Semi implicit solver for high fidelity LES/DNS solutions of reacting flows

Abstract

A semi-implicit/point-implicit stiff solver (ODEPIM) for integrating chemistry in context of high fidelity LES/DNS simulations is presented. A detailed overview of the algorithm and its numerical formulation is discussed. The solver is then compared against a state-of-the-art multi-order implicit solver CVODE in terms of accuracy and costs. It was found that for typical LES/DNS timestep sizes ODEPIM was about one order faster than CVODE, which would make it a compelling alternative to pure implicit methods. ODEPIM, as mentioned in the literature depends on a fixed sub-timestep size to do the integration steps, this limits the speedup that can be achieved by the solver. A modification to the ODEPIM algorithm to determine the sub-timestep size dynamically is proposed enabling greater speedup. Solutions of a triple flame problem obtained using static and dynamic ODEPIM solvers are compared against the reference solutions obtained with CVODE. The dynamic ODEPIM solver was found to use the maximum permissible sub-timestep size, which on average was 8 to 4 times higher that the fixed sub-timestep size of the static ODEPIM solver. The size of the sub-timestep size directly correlates to the cpu cost, hence the dynamic ODEPIM solver is significantly faster than the static solver, this improvement however, comes at negligible loss in accuracy.