Journal of Theoretical
and Applied Mechanics

47, 1, pp. 17-40, Warsaw 2009

An influence matrix technique for multi-domain solution of the Navier-Stokes equations in a vorticity-streamfunction formulation

Andrzej Bogusławski, Sławomir Kubacki
The paper presents new multi-domain algorithms based on the influence matrix technique applied together with the non-overlapping iterative domain decomposition method for solution of the incompressible Navier-Stokes equations in vorticity-streamfunction formulation. The spectral Chebyshev collocation method and the influence matrix algorithm are applied for solution of the Stokes problem in each subdomain resulting from time discretization of the Navier-Stokes equations, while the patching conditions (continuity of the solution and continuity of its first order derivative) at the interfaces between subdomains are satisfied using the iterative domain decomposition algorithm.
Keywords: spectral methods; domain decomposition method; influence matrix technique