Central discontinuous Galerkin（CDG）method is used to solve the Navier-Stokes equations for viscous flow in this paper.The CDG method involves two pieces of approximate solutions defined on overlapping meshes.Taking ...Central discontinuous Galerkin（CDG）method is used to solve the Navier-Stokes equations for viscous flow in this paper.The CDG method involves two pieces of approximate solutions defined on overlapping meshes.Taking advantages of the redundant representation of the solution on the overlapping meshes,the cell interface of one computational mesh is right inside the staggered mesh,hence approximate Riemann solvers are not needed at cell interfaces.Third order total variation diminishing（TVD）Runge-Kutta（RK）methods are applied in time discretization.Numerical examples for 1D and2 D viscous flow simulations are presented to validate the accuracy and robustness of the CDG method.展开更多
Several numerical methods of differential equations and their applications in ballistic calculation are discussed for the purpose of simplification of the dynamic differential equations of projectile trajectory.Progra...Several numerical methods of differential equations and their applications in ballistic calculation are discussed for the purpose of simplification of the dynamic differential equations of projectile trajectory.Program simulations of Euler method,Heun method,lassic fourth-order Runge Kutta（RK4）method,ABM method and Hamming method are achieved based on Matlab.In addtion,the approximate solutions,local truncation errors and calculation time of the dynamic differential equations are obtained.By analyzing the simultaion results,the advantages and disadvantages of these methods are compared,which provides a basis for choice of ballistic calculation methods.展开更多
基金Supported by the National Natural Science Foundation of China(11602262)
文摘Central discontinuous Galerkin（CDG）method is used to solve the Navier-Stokes equations for viscous flow in this paper.The CDG method involves two pieces of approximate solutions defined on overlapping meshes.Taking advantages of the redundant representation of the solution on the overlapping meshes,the cell interface of one computational mesh is right inside the staggered mesh,hence approximate Riemann solvers are not needed at cell interfaces.Third order total variation diminishing（TVD）Runge-Kutta（RK）methods are applied in time discretization.Numerical examples for 1D and2 D viscous flow simulations are presented to validate the accuracy and robustness of the CDG method.
文摘Several numerical methods of differential equations and their applications in ballistic calculation are discussed for the purpose of simplification of the dynamic differential equations of projectile trajectory.Program simulations of Euler method,Heun method,lassic fourth-order Runge Kutta（RK4）method,ABM method and Hamming method are achieved based on Matlab.In addtion,the approximate solutions,local truncation errors and calculation time of the dynamic differential equations are obtained.By analyzing the simultaion results,the advantages and disadvantages of these methods are compared,which provides a basis for choice of ballistic calculation methods.
