Low-storage implicit/explicit Runge-Kutta schemes for the simulation of stiff high-dimensional ODE systems

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 talk and the associated paper, we develop and characterize eight new it low-storage implicit/explicit RK schemes which have higher accuracy and better stability properties than the only low-storage implicit/explicit RK scheme available previously, the venerable second-order two/three-register Crank-Nicolson/Runge-Kutta-Wray (CN/ RKW3) algorithm that has dominated the DNS/LES literature for the last 25 years, while requiring similar storage (two, three, or four registers of length N) and comparable floating-point operations per timestep.