DOI: 10.1016/0021-9991(88)90144-1
published in: Journal of Computational Physics
publication date: 1988-01-01T00:00:00Z
review text: Two random vortex methods of Runge-Kutta type are presented for solving the two-dimensional Navier-Stokes equations. We investigate 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 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 Runge-Kutta methods are derivations of similar schemes proposed by us in an earlier time for solving stochastic differential equations with constant diffusion coefficients.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76M35
Mathematics Subject Classification ID: 76D33
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4047263
zbMATH Keywords: random vortex methods of Runge-Kutta type
zbMATH Keywords: two-dimensional Navier-Stokes equations
zbMATH Keywords: accuracy
zbMATH Keywords: rotating flow
zbMATH Keywords: Monte Carlo estimates
zbMATH Keywords: efficient variance reduction
zbMATH Keywords: Euler's method
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: constant diffusion
author: Chien-Cheng Chang
MaRDI profile type: Publication
full work available at URL: 0021-9991(88)90144-1
OpenAlex ID: W1965053933
cites work: On Vortex Methods
cites work: Q4404205
cites work: Q5532416
cites work: Vortex Methods. I: Convergence in Three Dimensions
cites work: Vortex Methods. II: Higher Order Accuracy in Two and Three Dimensions
cites work: Q4197800
cites work: Numerical Solution of Stochastic Differential Equations with Constant Diffusion Coefficients
cites work: Note on product formulas for operator semigroups
cites work: Hermite expansions in Monte-Carlo computation
cites work: Discretization of a vortex sheet with an example of roll-up
cites work: Product formulas and numerical algorithms
cites work: Applications of analysis on nilpotent groups to partial differential equations
cites work: Numerical modelling of turbulent flow in a combustion tunnel
cites work: Convergence of Vortex Methods for Euler's Equations
cites work: Convergence of a Random Method with Creation of Vorticity
cites work: Q5732992
cites work: Variance reduction in Monte Carlo computations using multi-dimensional Hermite polynomials
cites work: Vortex methods in two-dimensional fluid dynamics
cites work: The calculation of large Reynolds number two-dimensional flow using discrete vortices with random walk
cites work: Accuracy of the random vortex method for a problem with non-smooth initial conditions
cites work: Turbulent combustion in open and closed vessels
cites work: On the Construction and Comparison of Difference Schemes
description: scientific article; zbMATH DE number 4047263