Parallel, Gradient-Based Anisotropic Mesh Adaptation for Re-entry Vehicle Configurations

Two gradient-based adaptation methodologies have been implemented into the Fun3d refine GridEx infrastructure. A spring-analogy adaptation which provides for nodal movement to cluster mesh nodes in the vicinity of strong shocks has been extended for general use within Fun3d, and is demonstrated for a 70 sphere cone at Mach 2. A more general feature-based adaptation metric has been developed for use with the adaptation mechanics available in Fun3d, and is applicable to any unstructured, tetrahedral, flow solver. The basic functionality of general adaptation is explored through a case of flow over the forebody of a 70 sphere cone at Mach 6. A practical application of Mach 10 flow over an Apollo capsule, computed with the Felisa flow solver, is given to compare the adaptive mesh refinement with uniform mesh refinement. The examples of the paper demonstrate that the gradient-based adaptation capability as implemented can give an improvement in solution quality.

[1]  Marius Paraschivoiu,et al.  A posteriori finite element bounds for linear-functional outputs of coercive partial differential equations and of the Stokes problem , 1997 .

[2]  Michael Andrew Park,et al.  Adjoint-Based, Three-Dimensional Error Prediction and Grid Adaptation , 2004 .

[3]  Michael A. Park,et al.  Three-Dimensional Turbulent RANS Adjoint-Based Error Correction , 2003 .

[4]  Peter A. Gnoffo,et al.  Heating analysis for a Lunar Transfer Vehicle at near-equilibrium flow conditions , 1993 .

[5]  William Jones.  GridEx - An Integrated Grid Generation Package for CFD , 2003 .

[6]  E. Nielsen,et al.  Aerodynamic design sensitivities on an unstructured mesh using the Navier-Stokes equations and a discrete adjoint formulation , 1998 .

[7]  Peter A. Gnoffo,et al.  Computational Fluid Dynamics Technology for Hypersonic Applications , 2003 .

[8]  W. K. Anderson,et al.  Grid convergence for adaptive methods , 1991 .

[9]  Eric J. Nielsen,et al.  Validation of 3D Adjoint Based Error Estimation and Mesh Adaptation for Sonic Boom Prediction , 2006 .

[10]  D. Venditti,et al.  Grid adaptation for functional outputs: application to two-dimensional inviscid flows , 2002 .

[11]  Michael B. Giles,et al.  Adjoint Recovery of Superconvergent Functionals from PDE Approximations , 2000, SIAM Rev..

[12]  O. C. Zienkiewicz,et al.  Adaptive remeshing for compressible flow computations , 1987 .

[13]  David Nixon,et al.  Automatic Generation of CFD-Ready Surface Triangulations from CAD Geometry , 1999 .

[14]  William L. Kleb,et al.  On Multi-Dimensional Unstructured Mesh Adaption , 1999 .

[15]  M. Giles,et al.  Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality , 2002, Acta Numerica.

[16]  J. Peraire,et al.  A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations , 1997 .

[17]  Jaime Peraire,et al.  Hypersonic Flow Computations on Unstructured Meshes , 1997 .

[18]  Timothy J. Baker,et al.  Mesh adaptation strategies for problems in fluid dynamics , 1997 .

[19]  Dominique Pelletier,et al.  Adaptivity, Sensitivity, and Uncertainty: Toward Standards of Good Practice in Computational Fluid Dynamics , 2003 .

[20]  Anthony T. Patera,et al.  Asymptotic a Posteriori Finite Element Bounds for the Outputs of Noncoercive Problems: the Helmholtz , 1999 .

[21]  Endre Süli,et al.  The Adaptive Computation of Far-Field Patterns by A Posteriori Error Estimation of Linear Functionals , 1998 .

[22]  Oh Joon Kwon,et al.  A parallel unstructured dynamic mesh adaptation algorithm for 3‐D unsteady flows , 2005 .

[23]  D. Venditti,et al.  Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows , 2003 .

[24]  Dimitri J. Mavriplis,et al.  Adaptive meshing techniques for viscous flow calculations on mixed element unstructured meshes , 1997 .

[25]  W. K. Anderson,et al.  An implicit upwind algorithm for computing turbulent flows on unstructured grids , 1994 .

[26]  Elizabeth M. Lee-Rausch,et al.  Application of Parallel Adjoint-Based Error Estimation and Anisotropic Grid Adaptation for Three-Dimensional Aerospace Configurations , 2005 .

[27]  Peter A. Cavallo,et al.  Further Extension and Validation Of A Parallel Unstructured Mesh Adaptation Package , 2005 .

[28]  E. Nielsen,et al.  Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables , 2005 .

[29]  M. Jahed Djomehri,et al.  An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA , 1994 .

[30]  M. Fortin,et al.  Anisotropic mesh adaptation: towards user‐independent, mesh‐independent and solver‐independent CFD. Part I: general principles , 2000 .

[31]  W. K. Anderson,et al.  Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids , 1995 .

[32]  William Jones.  An Open Framework for Unstructured Grid Generation , 2002 .

[33]  Rolf Rannacher,et al.  Adaptive Galerkin finite element methods for partial differential equations , 2001 .

[34]  D. Darmofal,et al.  An implicit, exact dual adjoint solution method for turbulent flows on unstructured grids , 2004 .

[35]  Frédéric Hecht,et al.  Anisotropic unstructured mesh adaption for flow simulations , 1997 .

[36]  Michael B. Giles,et al.  Solution Adaptive Mesh Refinement Using Adjoint Error Analysis , 2001 .

[37]  S. Pirzadeh.  A Solution-Adaptive Unstructured Grid Method by Grid Subdivision and Local Remeshing , 2000 .

[38]  Michael J. Aftosmis,et al.  Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries , 2002 .

[39]  Juan J. Alonso,et al.  Numerical and Mesh Resolution Requirements for Accurate Sonic Boom Prediction of Complete Aircraf , 2004 .

[40]  Peter A. Gnoffo,et al.  Computational Aerothermodynamic Simulation Issues on Unstructured Grids , 2004 .

[41]  David Anthony Venditti,et al.  Grid adaptation for functional outputs of compressible flow simulations , 2000 .