Title: A switching ILU(0)-SGS preconditioner for matrix systems of incompressible flow and heat transfer using condition number estimates

Authors: Krishna Chandran; Krishnamurthy Muralidhar

Addresses: Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India ' Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

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.

Keywords: unstructured finite volume method; singular values; condition number; Gershgorin estimates; switching preconditioning.

DOI: 10.1504/PCFD.2020.111392

Progress in Computational Fluid Dynamics, An International Journal, 2020 Vol.20 No.6, pp.315 - 331

Received: 01 Aug 2019
Accepted: 16 Dec 2019
Published online: 25 Nov 2020 *

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