A spectral solver for the Navier-stokes equations in the velocity-vorticity formulation for flows with two nonperiodic directions

摘要

A novel pseudospectral solution procedure for the Navier-Stokes equa- tions in the velocity-vorticity formulation, suitable to simulate flows with two nonperiodic directions, is proposed. An influence matrix method, including a tau correction procedure, has been employed to elicit an algorithmic substitute for the a priori lacking boundary conditions for the voritcity. Following O. Dauvbe (J. Comput. Phys. 103, 402 (1992)) the influence matrix is built by Enforcing either the definition of the vorticity or the continuity equation at The boundary of the domain. The influence matrix is nonsingular in both Cases.