Implementation and comparisons of parallel implicit solvers for hypersonic flow computations on unstructured meshes

A study of parallel implicit solvers for accelerating convergence to steady state solutions of the compressible Navier-Stokes equations with finite-rate chemistry is presented. The solvers in question are pertinent to applications of hypersonic flows that can be modeled as laminar, or to turbulent flows that can be simulated using the Reynolds averaged (RANS) equations. The current state-of-the-art method, the Data-Parallel Line Relaxation (DPLR), is examined. Its convergence properties are evaluated for a class of challenging external aerodynamics problems. A more sophisticated method based on the GMRES linear system solver is built around the DPLR method, where the DPLR is used as a preconditioner. The convergence characteristics of the augmented method are studied for model problems of practical interest. Results show that the more sophisticated method has better convergence properties, but exhibits higher cost and should be used selectively.

[1]  Paul D. Orkwis,et al.  Newton's method solver for high-speed viscous separated flowfields , 1992 .

[2]  Paul D. Orkwis,et al.  Comparison of Newton's and quasi-Newton's method solvers for the Navier-Stokes equations , 1993 .

[3]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

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

[5]  G. Candler,et al.  Data-Parallel Line Relaxation Method for the Navier -Stokes Equations , 1998 .

[6]  Graham V. Candler,et al.  Hypersonic inward turning inlets: Design and optimization , 2006 .

[7]  R. Maccormack Current status of numerical solutions of the Navier-Stokes equations , 1985 .

[8]  I. Nompelis Computational study of hypersonic double-cone experiments for code validation , 2004 .

[9]  Graham V. Candler,et al.  A parallel unstructured implicit solver for hypersonic reacting flow simulation , 2005 .

[10]  Stephane Catris,et al.  Density corrections for turbulence models , 2000 .

[11]  Graham V. Candler,et al.  Effect of numerics on navier-stokes computations of hypersonic double-cone flows , 2005 .

[12]  Graham V. Candler,et al.  The solution of the Navier-Stokes equations using Gauss-Seidel line relaxation , 1989 .

[13]  P. Orkwis,et al.  Newton's Method Solver for the Axisymmetric Navier-Stokes Equations , 1992 .

[14]  Graham V. Candler,et al.  Effect of Vibrational Nonequilibrium on Hypersonic Double-Cone Experiments , 2003 .

[15]  Graham V. Candler,et al.  Performance comparisons of parallel implicit solvers for hypersonic flow computations on unstructured meshes , 2007 .