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The research of p-multigrid solution for discontinuous Galerkin method

Yang Yong

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Abstract

A discontinuous Galerkin method with p-multigrid is presented to solve the 2D and 3D transonic Euler equations on unstructured grids.The p-multigrid approximates the polynomial expressions of different orders by using recursive iteration method.In this way the convergence of discontinues Galerkin method is accelerated and the efficiency of the computation is greatly improved.In this paper,explicit scheme is applied for high-order approximation(p0),while implicit scheme(LU-SGS) is applied for the low-order approximation(p=0).Simulation results for transonic inviscid flows over NACA0012 airfoil and ONERA M6 wing verified the efficiency of the p-multigrid method,and its accuracy is the same as that of Runge-Kutta discontinuous Galerkin method(RKDG).

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What this paper is about

A discontinuous Galerkin method with p-multigrid is presented to solve the 2D and 3D transonic Euler equations on unstructured grids.The p-multigrid approximates the polynomial expressions of different orders by using recursive iteration method.In this way the convergence of discontinues Galerkin method is accelerated and the efficiency of the computation is greatly improved.In this paper,explicit scheme is applied for high-order approximation(p0),while implicit scheme(LU-SGS) is applied for the low-order approximation(p=0).Simulation results for transonic inviscid flows over NACA0012 airfoil and ONERA M6 wing verified the efficiency of the p-multigrid method,and its accuracy is the same as that of Runge-Kutta discontinuous Galerkin method(RKDG).

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Available abstract

A discontinuous Galerkin method with p-multigrid is presented to solve the 2D and 3D transonic Euler equations on unstructured grids.The p-multigrid approximates the polynomial expressions of different orders by using recursive iteration method.In this way the convergence of discontinues Galerkin method is accelerated and the efficiency of the computation is greatly improved.In this paper,explicit scheme is applied for high-order approximation(p0),while implicit scheme(LU-SGS) is applied for the low-order approximation(p=0).Simulation results for transonic inviscid flows over NACA0012 airfoil and ONERA M6 wing verified the efficiency of the p-multigrid method,and its accuracy is the same as that of Runge-Kutta discontinuous Galerkin method(RKDG).

Key concepts: Transonic, Discontinuous Galerkin method, Multigrid method, Mathematics, Inviscid flow, Applied mathematics, Euler equations, Airfoil

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