Implicit/multigrid algorithms for incompressible turbulent flows on unstructured grids

Abstract

SummaryAn implicit code for computing inviscid and viscous incompressible flows on unstructured grids is described. The foundation of the code is a backward Euler time discretization for which the linear system is approximately solved at each time step with either a point implicit method or a preconditioned Generalized Minimal Residual (GMRES) technique. For the GMRES calculations, several techniques are investigated for forming the matrix-vector product. Convergence acceleration is achieved through a multigrid scheme that uses non-nested coarse grids that are generated using a technique described in the present paper. Convergence characteristics are investigated and results are compared with an exact solution for the inviscid flow over a four-element airfoil. Viscous results, which are compared with experimental data, include the turbulent flow over a NACA 4412 airfoil, a three-element airfoil for which Mach number effects are investigated, and three-dimensional flow over a wing with a partial-span flap.

Numerical prediction of the interference drag of a streamlined strut intersecting a surface in transonic flow

“…In this section, the flow solvers FUN2D and FUN3D [104,105] used for this work are described in detail. These codes were chosen because our studies were conducted for NASA Langley, so close cooperation was facilitated.…”

Boundary-Layer Stability Analysis of the Mean Flows Obtained Using Unstructured Grids

“…FUN3D, [3][4][5][6][7][8] an unstructured CFD code developed at NASA Langley, provides extensive adjoint-based capabilities for design optimization for many design parameters. The ultimate long-term goal of the research conducted by the authors is to develop an adjoint formulation for LASTRAC and integrate it with the adjoined-based capabilities of FUN3D to enable design optimization that directly maximizes the laminar-flow regions.…”

Artificial Compressibility 3-D Navier-Stokes Solver for Unsteady Incompressible Flows with Hybrid Grids

“…The refinement factor "r" is defined as "r=h k+1 /h k " where "h k " and "h k+1 " are successive values of parameter "h". More specifically if h 1 , h 2 and h 3 are three levels of parameter "h" such that r 12 =h 2 /h 1 =2 and r 23 =h 3 /h 2 =2 and the corresponding numerical solutions for "Φ" are 1  , 2  , 3  then we can write the following equations:…”

“…The symbol "" means that the various quantities are evaluated with algebraic averaging of " L Q ", " R Q ". In two dimensions we used the eigensystem of Roe's matrix that was reported by Anderson et al (1995), while in three dimensions we used the eigensystem reported by Shin (2001). The left and right state vectors are evaluated by a third-order accurate upwind interpolation scheme along edge "ij" (Tai et al, 2005):…”