Low-storage implicit/explicit Runge-Kutta schemes for the simulation of turbulent flows

Daniele Cavaglieri
University of California, San Diego (UCSD)

Implicit/explicit Runge-Kutta schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS. Ssuch 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 scheme for the non-stiff 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 the present work, we develop and characterize new low-storage implicit/explicit Runge-Kutta 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 and comparable floating-point operations per timestep.

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