A cartesian embedded boundary method for the compressible Navier-Stokes equations

Journal of Scientific Computing

Volumn 41, Issue 1, 2009, Pages 94-117

  Kupiainen, Marco ^a   Sjögreen, Björn ^b  

^a SORBONNE UNIVERSITÉ   (France)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Compressible fluids; Embedded boundary; Finite difference scheme; Navier Stokes equations

Indexed keywords

CARTESIANS; COMPRESSIBLE FLUID FLOW; COMPRESSIBLE FLUIDS; COMPRESSIBLE NAVIER-STOKES EQUATIONS; DISCRETIZATIONS; EMBEDDED BOUNDARY; EMBEDDED BOUNDARY METHODS; EMBEDDED OBJECT; FINITE DIFFERENCE SCHEME; PARALLEL COMPUTER; PETERSON; SECOND ORDERS;

DIFFERENCE EQUATIONS; EULER EQUATIONS; FLUID DYNAMICS; FRICTION; SKIN; VISCOUS FLOW; WAVE EQUATIONS;

NAVIER STOKES EQUATIONS;

EID: 69949109555     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-009-9289-x     Document Type: Article

References (29)

1. S. Abarbanel A. Ditkowski 1997 Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes J. Comput. Phys. 133 279 288
2. S. Abarbanel A. Ditkowski 1999 Multi-dimensional asymptotically stable finite difference schemes for the advection-diffusion equation Comput. Fluids 28 481 510
3. S. Abarbanel A. Ditkowski A. Yefet 2006 Bounded error schemes for the wave equation on complex domains J. Sci. Comput. 26 67 81
4. M.J. Berger C. Helzel R.J. LeVeque 2003 H-box methods for the approximation of hyperbolic conservation laws on irregular grids SIAM J. Numer. Anal. 41 893 918
5. D. Calhoun R.J. LeVeque 2000 A Cartesian grid finite-volume method for the advection-diffusion equation in irregular geometries J. Comput. Phys. 157 143 180
6. W.J. Coirier K.G. Powell 1995 An accuracy assessment of Cartesian-mesh approaches for the Euler equations J. Comput. Phys. 117 121 131
7. P. Colella D.T. Graves B.J. Keen D. Modiano 2006 A Cartesian grid embedded boundary method for hyperbolic conservation laws J. Comput. Phys. 211 347 366
8. L. Ferm P. Lötstedt 2004 Accurate and stable grid interfaces for finite volume methods Appl. Numer. Math. 49 407 224
9. H. Forrer R. Jeltsch 1998 A higher-order boundary treatment for Cartesian-grid methods J. Comput. Phys. 140 259 277
10. B. Gustafsson H.-O. Kreiss A. Sundström 1972 Stability theory of difference approximations for mixed initial boundary value problems. ii Math. Comput. 26 119 649 686
11. Helzel, C.: Accurate methods for hyperbolic problems on embedded boundary grids. In: Asakura, F., Aiso, H., Kawashima, S., Matsumura, A., Nishibata, S., Nishihara, K. (eds.) Hyperbolic Problems, Theory, Numerics and Applications. Yokohama Publishers, Yokohama (2006)
12. C. Helzel M.J. Berger R.J. LeVeque 2005 A high-resolution rotated grid method for conservation laws with embedded geometries SIAM J. Sci. Comput. 26 785 809
13. Knuth, D.E.: Sorting and Searching, 2nd edn. The Art of Computer Programming, vol. 3. Addison-Wesley, Reading (1998)
14. H.-O. Kreiss N.A. Peterson 2006 A second order accurate embedded boundary method for the wave equation with Dirichlet data SIAM J. Sci. Comput. 27 1141 1167
15. H.-O. Kreiss N.A. Peterson J. Yström 2002 Difference approximations for the second order wave equation SIAM J. Numer. Anal. 40 5 1940 1967
16. H.-O. Kreiss N.A. Peterson J. Yström 2004 Difference approximations of the Neumann problem for the second order wave equation SIAM J. Numer. Anal. 42 1292 1323
17. D. Michelson 1987 Convergence theorem for difference approximations of hyperbolic quasi-linear initial-boundary value problems Math. Comput. 49 445 459
18. R. Mittal G. Iaccarino 2005 Immersed boundary methods Annu. Rev. Fluid. Mech. 37 239 261
19. Olsen, O.K.: Embedded boundary method for Navier-Stokes equations. Master's Thesis, Royal Institute of Technology (2005)
20. R.B. Pember J.B. Bell P. Colella W.Y. Crutchfield M.L. Welcome 1995 An adaptive Cartesian grid method for unsteady compressible flow in irregular regions J. Comput. Phys. 120 278 304
21. C.S. Peskin 2002 The immersed boundary method Acta Numer. 11 479 517
22. Petersson, A.: http://www.andrew.cmu.edu/user/sowen/software/xcog.html
23. J.J. Quirk 1994 An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies Comput. Fluids 23 1 125 142
24. B. Sjögreen H.C. Yee 2004 Multiresolution wavelet based adaptive numerical dissipation control for high order methods J. Sci. Comput. 20 2 211 255
25. B. Sjögreen N.A. Peterson 2007 A Cartesian embedded boundary method for hyperbolic conservation laws Commun. Comput. Phys. 2 1199 1219
26. B. Sjögreen H. Yee 2009 Variable high order multiblock overlapping grid methods for mixed steady and unsteady multiscale viscous flows Commun. Comput. Phys. 5 730 744
27. Skogqvist, P.: High order adaptive difference methods for combustible flows. Ph.D. Thesis, Royal Institute of Technology, Stockholm, Sweden (2001)
28. G. van Albada B. van Leer J.W.W. Roberts 1982 A comparative study of computational methods in cosmic gas dynamics Astron. Astrophys. 108 76 84
29. H. Yee B. Sjögreen 2007 Development of low dissipative high order filter schemes for multiscale Navier-Stokes/MHD systems J. Comput. Phys. 225 1 910 934