“…Historically, developments of numerical algorithms for ® nite-rate reactinḡ ows were aimed primarily at high-speed¯ows using the density-based method [3] and most unstructured ® nite-volume methods (FVMs) have been developed to solve the Euler equations for inviscid¯ows in aerodynamics applications and nonlinear wave propagation problems using the density-based method [4,5]. The basic merit of the density-base d method is its accuracy and robustness, especially for high-speed ow simulation.…”