Mesh-Resolved Airfoil Simulations Using Finite Volume and Discontinuous Galerkin Solvers

A traditional second-order accurate finite volume unstructured mesh solver and a high-order discontinuous Galerkin solver are used to simulate turbulent flow over a NACA 0012 airfoil. Using a family of standardized high-density grids, mesh-resolved solutions are obtained. The flow is simulated by solving the Reynolds-averaged Navier–Stokes equations closed by the negative Spalart–Allmaras turbulence model. The flow conditions for this case are α=10, M=0.15, and Re=6×106. Lift, drag, pitching moment, pressure, and skin friction coefficients are provided for multiple grids and discretization orders and are compared against other simulation results from well known solvers. The current simulations give very similar results to these benchmark solvers, pointing toward fully mesh-resolved simulations and providing verification evidence of correct and consistent implementation of these discretizations. Results obtained using the high-order discontinuous Galerkin discretizations show higher accuracy using fewer de...

[1]  Dimitri J. Mavriplis,et al.  Agglomeration multigrid for two-dimensional viscous flows , 1995 .

[2]  Dimitri J. Mavriplis,et al.  3D Mixed Element Discontinuous Galerkin with Shock Capturing , 2013 .

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

[4]  Yousef Saad,et al.  A Flexible Inner-Outer Preconditioned GMRES Algorithm , 1993, SIAM J. Sci. Comput..

[5]  Dimitri J. Mavriplis,et al.  An hp-Adaptive Discontinuous Galerkin Solver for Aerodynamic flows on Mixed-Element Meshes , 2011 .

[6]  Dimitri J. Mavriplis,et al.  Navier-stokes applications to high-lift airfoil analysis , 1995 .

[7]  Dimitri J. Mavriplis,et al.  Multigrid algorithms for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations , 2009, J. Comput. Phys..

[8]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[9]  Kazuyoshi Takayama,et al.  An artificially upstream flux vector splitting scheme for the Euler equations , 2003 .

[10]  Dimitri J. Mavriplis,et al.  Multigrid solution of the Navier-Stokes equations on triangular meshes , 1989 .

[11]  Dimitri J. Mavriplis,et al.  Adjoint-based Shape Optimization of High-lift Airfoil using the NSU2D Unstructured Mesh Solver , 2014 .

[12]  Ralf Hartmann,et al.  An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations , 2008, J. Comput. Phys..

[13]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[14]  P. Lax.  Weak solutions of nonlinear hyperbolic equations and their numerical computation , 1954 .

[15]  Dimitri J. Mavriplis,et al.  NSU3D Results for the Fourth AIAA Drag Prediction Workshop , 2010 .

[16]  A. Jameson.  ANALYSIS AND DESIGN OF NUMERICAL SCHEMES FOR GAS DYNAMICS, 1: ARTIFICIAL DIFFUSION, UPWIND BIASING, LIMITERS AND THEIR EFFECT ON ACCURACY AND MULTIGRID CONVERGENCE , 1995 .

[17]  Krzysztof J. Fidkowski,et al.  Pseudo-transient Continuation, Solution Update Methods, and CFL Strategies for DG Discretizations of the RANS-SA Equations , 2013 .