A methodology for the integration of stiff chemical kinetics on GPUs

Numerical schemes for reacting flows typically invoke the method of fractional steps in order to isolate the chemical kinetics model from diffusion/convection phenomena. Here, the reaction fractional step requires the solution of a collection of independent ODE systems which may be severely stiff. Recently, researchers have begun to explore the highly parallel structure of graphics processing units (GPUs) in order to accelerate integration schemes for these ODE systems. However, much of the existing work concentrates on explicit integration algorithms which may fall short in the presence of stiffness. In this light, we have carefully reimplemented in OpenCL C the Fortran 77 program of the 3-stage/5th order implicit Runge–Kutta method Radau5 by Hairer and Wanner (1991) and tested it extensively in the context of a transient equilibrium scheme for the flamelet model. Our implementation can easily be integrated with any existing reactive flow software in order to solve the reaction fractional step on an OpenCL-enabled GPU. Moreover, it is suited for any Chemkin-format reaction mechanism with ≲200≲200 species without incurring a loss in occupancy and it reaches its limit speedup (which is largely independent of the mechanism size) at a small problem size (≈500 ODE systems). In view of memory constraints, we include an optimized scheme for splitting the ODE systems across several kernel invocations and overlapping the kernel execution with data transfers. An in-depth evaluation is based upon runtime measurements of the CPU and the GPU implementation on a user level and a high-end CPU/GPU for an increasing number of ODE systems, reduced and detailed reaction mechanisms and a range of time step sizes

A global method for coupling transport with chemistry in heterogeneous porous media

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection-diffusion PDE's coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper a global solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies the Newton-Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that on be able to solve chemical equilibrium problems (and compute derivatives), without having to know the solution method. An additional advantage of the Newton-Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times vector product. The proposed method is tested on the MoMaS reactive transport benchmark.Comment: Computational Geosciences (2009) http://www.springerlink.com/content/933p55085742m203/?p=db14bb8c399b49979ba8389a3cae1b0f&pi=1

Numerical Structure Analysis of Regular Hydrogen-Oxygen Detonations

Large-scale numerical simulations have been carried out to analyze the internal wave structure of a regular oscillating low-pressure H2 : O2 : Ar-Chapman-Jouguet detonation in two and three space-dimensions. The chemical reaction is modeled with a non-equilibrium mechanism that consists of 34 elementary reactions and uses nine thermally perfect gaseous species. A high local resolution is achieved dynamically at run-time by employing a block-oriented adaptive finite volume method that has been parallelized efficiently for massively parallel machines. Based on a highly resolved two-dimensional simulation we analyze the temporal development of the ow field around a triple point during a detonation cell in great detail. In particular, the influence of the reinitiation phase at the beginning of a detonation cell is discussed. Further on, a successful simulation of the cellular structure in three space-dimensions for the same configuration is presented. The calculation reproduces the experimentally observed three-dimensional mode of propagation called "rectangular-mode-in-phase" with zero phase shift between the transverse waves in both space-directions perpendicular to the detonation front and shows the same oscillation period as the two-dimensional case