A conservative multirate explicit time integration method for computation of compressible flows

Abstract

In the context of high fidelity simulation of compressible flows (LES and DNS) at extreme scale (small time steps) on massively parallel supercomputers, explicit time integration methods are widely used since they both have a good computational cost trade-off at small time scales and require a small number of parallel communications, thus having little impact on the parallel strategy compared to their implicit counterpart. However, the synchronous nature of the time integration of the governing equations can be a severe constraint when the stability condition is applied globally since the time scales are related to the flow properties and the mesh resolution, which may show strong variations throughout the computational domain. We propose to further improve the efficiency (CPU wall-time reduction) of explicit Runge–Kutta methods by developing a multirate explicit time integration method, by means of flux interpolation at the boundary between cells evolving with different time-steps, which enforces the conservation properties. In terms of computational efficiency, the presented multirate time integration method is easy to implement in pre-existing Eulerian compressible Navier–Stokes codes, requires less additional memory storage, and provides a considerable speed-up while being robust and preserving the order of accuracy of the legacy explicit Runge–Kutta time integration method. The multirate time integration method is implemented in the massively parallel finite volume and high-order (spectral difference) IC3 code (Bodart et al., 2016) (fork of the solver CharLESX), but it can also be applied to any flux-based spatial method such as discontinuous Galerkin or others. For a targeted y+=0.2 on the developed turbulent channel flow test case at Reτ=392; a 2.48 effective speedup is obtained versus an expected theoretical speedup of 2.53.