Comparison of approximate inverse preconditioners for the fractional step Navier-Stokes equations

Sparse approximate inverses are applied as preconditioners for the fractional step solution of the Navier-Stokes equations. An advantage of this method is that its implementation requires only matrix-vector products and hence is relatively easy to parallelise. Since the coeffcients for the pressure Poisson equation are constant, sparse approximate inverses need to be constructed only once, and are recalled in the subsequent iterations. Using the three dimensional turbulent channel flow as a test case, this study shows that the sparse approximate inverse preconditioners have comparable sequential performance to the Incomplete Lower-Upper preconditioner with same amount of fill to the original coeffcient matrix.