Convergence acceleration procedures for the computation of 2-D transonic flows

This study addresses a novel adaptive time stepping procedure, which leads to selection of larger time steps allowed by the physics of the problem. Information about the gradients of the flow variables can be regarded as an indicator for determining proper amount of time step, in which the system evolved. The signals from the pressure sensors, which act according to the pressure gradients, are chosen as a measure to determine the magnitude of the local CFL number. Thus, the aimed methodology for the selection of the local time step with the use of Pressure Sensor introduces optimal time steps to the implicit solution method by accounting for the pressure gradient in the solution domain, such that sharp pressure gradients encourages small time steps and vice versa. To illustrate the effect of proposed procedure, Newton Krylov (NK), with implicit pseudo time stepping method, has been employed to solve the compressible Euler equations for steady transonic case by turning on the pressure switch. Numerical experiments show that the introduced adaptive time stepping procedure decreases the computation time and the number of iterations, effectively. Additionally, a comparison study on the performances of Newton Krylov (NK) and nonlinear multigrid (FMG-FAS) methods are presented. The longer computation time required by NK can be a result of the requirement of Newton's method for a better initial guess. When the free stream values are used as initial guess, a more sophisticated method for time step selection is needed for a better NK performance especially at the start up phase.