A new algorithm for the acceleration of explicit iterative schemes for a system of partial differential equations has been developed. The method is based on the idea of allowing each partial differential equation in the system to approach the converged solution at its own optimal speed. The DMR (Distributed Minimal Residual) method allows a separate sequence of optimal weighting factors to be used for each component of the general solution vector. The acceleration scheme was applied to the system of time-dependent Euler equations of inviscid gas dynamics in conjunction with the finite volume Runge-Kutta explicit time-stepping method with the Jameson's Artificial Dissipation (AD) terms and the newly formulated Physically Based Dissipation (PBD) model. Test were performed for various flow conditions, including internal flow, flow around a cylinder and flow over an airfoil with AD and PBD. Using DMR, between 30% and 70% of the computational efforts were saved in the subsonic compressible flow calculations.
