Simulation Analysis Of Discontinuous Galerkin Method Algorithm For Nonlinear Parabolic Equation

Firstly,this paper establishes Local discontinuous Galerkin method(LDG)and interior penalty discontinuous Galerkin method(IPDG)formats for the incompressible Navier-Stoke equation,the advantages and disadvantages of the two methods are compared.Based on unstructured grids,combined Adams-Bashforth second order time discretization,the IPDG formula for solving the non-compressive Navier-Stokes equation is derived in detail;Numerical examples are given to simulate the problem of square cavity driven flow(time dependent flow)and back-stage winding flow in classical flow.The results verify that the proposed method has high computational accuracy and good stability.Secondly,the direct discontinuous Galerkin method(DDG)scheme is established for solving the nonlinear diffusion equation.The numerical flux is introduced directly at the discontinuous point,and only through the compatible and conserved numerical flow relations between the elements.The convergence of the scheme is analyzed in detail,which can effectively simulate the complex problems including high order equations and discontinuous points.The numerical simulation results show that:DDG method has high calculation accuracy,can help constructing higher efficiency algotithm with high-order element.