A DIRECT SCHUR-FOURIER DECOMPOSITION FOR THE SOLUTION OF THE THREE-DIMENSIONAL POISSON EQUATION OF INCOMPRESSIBLE FLOW PROBLEMS USING LOOSELY COUPLED PARALLEL COMPUTERS

• Published in: Numerical heat transfer. Part B, Fundamentals Vol. 43; no. 5; pp. 467 - 488
• Main Authors: Soria, M., Pérez-Segarra, C. D., Oliva, A.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Informa UK Ltd 01.05.2003; Taylor & Francis
• Subjects: Computational methods in fluid dynamics; Convection and heat transfer; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Physics; Turbulent flows, convection, and heat transfer; Algorithms; Turbulent flow; Three dimensional flow; Computational fluid dynamics; Digital simulation; Parallel processing; Poisson equation; Natural convection; Incompressible fluid; Heat transfer
• ISSN: 1040-7790; 1521-0626
• DOI: 10.1080/713836244

Parallel computers based on PC-class hardware (Beowulf clusters) provide a matchless computing power per cost unit. However, their network performance tends to be too low for standard parallel computational fluid dynamics (CFD) algorithms. A relevant example is the solution of the Poisson equations. The subject of this article is a direct Schur-Fourier decomposition (DSFD) algorithm that, for certain three-dimensional flows, produces an accurate solution of each Poisson equation with just one message, providing speed-ups of at least 24 in a low-cost PC cluster with a conventional network and 36 processors. Direct Numerical Simulation (DNS) of turbulent natural convection flow is used as a benchmark problem.