Adaptive Conservative Time Integration (ACTI) for Compressible Flow

For time dependent simulations the time steps have to be chosen appropriately small to guarantee stability and to minimize time integration errors. Opposed to classical time stepping schemes, which employ the same time step everywhere, time adaptive solution algorithms allow for large time steps wherever possible, while resorting to high temporal resolution only where needed. Regarding computational  efficiency such schemes are very attractive, but it is not straight forward to also achieve stability, high accuracy, and conservation.

Recently, an adaptive conservative time integration (ACTI) scheme for finite volume methods was devised. Besides being adaptive in time, ACTI is conservative, all operations are local, and it is of high order in space and time. The performance of ACTI has been demonstrated for various hyperbolic conservation laws.

Here, an ACTI scheme for the compressible Navier-Stokes-Fourier system is introduced, which is particularly attractive for unsteady flows involving boundary layers. Unlike in inviscid flow simulations, the time step size not only is restricted by a CFL criterion, but also by the viscous terms. Further, in order to preserve 2nd order in space and time, a novel discretization scheme for the viscous fluxes is devised.

Results of various unsteady flows, including shock boundary layer interaction, demonstrate efficiency and accuracy of the new ACTI scheme. Further, given that all operations are local, it is an ideal candidate for massive parallel computations.