Fourier-Chebyshev pseudospectral method for three-dimensional Navier-Stokes equations
A Fourier-Chebyshev pseudospectral method is proposed for solving the three-dimensional Navier-Stokes equations. A set of discrete schemes is constructed for the solution of this problem. In the numerical experiments using the explicit scheme two solution methods are compared. Namely, one, when solving the problem with the help of a scheme constructed during the working process and the other, when using a pseudo-spectral finite-element Fourier scheme. The first scheme, in main, has an error which is by three orders less than the error in the second one. The stability and convergence of the discrete scheme is proved. The problem is ill-conditioned. In this paper, in order to solve a two-dimensional boundary value problem for a second-order parabolic equation the authors construct two classes of finite difference schemes on the base of a domain decomposition for a parallel implementation. The first class of them is similar to the usual schemes of component-wise decomposition, and it is treated as a one-iteration synchronous variant of the classical alternating Schwartz' method. The second class of regional-additive finite difference schemes corresponds to the application of additive-averaged finite difference schemes. It can be considered as a one-iterative asynchronous variant of Schwarz' method. Estimates of the convergence rate and accuracy of the solution are investigated.
three-dimensional Navier-Stokes equations
scientific article; zbMATH DE number 1080128
scientific article