Convergence Acceleration with Multidimensional Implicit Residual Averaging Technique using Block Iterative Method for the Two-Dimensional Compressible Euler Equations.

Abstract

The multidimensional residual averaging technique using the block iterative method has been applied for the two-dimensional Euler equations. The governing equations are spatially discretized using a central difference approximation and subsequent time integration using the rational Runge-Kutta (RRK) scheme. The implicit residual averaging (IRA) technique in multidimensional form has been applied for the purpose of accelerating convergence to a steady state. As a numerical scheme for the Poisson-like equation resulting from residual averaging, the block iterative method, also known as block successive over-relaxation, has been adopted. This method leads to a reduction in the number of steps required to reach the steady state in comparison with the technique of conventional residual averaging with approximate factorization (AF). It has also been shown that the present method can be combined with a block checkerboard iterative technique, which is suitable for a vector computer.