Relaxed ILU Preconditioning for the CG Solution of a Singular Boundary Value Problem for Pressure
A splitting technique for solving the incompressible Navier-Stokes equations, whereby operations on pressure and velocity are decoupled, leads to a second-order singular boundary value problem for the determination of pressure. A finite volume discretization based on a nonuniform grid is applied to this problem, producing a linear system of equations whose coefficient matrix is symmetric positive semidefinite. We give an account of our experience with solving this system by the conjugate gradient method with relaxed ILU preconditioning. Particular attention is given to the effect of the nonuniformity of the grid.
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