Convergence of an Iterative Implicit Solver for Incompressible Flows with Direct Divergence-linked Pressure Corrector

• Published in: Numerical heat transfer. Part B, Fundamentals Fundamentals, 2008-07, Vol.54 (1), p.23-51
• Main Authors: Kuo, Cheng-Shu, Chen, Michael M.
• Format: Article
• Language: English
• ISSN: 1040-7790; 1521-0626
• DOI: 10.1080/10407790802151278

This communication presents an investigation of the convergence criteria for an iterative implicit solver for incompressible flows with a direct, divergence-linked pressure corrector. Such a method for the modified Crank-Nicolson formulation of the implicit discretized Navier-Stokes equations presents an attractive alternative to the popular semiexplicit procedures, which typically require a slow implicit step for the pressure. Although the direct iteration approach was successively demonstrated by Peyret and associates, their convergence analysis was based on the neglect of inertia terms and the use of a synchronous updating scheme similar to Jacobi iteration. The present analysis includes the inertia terms that are important at high Reynolds numbers, and is based on a more efficient immediate-updated iteration pattern similar to the Gauss-Seidel iteration, which was judged to be too difficult to analyze by Peryet and associates. The results suggest the need to modify the method to employ variable relaxation factors, dependent on local flow and mesh parameters. In addition, the computation procedure is based on a collocated mesh, which is more easily adaptable to curved and moving boundaries.