1 Tenth International Conference on Computational Fluid Dynamics (ICCFD10), Barcelona, Spain, July 9-13, 2018 ICCFD10-069 Parallel Preconditioners for Pressure-Velocity Matrix Systems for Incompressible Flows Krishna Chandran * Corresponding author: kchandrn@iitk.ac.in * Dept. of Mechanical Engineering Indian Institute of Technology Kanpur, India. PINCODE 208016 Abstract: Parallel preconditioners for matrix systems arising from an unstructured finite volume formulation for the general thermal transport problem are studied with the primary focus on the CPU time of simulation. The fluid is assumed incompressible. The pressure, velocity and temperature matrix equations are solved using a preconditioned-BiCGSTAB algorithm with the matrices represented in the compressed sparse row format. The pressure matrices are highly ill-conditioned and require powerful preconditioners. Velocity and temperature matrices being well- conditioned require computationally inexpensive preconditioners such as the diagonal preconditioner. Although SGS and ILU preconditioners have better convergence characteristics, the present work shows that the use of these preconditioners for well-conditioned matrix could prove detrimental to the overall simulation time due to its weak parallelizability. Sparse Aproximate Inverse (SPAI) based preconditioners have better convergence and are highly suitable for parallel computing and hence is used for the pressure matrix. Parallelization is based on the OpenMP framework. The relatively high setup time required to compute the approximate inverse is compensated by tailoring the discretized governing equations for pressure correction such that the approximate inverse needs to be computed only once at the beginning of the simulation. The present work shows that this new formulation enables a computationally inexpensive way of using SPAI preconditioner which guarantees a superior convergence and an overall reduction in CPU time when compared with diagonal, SGS and ILU(0) preconditioners. Keywords: Parallel Preconditioner, Sparse Approximate Inverse Preconditioner, SIMPLE, Pressure Matrix, Weighted Least Squares Gradient. 1 Introduction Discretized Navier-Strokes equations generally result in a system of equations which are solved iteratively depending on the number of grid points used. Unstructured finite volume method which has acquired wide popularity in large-scale applications result in linear systems for which the matrix structure may be highly sparse thereby making the iterative solution more difficult. Early finite volume formulations were based on SIMPLE and its variants [1] which were used to resolve the pressure- velocity decoupling by using a staggered grid arrangement. However, this approach is inappropriate for unstructured grid where the pressure and velocity need to be defined at the cell centroid. The smoothing pressure correction approach [2] is a remedy which eliminates the checkerboard oscillations for pressure and velocity defined on a non-staggered grid.