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| A Survey on the Performance ofKrylov Subspace Methods in HighOrder Compact Schemes for SolvingPoisson’s Equation for Application inIncompressible Fluid Flow Solvers |
| Iman Farahbakhsh,Benyamin Barani Nia,Mehdi Dehgha |
| (Department of Maritime Engineering, Amirkabir University of
Technology (Tehran Polytechnic), Tehran, Iran;Department of Applied Mathematics, Faculty of Mathematics and
Computer Sciences, Amirkabir University of Technology (Tehran
Polytechnic), Tehran, Iran) |
| DOI： |
| Abstract: |
| The efficiency of three Krylov subspace methods with their ILU0-
preconditioned version in solving the systems with the nonadiagonal sparse matrix is examined. The systems have arisen from the discretization of Poisson’s
equation using the 4th and 6th-order compact schemes. Four matrix-vector
multiplication techniques based on four sparse matrix storage schemes are considered in the algorithm of the Krylov subspace methods and their effects are
explored. The convergence history, error reduction, iteration-resolution relation and CPU-time are addressed. The efficacy of various methods is evaluated
against a benchmark scenario in which the conventional second-order central
difference scheme is employed to discretize Poisson’s equation. The Krylov subspace methods, paired with four distinct matrix-vector multiplication strategies
across three discretization approaches, are tested and implemented within an incompressible fluid flow solver to solve the elliptic segment of the equations. The
resulting solution process CPU-time surface gives a new vision regarding speeding up a CFD code with proper selection of discretization stencil and matrixvector multiplication technique. |
| Key words: High order compact, Krylov subspace methods, Navier-Stokes equations,
Poisson’s equation, CPU-time, matrix-vector multiplication, sparse storage schemes. |