Investigation Of High Resolution Positivity-preserving Scheme For Gas Detonation And Its Application

Combustible gas detonation propagation is a supersonic process accompanied by highly nonlinear and complex reactive fluid dynamics.Due to these special characteristics,the detailed information of gas detonation obtained through experimental research is largely limited,thus numerical simulation is widely used.Investigation of detonation mechanism is an important research subject in the explosion field.In numerical simulation of gas detonation,due to the complexity of the computational domain in high resolution numerical computing,density,pressure or chemical reaction mass fraction often emerge negative,which is contrary to the physical process and leads to blow-ups.Replacement of negative values by positive ones not only destroys conservation,but also often influences the stability.In this paper,to solve this problem,the positivity-preserving high resolution RKDG(Runge-Kutta discontinuous Galerkin)and WENO(weighted essentially non-oscillatory)finite difference schemes are constructed based on the traditional RKDG and WENO finite difference.These schemes can be well applied to numerical simulation of detonation without influencing conservation,accuracy and stability.By coupling these two types of positivity-preserving schemes,hybrid positivity-preserving scheme is constructed.The main researches are as follows:(1)Theoretically identified the necessary conditions of non-negative density,pressure and chemical reaction mass fraction in RKDG scheme,and revealed that the cell-averages are non-negative under a certain time step.Based on the above research,the high resolution positivity-preserving RKDG scheme was constructed and applied to 2D Euler equations with two-step chemical reaction,which addresses the negativity of density,pressure,or chemical reaction process in numerical simulation.(2)Constructed positivity-preserving high resolution RKDG schemes for 3D Euler equations with reaction source;theoretically identified the necessary conditions of non-negative density,pressure and chemical reaction mass fraction.(3)Based on MPI(Message Passing Interface)parallel technology,developed the large-scale parallel codes of 3D high resolution positivity-preserving RKDG scheme,and simulated detonation propagation in complex computational domain.Numerical results show that 3D high resolution parallel program can simulate detonation propagation in large-sized pipeline,and capture the front structure clearly.(4)Taking advantage of the relationship between the finite difference and finite volume,constructed the 3D high resolution positivity-preserving WENO finite difference schemes.Based on MPI parallel technology,developed the large-scale parallel codes of 3D high resolution positivity-preserving WENO finite difference scheme,and used OpenMp technology to solve the problem of load imbalance,then simulated some large explosion problems.(5)By combining the WENO finite difference scheme with the Krylov implicit integral factor method,the Krylov implicit integral factor method is applied to the numerical simulation of combustion and explosion.We use explicit scheme to discretize the non-stiff terms and implicit scheme to discretize the stiff term.The stiff problem caused by the different time scale between advection–diffusion terms and reaction term is solved.Conducted experiments for air explosion and deflagration to detonation in small pipeline.The numerical simulation results are compared with the experimental results.(6)Investigated the relationship between high resolution positivity-preserving RKDG scheme and WENO finite difference scheme.Constructed coupling scheme to solve Euler equations which uses triangular meshes of RKDG method in complex boundary and rectangle meshes of finite difference in inner domain and simple boundary.RKDG scheme is used to deal with the advantage of the complex boundary,and WENO finite difference scheme also takes the advantage of calculation speed.