Investigation of high-order temporal schemes for the discontinuous Galerkin solution of the navier-stokes equations

In this work different high-order temporal schemes, used to advance in time the DG space discretized equations, are investigated: the Explicit Singly Diagonally Implicit Runge Kutta (ESDIRK), the Modified Extended BDF (MEBDF), the Two Implicit Advanced Step-point (TIAS) and a Rosenbrock method. The proposed schemes are evaluated in terms of accuracy and efficiency for two unsteady test-cases: (i) the convection of an inviscid isentropic vortex and (ii) the laminar flow around a cylinder.

[1]  H. Kredel,et al.  Integrated Performance Analysis of Computer Systems (IPACS). Benchmarks for Distributed Computer Systems , 2005, Prax. Inf.verarb. Kommun..

[2]  Alessandro Colombo,et al.  Very High-Order Accurate Discontinuous Galerkin Computation of Transonic Turbulent Flows on Aeronautical Configurations , 2010 .

[3]  Gerd Steinebach,et al.  Order-reduction of ROW-methods for DAEs and method of lines applications , 1995 .

[4]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[5]  Valerio D’Alessandro,et al.  Assessment of a high-order discontinuous Galerkin method for incompressible three-dimensional Navier–Stokes equations: Benchmark results for the flow past a sphere up to Re = 500 , 2013 .

[6]  Douglas N. Arnold,et al.  Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems , 2001, SIAM J. Numer. Anal..

[7]  S. Rebay,et al.  A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations , 1997 .

[8]  F. Brezzi,et al.  Discontinuous Galerkin approximations for elliptic problems , 2000 .

[9]  Alessandro Colombo,et al.  Simulation of the transitional flow in a low pressure gas turbine cascade with a high-order discontinuous Galerkin method , 2013 .

[10]  P. Tesini,et al.  On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations , 2012, J. Comput. Phys..

[11]  Hester Bijl,et al.  Fourth-Order Runge–Kutta Schemes for Fluid Mechanics Applications , 2005, J. Sci. Comput..

[12]  Jeff Cash,et al.  The integration of stiff initial value problems in ODEs using modified extended backward differentiation formulae , 1983 .

[13]  Jeff Cash,et al.  A stability result for general linear methods with characteristic function having real poles only , 1998 .