Redesigning combustion modeling algorithms for the Graphics Processing Unit (GPU): Chemical kinetic rate evaluation and ordinary differential equation integration

Detailed modeling of complex combustion kinetics remains challenging and often intractable, due to prohibitive computational costs incurred when solving the associated large kinetic mechanisms. The Graphics Processing Unit (GPU), originally designed for graphics rendering on computer and gaming systems, has recently emerged as a powerful, cost-effective supplement to the Central Processing Unit (CPU) for dramatically accelerating scientific computations. Complex scientific computations are now being performed on the GPU in several research fields, such as quantum chemistry, molecular dynamics, and atmospheric modeling. Here, we present methods for exploiting the highly parallel structure of GPUs for combustion modeling. This paper outlines simple algorithm revisions that can be applied to the majority of existing combustion modeling algorithms for GPU computations. Significant simulation acceleration and predictive capability enhancements were obtained by using these GPU-enhanced algorithms for reaction rate evaluation and in ODE integration. For the demonstrations, we implemented the rate evaluation revisions in CHEMKIN and the ODE integration revisions in DASAC and DVODE and we tested the performance for simulating constant-volume ignition using SENKIN. The simulations using the revised algorithms are more than an order of magnitude faster than the corresponding CPU-only simulations, even for a low-end (double-precision) graphics card. Additionally, the computational time scales less than quadratically with the number of chemical species in the kinetic mechanism when using the GPU, as compared to the super-quadratic scaling normally seen with CPU-only chemical kinetics computations; and the GPU-based revisions do not involve approximations to the detailed kinetics. An analysis of the growth rates of combustion mechanism sizes versus computational capabilities of CPUs and GPUs further reveals the important role that GPUs are expected to play in the future of combustion modeling. Finally, we briefly outline practical steps for effectively transitioning from CPU-only to GPU-enhanced combustion modeling.