Computing the effective Hamiltonian in the Majda-Souganidis model of turbulent premixed flames

摘要

Turbulence enhances the speed of propagation of a premixed flame front. According to the Majda-Souganidis model, the procedure to predict this enhancement involves computing the effective Hamiltonian in a small-scale nonlinear cell-problem. We first discuss how to transform this problem into computing the steady-state solution of a system of conservation laws whose vector solution represents the gradient of the eigenfunction associated with the effective Hamiltonian. Theoretical arguments as well as numerical evidence are presented to emphasize the importance of enforcing the constraint that the vector solution must effectively be the gradient of a scalar function. We introduce a scheme that satisfies this constraint exactly by relying on staggered grids for the gradient components. Also discussed is the issue of selecting a time integrator to achieve fast convergence to a steady state. Validation is performed by examining convergence under grid refinement and by comparison with analytical results when available. [References: 18]