A Conservative Method For Multiphase Flows Driven Dy Detonation With Complex EOS

The research on Computational Fluid Dynamics(CFD)has played an im-portant role in many engineering and scientific fields,such as aerospace field,national defense project,automobile and biological manufacturing engineerings.Particularly,the numerical simulation for detonation and deflagration issues has always been a hot topic.Two kinds of models for dealing with detonation problelms are usually uti-lized including CJ model and ZND model.The CJ model is proposed by Chap-man and Jouguet respectively.In this model,the combustion front is regarded as a jump discontinuity where the chemical reaction between unburnt and burn-t materials is completed instantaneously.The second model is known as ZND model,since the theory is presented by Zeldovich.von Neumann and Doering.Compared with the CJ theory,a finite reaction rate ranging from zero to one is considered in ZND model.In the model,the chemical reaction is assumed to be triggered by the detonation front,a shock discontinuity.In this paper,we propose the conservative numerical methods for compressible reactive flows in the Eulerian framework,applying both CJ model and ZND model.Firstly,we introduce the conservative numerical method for the issue of CJ detonation.In this method,the detonation front is tracked using the level set technique.In the computational cells cut by the detonation front,the finite volume method is applied to obtain the computational schemes for the detonation reactant and product respectively.In this algorithm.the level set function is not only used to determine the position of the detonation front.but also help to define the geometric parameters in the computational scheme.In order to calculate the numerical fluxes on the boundary of computational cells and interface exchanges for updating the conserved variables.we utilize the ghost fluid method in the computational cells near the interface.Then according to the solution of the Riemann problem with a detonation wave,the veloeity of detonation wave and the exchanges of conserved variations on the detonation interface are calculated.The Riemann solver with a detonation wave is also proposed in this paper.This method can be extended to high-dimensional space cases naturally.In addition,we have implemented the algorithm with a adaptive inulti-resolution technique in high-dimensional space successfully.For both ideal gases and non-ideal fluids,numerical tests in one-dimensional,two-dimensional and high-dimensional space are presented to demonstrate the robustness and effectiveness of the method.A conservative numerical method for dealing with the CJ deflagration prob-lem is also proposed in this paper.Similarly,in the computational cell cut by the deflagration front,the computational schemes for the reactant and product can be obtained based on the finite volume method.Due to the differences between the structure of Riemann solution with a deflagration wave and that with a det-onation wave,the Riemann solver is presented in the condition that the speed of deflagration wave is known.Subsequently.the exchanges on the deflagration interface are obtained according to the Riemann solution.We have extended this algorithm to high dimensional space in addition.The numerical examples of the simulations for CJ deflagration in one-dimensional,two-dimensional and high-dimensional space show the robustness and accuracy of the method.Additionally,a conservative numerical method is presented for the ZND det-onation model.In this algorithm,we use the level set method to track the shock discontinuity in front of the chemical reaction zone.Thus,in the computational cells cut by the shock interface,detonation reactant is in the region ahead the shock front and a mixture of reactant and product is in the chemical reaction zone behind it.Based on the finite volume method,the discrete schemes for the unshocked and shocked fluids are obtained.Then.in the computational cells near the shock interface,we construct the ghost fluid and solve the Riemann problem in order to calculate the average exchanges on the shock interface.The numerical results of ZND detonation problems for ideal gases and non-ideal fluids also illustrate the current method is reliable.