We study relation of chemical energy and equation of state of plane detonation,and obtain the plane detonation shock equations and CJ eonditons.Detonation relations depending on curvature are gained with coordinate transformations of one-dimensional eylindrincal fluid dynamics equations.And at the same time we get a general sonic condition.Based on pressure and temperature equillibrium in reaction zone.we get relations between velocity of detonation and curvature of PBX9404 and PBX9502 as equations of state of products and reactants and reaction rates 8re known.As experiment data of explosive are known.tlIe method can be used to adjust parameters of equations of state and reaction rates.

Assuming that detonation normal velocity is a linear function of curvature,we study propagation of detonation front on unstructured quadrilaterals with level set method.Convection term in leve set equation is solved by positive scheme,and curvature term is solved by Galerkin isoparametric finite element method and semi-implicit time stepping.On Cartesian meshes and random meshes,the scheme of level set equations containing curvature is more than first order accuracy in L₂ and L_∝ norms.Examples of nonsmooth level sets shortening and three detonation fronts colliding show that the schemes can be used to simulate propagation of detonation front on curvature.

We analyze unphysical grid distortion caused by one-point quadrature in 4-node isoparametric finite element computer program.It is concluded that the rank deficiency of stiffness matrix results in hourglass distortion.A method that controlls hourglass distortion by eliminating rank deficiency is developed and validated by patch tests.