Eventos Anais de eventos
COBEM 2019
25th International Congress of Mechanical Engineering
NONLINEAR TIME-STEP RESTRICTION ON MINIMAL GAIN MARCHING SCHEMES
Submission Author:
Ricardo Dias dos Santos , RJ
Co-Authors:
Ricardo Dias dos Santos, Mariana Resende Volpini, Leonardo Santos de Brito Alves
Presenter: Ricardo Dias dos Santos
doi://10.26678/ABCM.COBEM2019.COB2019-2277
Abstract
When nonlinear stability properties must be preserved, as in solutions involving shocks and discontinuities, solution monotonicity is guaranteed by a time step restriction. For steady-state solutions with discontinuities, the use of time integration methods can be limited to a time step restriction even for implicit schemes, going in the opposite direction of the asymptotical linear stability analysis. Since minimal gain marching schemes are based on the linear stability analysis, the study of time step restriction can indicate the viability of these methods. All simulations used to test this scheme so far, however, did not contain discontinuities such as shock waves. In such a scenario, the nonlinear stability properties of the marching scheme must also be considered in order to preserve the shock-capturing capabilities of the chosen spatial discretization. Two classical test cases are used in this paper for a comparative analysis of time integration schemes under gain restriction. This restriction analysis is important to understand how minimal gain marching schemes depend on the time-step to reach steady-state.
Keywords
Linear Stability Analysis, Total Variation Diminishing, Numerical analysis
