Improvement of convective concentration fluxes in a one step reactive flow solver

The MUSCL approach appeared 25 years ago. This extension of Godunov's scheme increases its accuracy. In order to restrict the amplitude of the gradients, it has been associated with nonlinear limiters (TVD conditions). Since then, the MUSCL-TVD couple has been widely used and improved. Pursuing our work in [J. Comput. Phys. 170 (2001) 161], where adaptive limiters have been considered, and in [Comput. Fluids 32 (2003) 1473], where a simple model preserving pressure and velocity across contact discontinuities in reactive flows has been proposed, we develop an optimal limiter for species convection. All these improvements are introduced in a one step scheme to simulate unsteady reactive flows for a wide range of Mach number. For M ≪ 1, the present algorithm has been applied to a 1D premixed and diffusion flames and the results are compared with a DNS reactive code. The algorithm has also been validated on a 2D supersonic reactive flow concerning fuel break up and compared with high-order methods (ACM and wavelet filter schemes, WENO, pseudospectral). A planar acoustic wave interacting with circular and spherical diffusion flames is also analyzed. From these various cases, we show that accurate results can be obtained by using a one step algorithm which is definitely less expensive compared to multistage high-order schemes.