Convergence Acceleration of High Order Numerical Simulations using a Hybrid Spectral Dierence - Finite

The goal of this paper is to show how numerical simulations of uid ow using high order methods for unstructured meshes can be sped up using a hybrid multigrid method. In our work we accelerate the steady state convergence of a Spectral Dierence code by coupling it to a Finite Volume solver. While we want to obtain the solution for the SD code, low frequency corrections to the solution are computed using the nite volume code.

[1]  D. R. McCarthy,et al.  Multigrid Code for Three-Dimensional Transonic Potential Flow about Inlets , 1982 .

[2]  H. T. Huynh,et al.  A Flux Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin Methods , 2007 .

[3]  Claus-Dieter Munz,et al.  A new class of preconditioners for discontinuous Galerkin methods for unsteady 3D Navier-Stokes equations: ROBO-SGS , 2012 .

[4]  Per-Olof Persson,et al.  High-Order LES Simulations using Implicit-Explicit Runge-Kutta Schemes , 2011 .

[5]  Marcel Vinokur,et al.  Spectral difference method for unstructured grids I: Basic formulation , 2006, J. Comput. Phys..

[6]  A. Jameson Solution of the Euler equations for two dimensional transonic flow by a multigrid method , 1983 .

[7]  Per-Olof Persson,et al.  Newton-GMRES Preconditioning for Discontinuous Galerkin Discretizations of the Navier--Stokes Equations , 2008, SIAM J. Sci. Comput..

[8]  D. Kopriva A Conservative Staggered-Grid Chebyshev Multidomain Method for Compressible Flows. II. A Semi-Structured Method , 1996 .

[9]  Chunlei Liang,et al.  A Spectral Difference Method for Viscous Compressible Flows With Shocks , 2009 .

[10]  Antony Jameson,et al.  Acceleration of transonic potential flow calculations on arbitrary meshes by the multiple grid method , 1979 .

[11]  Achi Brandt,et al.  Application of a multi-level grid method to transonic flow calculations , 1976 .

[12]  Chunlei Liang,et al.  Computation Of Flows with Shocks Using Spectral Dierence Scheme with Articial Viscosity , 2010 .

[13]  Antony Jameson,et al.  A Proof of the Stability of the Spectral Difference Method for All Orders of Accuracy , 2010, J. Sci. Comput..

[14]  Antony Jameson,et al.  Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations , 2007, J. Sci. Comput..