A numerical algorithm for flame propagation in premixed gases

The propagation speed of a premixed laminar flame or a weak deflagration wave is not uniquely determined in the hyperbolic theory of reactive gas flow. In this paper, we take a hyperbolic system of conservation laws as a governing system of equations for reacting gases and propose an algorithm to determine a wave propagation speed uniquely. The wave speed and states around a flame are computed through solving a Riemann problem near a flame in the phase space. The Riemann problem can be solved by combining the information from the internal wave structure, which is ignored in the hyperbolic approximation, and characteristic information. Therefore, the wave speed comes to depend on the internal variables such as viscosity and diffusion. This method can be used to track a premixed laminar flame when combined with any front tracking method. Some computational results are also presented.