Low-storage IMEX Runge-Kutta schemes for the simulation of Navier-Stokes systems

Abstract

Implicit/Explicit (IMEX) Runge-Kutta (RK) schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS; such schemes implement an (often A-stable or better) implicit RK scheme for the stiff part of the ODE, which is often linear, and, simultaneously, a (more convenient) explicit RK scheme for the nonstiff part of the ODE, which is often nonlinear. Low-storage RK schemes are especially effective for time-marching high-dimensional ODE discretizations of PDE systems on modern (cache-based) computational hardware, in which memory management is often the most significant computational bottleneck. In this paper, we develop one second-order, three thirdorder and one fourth-order IMEXRK schemes of the low-storage variety, all of which have the same or comparable low storage requirements, better stability properties, and either fewer or slightly more floating-point operations per timestep as the venerable (and, up to now, unique) second-order tworegister Crank-Nicolson/Runge-Kutta-Wray (CN/RKW3) IMEXRK algorithm that has dominated the DNS/LES literature for the last two decades.