Boundary treatments for implicit solutions to Euler and Navier-Stokes equations (Q789269)

The authors explore computationally the implication of rather large disparity in the stability bounds between the use of explicit or implicit extrapolation procedures. A few two-dimensional Euler and Navier-Stokes simulations have been investigated for this purpose. The authors have been able to compute the solutions accurately with time steps 50 to 100 times larger than explicit time limits while retaining the ability to choose rather arbitrary initial conditions. The limiting time steps for the two-dimensional test problems are larger than the limit suggested by one-dimensional analysis. It has been shown that while an improved appreciation of boundary treatment did allow very large time step sizes to be used, the largest convergence rates to the steady state exist at relatively small time step size.