A monotone time relaxation matrix procedure for improved convergence to steady-state for CFD algorithms Original Research Article

For a time independent formulation, temporal schemes are traditionally employed for stable convergence to steady state. However, the pseudo-transient solution process may become slow as it suffers heavily from oscillations at large timesteps. This paper develops a theory, involving a scaling parameter embedded in the statically-condensed weak statement finite element time-term (mass) matrix, leading to monotone convergence to steady state using significantly fewer timesteps. Verification tests for a heat transfer and a compressible flow problem in 1-D and 2-D document the developed procedure.