The Discontinuous Galerkin Method For Solving Lagrangian Flow Equations With Chemical Reaction

The detonation is an important research field of the weapon physics.Fluid's motion is very complex in the process of the detonation.Therefore,the numerical simulation of detonation is main study work of the weapon physics.The discontinuous Galerkin(DG)methods plays an important role in computational fluid dynamics.These methods are currently being applied to a variety of research,in this thesis,we mainly apply RKDG method to solve the Lagrangian detonation problems.In the Gas Dynamics,the detonation problems always be described as the flow equations with the chemical reaction,Which is the Euler equations couple to the rate equation of the chemical reaction,generally can be called reactive Euler equations.For the reactive Euler equations in the state of ideal fluid,the thesis first utilizes the Li's method to derive the(semi)Lagrangian differential form of the equations.Which avoids the physical part and geometrical part from the(completely)Lagrangian differential form,and make it easier to solve a number of problems with the complex boundary conditions.Then,we derive the weak integral form for the(semi)Lagrangian differential form of the equations,which is discretized by the discontinuous Galerkin(DG)method.In the discrete process,we take the L-F numerical flux.The time marching is discretized by a type of Runge-Kutta(RK)methods which is corresponding to the same order of the spatial discretization.The velocity of the vertex is determined by the Roe average algorithm.Finally,in order to eliminate the possible spurious oscillations of the numerical solutions,we utilize a Hweno limiter in the scheme.The numerical examples in this thesis are presented to demonstrate that the scheme can achieve uniformly second order accuracy on the moving meshes,it is essentially nonoscillatiory and more efficient in capturing the location of the detonation front.