Based on C-J (Chapman-Jouguet) theory different reference states of gaseous detonation products and unreacted explosives in detonation problem are considered. According to these reference states, specific Mie-Grüneisen EOS (equation of states) is selected. As chemical reaction process is neglected, a zero-thickness section of guided shock wave exists as an interface in front of the detonation wave. In numerical simulation, evolution of detonation wave includes two parts:Propagation of wave section, as well as interaction with unreacted medium. In the propagation process, speed is defined as the constant detonation speed, and detonation products forms instantly. In the interaction process, Mie-Grüneisen mixture model is employed to simulate continuous impact of detonation wave. With Mie-Grüneisen EOS, as well as the Mie-Grüneisen mixture model, motion of detonation wave is simulated well. Comparing with related theoretical data and numerical results good performance was found.

A revised robust HLLC(Harten-Lax-Van Leer-Contact) solver for multi-component Mie-Grüneisen mixture model is established. In Mie-Grüneisen mixture model, flux can be divided into conservative part and non-conservative part. Original HLLC scheme can well adapt to conservative part. As the original HLLC solver is directly extended to non-conservative part, oscillation is hard to be controlled. In original scheme, moving speed of discontinuous section refers to velocity at left or right side of the gird. It is replaced by average velocity within the grid. After the revision, the HLLC scheme is deduced again and extended to 2D problem. Numerical tests show that Mie-Grüneisen mixture model is robust and accurate with the help of modified HLLC solver.