The research of p-multigrid solution for high-order discontinuous Galerkin finite element method

A p-multigrid discontinuous Galerkin method is presented for the solution of the compressible Euler equations on unstructured grids.The method operates on a sequence of solution approximations of different polynomial orders.A distinct feature of this p-multigrid method is to use different time integration schemes on different approximation levels,resulting in an accurate,fast,and low memory method that can accelerate the convergence of the Euler equations to a steady state.Transonic inviscid flow over a NACA0012 airfoil was simulated.The numerical results show that,compared with explicit Runge-Kutta method,p-multigrid method could accelerate the convergence speed nearly one order of magnitude,and maintain the original accuracy.