A switching ILU(0)-SGS preconditioner for matrix systems of incompressible flow and heat transfer using condition number estimates. (20th October 2020)

• Record Type: Journal Article
• Authors: Chandran, Krishna; Muralidhar, Krishnamurthy
• Is Part Of: Progress in computational fluid dynamics. Volume 20:Number 6(2020)
• Page Start: 315
• Page End: 331
• Publication Date: 2020-10-20
• Subjects: unstructured finite volume method -- singular values -- condition number -- Gershgorin estimates -- switching preconditioning; Fluid dynamics -- Data processing -- Periodicals; Fluid dynamics -- Mathematics -- Periodicals; 620.10640285
• Languages: English
• ISSNs: 1468-4349

Abstract

Preconditioning of matrix systems obtained from an unstructured finite volume discretisation of the incompressible NS equations are studied. The condition number is first estimated by providing Gershgorin-type theoretical bounds. The linear algebraic equations are solved using the preconditioned-BiCGSTAB algorithm. Condition numbers of velocity and temperature matrices show these to be well-conditioned compared to pressure. As a result, the symmetric Gauss Seidel (SGS) preconditioner performs well for velocity matrices on single and multiple processors when compared to ILU(0) that requires LU factorisation. The present study proposes a preconditioning algorithm that switches from ILU(0) to the SGS preconditioner for velocity and temperature. The composite algorithm shows a reduction in the overall simulation time. For a power law fluid, the upper bound of the condition number correlates with the power law index. For flow past a circular cylinder, the temporal oscillation of the largest singular value relates to the onset of vortex shedding.