Recent improvements in efficiency, accuracy, and convergence for implicit approximate factorization algorithms

In 1977 and 1978, general purpose centrally space differenced implicit finite difference codes in two and three dimensions have been introduced. These codes, now called ARC2D and ARC3D, can run either in inviscid or viscous mode for steady or unsteady flow. Since the introduction of the ARC2D and ARC3D codes, overall computational efficiency could be improved by making use of a number of algorithmic changes. These changes are related to the use of a spatially varying time step, the use of a sequence of mesh refinements to establish approximate solutions, implementation of various ways to reduce inversion work, improved numerical dissipation terms, and more implicit treatment of terms. The present investigation has the objective to describe the considered improvements and to quantify advantages and disadvantages. It is found that using established and simple procedures, a computer code can be maintained which is competitive with specialized codes.