Acceleration of iterative algorithms on highly clustered grids
A family of new methods has been developed to accelerate the convergence rate of iterative algorithms for obtaining a steady-state solution as an asymptotic limit of an unsteady second-order partial differential equation or a system of such equations. It was assumed that a central differencing has been used for spatial discretization. The new acceleration methods are based on the sensitivity of the future residual at every grid point to the change in the solution vector components at the neighboring grid points used in the local discretization approximation. The acceleration parameters introduced in the methods have been optimized with the objective to minimize the future global residual. The new sensitivity-based methods have been applied to finite difference codes for twoand three-dimensional, laminar, incompressible flow Navier-Stokes equations; two-dimensional, turbulent, incompressible flow Navier-Stokes equations; and two-dimensional, compressible flow Euler equations. The new sensitivity-based acceleration methods demonstrated superior performance in all test cases that involved severe grid clustering and grid nonorthogonality and included laminar and turbulent flows with closed and open flow separation.