A triangular cut-cell adaptive method for high-order discretizations of the compressible Navier-Stokes equations

Journal of Computational Physics

Volumn 225, Issue 2, 2007, Pages 1653-1672

  Fidkowski, Krzysztof J ^a   Darmofal, David L ^a  

^a Massachusetts Institute of Technology   (United States)

Author keywords

Anisotropic mesh adaptation; Compressible Navier Stokes; Discontinuous Galerkin; Output based error estimation; Triangular cut cells

Indexed keywords

ANISOTROPY; BOUNDARY LAYERS; CELLS; CYTOLOGY; DEGREES OF FREEDOM (MECHANICS); ERROR ANALYSIS; GALERKIN METHODS; MESH GENERATION; VISCOUS FLOW;

ADAPTIVE METHODS; ANISOTROPIC MESH ADAPTATION; COMPRESSIBLE NAVIER-STOKES; COMPRESSIBLE NAVIER-STOKES EQUATIONS; CUT CELLS; DISCONTINUOUS GALERKIN; HIGHER ORDER DISCRETIZATION; MESH ADAPTATION; OUTPUT-BASED ERROR ESTIMATION; TRIANGULAR CUT CELL;

NAVIER STOKES EQUATIONS;

EID: 34547538932     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.02.007     Document Type: Article

References (36)

1. Coirier W.J., and Powell K.G. Solution-adaptive cut-cell approach for viscous and inviscid flows. AIAA Journal 34 5 (1996) 938-945
2. Calhoun D., and LeVeque R.J. A Cartesian grid finite-volume method for the advection-diffusion equation in irregular geometries. Journal of Computational Physics 157 (2000) 143-180
3. Aftosmis M., Berger M., and Melton J. Adaptive Cartesian mesh generation. In: Thompson J., Soni B., and Weatherill N. (Eds). Handbook of Grid Generation (1998), CRC Press
4. Roe P.L. Approximate Riemann solvers, parametric vectors, and difference schemes. Journal of Computational Physics 43 (1981) 357-372
5. Fidkowski K.J., Oliver T.A., Lu J., and Darmofal D.L. p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. Journal of Computational Physics 207 (2005) 92-113
6. Bassi F., and Rebay S. GMRES discontinuous Galerkin solution of the compressible Navier-Stokes equations. In: Cockburn K., and Shu (Eds). Discontinuous Galerkin Methods: Theory, Computation and Applications (2000), Springer, Berlin 197-208
7. J. Lu, An A Posteriori Error Control Framework for Adaptive Precision Optimization Using Discontinuous Galerkin Finite Element Method, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 2005.
8. Purvis J.W., and Burkhalter J.E. Prediction of critical Mach number for store configurations. AIAA Journal 17 11 (1979) 1170-1177
9. Clarke D.K., Salas M.D., and Hassan H.A. Euler calculations for multielement airfoils using Cartesian grids. AIAA Journal 24 3 (1986) 353
10. R.L. Gaffney, M.D. Salas, H.A. Hassan, Euler calculations for wings using Cartesian grids, Paper 1987-0356, AIAA, 1987.
11. Young D.P., Melvin R.G., Bieterman M.B., Johnson F.T., Samant S.S., and Bussoletti J.E. A higher-order boundary treatment for Cartesian-grid methods. Journal of Computational Physics 92 (1991) 1-66
12. M.J. Berger, R.J. Leveque, An adaptive Cartesian mesh algorithm for the Euler equations in arbitrary geometries, Paper 1989-1930, AIAA, 1989.
13. S.L. Karman, Splitflow: A 3d unstructured Cartesian/prismatic grid CFD code for complex geometries, Paper 1995-0343, AIAA, 1995.
14. S.M. Murman, M.J. Aftosmis, S.E. Rogers, Characterization of space shuttle ascent debris aerodynamics using CFD methods, Paper 2005-1223, AIAA, 2005.
15. M. Nemec, M. Aftosmis, S. Murman, T. Pulliam, Adjoint formulation for an embedded-boundary Cartesian method, Paper 2005-0877, AIAA, 2005.
16. M.J. Aftosmis, M.J. Berger, J.J. Alonso, Applications of a Cartesian mesh boundary-layer approach for complex configurations, Paper 2006-0652, AIAA, 2006.
17. K.J. Fidkowski, D.L. Darmofal, Output-based adaptive meshing using triangular cut cells, M.I.T. Aerospace Computational Design Laboratory Report, ACDL TR-06-2, 2006.
18. Pierce N.A., and Giles M.B. Adjoint recovery of superconvergent functionals from PDE approximations. SIAM Review 42 2 (2000) 247-264
19. Becker R., and Rannacher R. An optimal control approach to a posteriori error estimation in finite element methods. In: Iserles A. (Ed). Acta Numerica (2001), Cambridge University Press
20. J.D. Müller, M.B. Giles, Solution adaptive mesh refinement using adjoint error analysis, Paper 2001-2550, AIAA, 2001.
21. Giles M.B., and Süli E. Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality. Acta Numerica 11 (2002) 145-236
22. Hartmann R., and Houston P. Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations. Journal of Computational Physics 183 2 (2002) 508-532
23. Barth T., and Larson M. A posteriori error estimates for higher order Godunov finite volume methods on unstructured meshes. In: Herban R., and Kröner D. (Eds). Finite Volumes for Complex Applications III (2002), Hermes Penton, London
24. Venditti D.A., and Darmofal D.L. Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows. Journal of Computational Physics 187 1 (2003) 22-46
25. Venditti D.A., and Darmofal D.L. Grid adaptation for functional outputs: application to two-dimensional inviscid flows. Journal of Computational Physics 176 1 (2002) 39-40
26. Houston P., and Süli E. A note on the design of hp-adaptive finite element methods for elliptic partial differential equations. Computational Methods in Applied Mechanical Engineering 194 (2005) 229-243
27. Peraire J., Vahdati M., Morgan K., and Zienkiewicz O.C. Adaptive remeshing for compressible flow computations. Journal of Computational Physics 72 (1987) 449-466
28. Habashi W.G., Dompierre J., Bourgault Y., Ait-Ali-Yahia D., Fortin M., and Vallet M.-G. Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part I: General principles. International Journal of Numerical Methods in Fluids 32 (2000) 725-744
29. Castro-Diaz M.J., Hecht F., Mohammadi B., and Pironneau O. Anisotropic unstructured mesh adaptation for flow simulations. International Journal for Numerical Methods in Fluids 25 (1997) 475-491
30. Solin P., and Demkowicz L. Goal-oriented hp-adaptivity for elliptic problems. Computational Methods in Applied Mechanical Engineering 193 (2004) 449-468
31. Zienkiewicz O., and Zhu J.Z. Adaptivity and mesh generation. International Journal for Numerical Methods in Engineering 32 (1991) 783-810
32. Rannacher R. Adaptive Galerkin finite element methods for partial differential equations. Journal of Computational and Applied Mathematics 128 (2001) 205-233
33. Brandt A. Guide to Multigrid Development (1982), Springer-Verlag
34. L. Formaggia, S. Micheletti, S. Perotto, Anisotropic mesh adaptation with applications to CFD problems, in: H.A. Mang, F.G. Rammerstorfer, J. Eberhardsteiner (Eds.), Fifth World Congress on Computational Mechanics, Vienna, Austria, 2002.
35. D.A. Venditti, Grid Adaptation for Functional Outputs of Compressible Flow Simulations, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 2002.
36. H. Borouchaki, P. George, F. Hecht, P. Laug, E. Saltel, Mailleur bidimensionnel de Delaunay gouverné par une carte de métriques. Partie I: Algorithmes, INRIA-Rocquencourt, France. Tech Report No. 2741, 1995.