Adaptive Iteration to Steady State of Flow Problems

Runge–Kutta time integration is used to reach the steady state solution of discretized partial differential equations. Continuous and discrete parameters in the method are adapted to the particular problem by minimizing the residual in each step, if this is possible, or the work to reach convergence. Algorithms for parameter optimization are devised and analyzed. Solutions of the linearized Euler equations and the nonlinear Euler and Navier–Stokes equations for compressible flow illustrate the methods.