Adaptive Wavelet Schwarz Methods for the Navier-Stokes Equation

On Schwarz Alternating Methods for the Incompressible Navier-Stokes Equations

The Schwarz alternating method can be used to solve linear elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an innnite sequence of functions which result from solving a sequence of elliptic boundary value problems in each of the subdomains. This paper considers four Schwarz alternating methods for the N-dimensional,...

Adaptive Wavelet Solvers for the Unsteady Incompressible Navier-Stokes Equations

Towards an adaptive wavelet - based 3 D Navier - Stokes

In this paper we present results obtained using wavelet methods for the analysis and simulation of two-dimensional turbulence, and a preliminary study of a three-dimensional turbulent channel ow. The two-dimensional results show the eeciency of wavelets for the numerical simulation of turbulence, and suggest new methods for modelling the ow, based on a decomposition into coherent and incoherent...

AN ADAPTIVE WAVELET SOLUTION TO GENERALIZED STOKES PROBLEM

In this paper we will present an adaptive wavelet scheme to solvethe generalized Stokes problem. Using divergence free wavelets, theproblem is transformed into an equivalent matrix vector system, thatleads to a positive definite system of reduced size for thevelocity. This system is solved iteratively, where the applicationof the infinite stiffness matrix, that is sufficiently compressible,is r...

Hybrid Schwarz-Multigrid Methods for the Spectral Element Method: Extensions to Navier-Stokes

The performance of multigrid methods for the standard Poisson problem and for the consistent Poisson problem arising in spectral element discretizations of the Navier-Stokes equations is investigated. It is demonstrated that overlapping additive Schwarz methods are effective smoothers, provided that the solution in the overlap region is weighted by the inverse counting matrix. It is also shown ...