Techniques for Solving Stiff Chemical Kinetics on Graphical Processing Units

Abstract

The cost of integrating detailed finite rate chemical kinetics mechanisms can be prohibitive in turbulent combustion simulations. Techniques that can significantly reduce these simulation times are of great interest to model developers and the broader propulsion and power community. Two new integration methods using graphical processing units are presented that can rapidly integrate the nonlinear ordinary differential equations at each grid point. The explicit graphical processing-unit-enabled fourth-order-accurate Runge–Kutta–Fehlberg ordinary differential equation solver achieved a maximum speed up of 20.2x over the baseline implicit fifth-order-accurate DVODE CPU run time for large numbers of independent ordinary differential equation systems with comparable accuracy. The graphical processing unit implementation of DVODE achieved a maximum speed up of 7.7x over the baseline CPU run time. The performance impact of mapping one graphical processing unit thread to each ordinary differential equation system was compared with mapping an entire graphical processing unit thread block per ordinary differential equation (i.e., multiple threads per ordinary differential equation). The one-thread-per-ordinary-differential-equation approach achieved greater overall speed up but only when the number of independent ordinary differential equations was large. The one-block-per-ordinary-differential-equation implementation of Runge–Kutta–Fehlberg and DVODE both achieved lower peak speed ups, but outperformed the serial CPU performance with as few as 100 ordinary differential equations. The new graphical processing-unit-enabled ordinary differential equation solvers demonstrate a method to significantly reduce the computational cost of detailed finite rate combustion simulations.