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
The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differ...The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differential quadrature(PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta(TVD-RK) method.The numerical solutions are satisfactorily coincident with the exact solutions.The method can compete against the methods applied in the literature.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The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differential quadrature(PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta(TVD-RK) method.The numerical solutions are satisfactorily coincident with the exact solutions.The method can compete against the methods applied in the literature.
