Efficient Pseudospectral Flow Simulations in Moderately Complex Geometries

✍ Scribed by Costas D. Dimitropoulos; Brian J. Edwards; Kyung-Sun Chae; Antony N. Beris

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 454 KB
• Volume: 144
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1998.6009

✦ Synopsis

A computationally efficient pseudospectral method is developed for incompressible flow simulations in two-dimensional geometries involving periodicity in one direction and significant surface deformations. A pseudoconformal mapping is used to map the flow domain into a rectangle, thereby establishing an orthogonal curvilinear coordinate system within which the governing equations are formulated. The time integration of the spectrally discretized, two-dimensional momentum equations is performed by a second-order mixed explicit/implicit time integration scheme. The satisfaction of the continuity equation is obtained through the solution of a Poisson equation for the pressure and the use of the influence matrix technique. A highly efficient iterative solver has been developed for the solution of a generalized Stokes problem at each time step based on a spectrally preconditioned biconjugate gradient algorithm, which exhibits almost linear scalability, requiring an order N log 2 N number of operations, where N is the number of unknowns. Numerical results are presented for two-dimensional steady, oscillatory, and peristaltic flows within an undulating channel, which agree well with previous results that have appeared in the literature.