Fourier-Legendre spectral method for the unsteady Navier-Stokes equations. (English) Zbl 0827.76060
The paper deals with stability and convergence of a spectral approximation scheme when applied to solving the unsteady incompressible two- or three-dimensional Navier-Stokes equations in the primitive variables. The solution is sought for a certain time interval under the assumption that all the given and the sought functions are \(2\pi\)- periodic in the first variable \(x_1\). Additionally, the non-slip boundary conditions for velocity are imposed at \(x_1= 1\) and \(x_1= -1\). Fourier spectral approximation in the periodic directions and Legendre spectral approximation in the non-periodic one are used. Heavy functional analytic apparatus prevails in the paper.
Reviewer: T.Zlatanovski (Skopje)
MSC:
76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
76D05 | Navier-Stokes equations for incompressible viscous fluids |
65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |