Development of a Balanced Adaptive Time-Stepping Strategy Based on an Implicit JFNK-DG Compressible Flow Solver

doi:10.1007/s42967-021-00138-1

Abstract

Abstract: A balanced adaptive time-stepping strategy is implemented in an implicit discontinuous Galerkin solver to guarantee the temporal accuracy of unsteady simulations. A proper relation between the spatial, temporal and iterative errors generated within one time step is constructed. With an estimate of temporal and spatial error using an embedded RungeKutta scheme and a higher order spatial discretization, an adaptive time-stepping strategy is proposed based on the idea that the time step should be the maximum without obviously infuencing the total error of the discretization. The designed adaptive time-stepping strategy is then tested in various types of problems including isentropic vortex convection, steady-state fow past a fat plate, Taylor-Green vortex and turbulent fow over a circular cylinder at Re=3 900. The results indicate that the adaptive time-stepping strategy can maintain that the discretization error is dominated by the spatial error and relatively high efciency is obtained for unsteady and steady, well-resolved and under-resolved simulations.

Key words: Adaptive time-stepping, Unsteady simulations, High order, Discontinuous Galerkin, Implicit time integration

CLC Number:

Yu Pan, Zhen-Guo Yan, Joaquim Peiró, Spencer J. Sherwin. Development of a Balanced Adaptive Time-Stepping Strategy Based on an Implicit JFNK-DG Compressible Flow Solver[J]. Communications on Applied Mathematics and Computation, 2022, 4(2): 728-757.

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