Implementation of Compressible Flow Solvers With Jameson-Schmidt-Turkel Timestepping Schemes in NGA

Emmet Cleary, California Institute of Technology

Compressible flow simulations often have longer runtimes than their
low-Mach-number counterparts as they require significantly smaller
timesteps to resolve pressure fluctuations. Runge-Kutta schemes are
often used for time discretizations, but several schemes must be
implemented to accommodate a range of desired accuracies and to ensure
stability. If not carefully chosen to match all conditions of a
simulation, additional unnecessary stages could be run to advance the
timestep. To account for this, we employ the Jameson-Schmidt-Turkel
scheme, a low-storage, generalized n-stage formulation of the
Runge-Kutta methods with O(n) error for linear cases. Through its
implementation in NGA, a fluids solver originally developed for
low-Mach flows and recently adapted for compressible flow, it will be
shown that second-order accuracy of the solvers is preserved. Standard test cases will demonstrate this, including the Taylor vortex and one-dimensional waves. Additionally, it will include a brief discussion on the JST scheme and its application to reacting flows.

Abstract Author(s): Emmet M. Cleary, Guillaume Blanquart