A comparative study of Lagrangian methods using axisymmetric and deforming blobs

SIAM Journal on Scientific Computing

Volumn 27, Issue 4, 2006, Pages 1168-1180

  Rossi, Louis F ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

Computational fluid dynamics; Convection diffusion; Deforming blobs; Particle methods

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; MATHEMATICAL MODELS; PARTICLE SIZE ANALYSIS; PERFORMANCE; PROBLEM SOLVING;

CONVECTION-DIFFUSION; DEFORMING BLOBS; ELLIPSOIDAL DISTRIBUTION; PARTICLE METHODS;

LAGRANGE MULTIPLIERS;

EID: 33746087617     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/030600679     Document Type: Article

References (25)

1. C. ANDERSON, A method of local corrections for computing the velocity field due to a distribution of vortex blobs, J. Comput. Phys., 62 (1986), pp. 111-123.
2. G.-H. COTTET AND P. D. KOUMOUTSAKOS, Vortex Methods: Theory and Practice, Cambridge University Press, Cambridge, New York, 2000.
3. C. I. DRAGHICESCU, A fast algorithm for vortex blob interactions, J. Comput. Phys., 116 (1995), pp. 69-78.
4. C. GREENGARD, The core spreading vortex method approximates the wrong equation, J. Comput. Phys., 61 (1985), pp. 345-348.
5. L. GREENGARD AND V. ROKHLIN, A fast algorithm for particle simulations, J. Comput. Phys., 73 (1987), pp. 325-348.
6. T. KIDA, Theoretical and numerical results of a deterministic two-dimensional vortex method, Sādhanā, 23 (1998), pp. 419-441.
7. T. KIDA AND T. NAKAJIMA, Core spreading vortex methods in two-dimensional viscous flows, Comput. Methods Appl. Mech. Engrg., 160 (1998), pp. 273-298.
8. T. KIDA, T. NAKAJIMA, AND H. SUEMITSU, Second order core spreading vortex method in two-dimensional viscous flows, JSME Int. J. Series B, 41 (1998), pp. 441-446.
9. -1) time step restriction, J. Comput. Phys., 104 (1993), pp. 457-469.
10. B. LEGRAS AND D. G. DRITSCHEL, A comparison of the contour surgery and pseudo-spectral methods, J. Comput. Phys., 104 (1993), pp. 287-302.
11. A. LEONARD, Large-eddy simulation of chaotic convection and beyond, in 35th Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, 1997.
12. J. S. MARSHALL AND J. R. GRANT, A method for determining the velocity induced by highly anisotropic vorticity blobs, J. Comput. Phys., 126 (1996), pp. 286-298.
13. J. S. MARSHALL, J. R. GRANT, A. A. GOSSLER, AND S. A. HUYER, Vorticity transport on a Lagrangian tetrahedral mesh, J. Comput. Phys., 161 (2000), pp. 85-113.
14. E. MEIBURG, Incorporation and test of diffusion and strain effects in the two-dimensional vortex blob technique, J. Comput. Phys., 82 (1989), pp. 85-93.
15. P. MOELEKER AND A. LEONARD, Lagrangian methods for the tensor-diffusivity subgrid model, J. Comput. Phys., 167 (2001), pp. 1-21.
16. W. H. PRESS, S. A. TEUKOLSKY, W. T. VETTERING, AND B. P. FLANNERY, Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, Cambridge, UK, 1992.
17. L. F. ROSSI, Resurrecting core spreading vortex methods: A new scheme that is both deterministic and convergent, SIAM J. Sci. Comput., 17 (1996), pp. 370-397.
18. L. F. ROSSI, Merging computational elements in vortex simulations, SIAM J. Sci. Comput., 18 (1997), pp. 1014-1027.
19. L. F. ROSSI, High Order Vortex Methods with Deforming Elliptical Gaussian Blobs 1: Derivation and Validation, Technical Report 2001-11, University of Delaware, Newark, DE, 2002.
20. L. F. ROSSI, Achieving high-order convergence rates with deforming basis functions, SIAM J. Sci. Comput., 26 (2005), pp. 885-906.
21. L. F. Rossi, J. F. LINGEVITCH, AND A. J. BERNOFF, Quasi-steady monopole and tripole attractors for relaxing vortices, Phys. Fluids, 9 (1997), pp. 2329-2339.
22. Z.-H. TENG, Elliptic-vortex method for incompressible flow at high Reynolds number, J. Comput. Phys., 46 (1982), pp. 54-68.
23. Z.-H. TENG, Variable-elliptical-vortex method for incompressible flow simulation, J. Comput. Math., 4 (1986), pp. 255-262.
24. Z.-H. TENG, L.-A. YING, AND P. ZHANG, Convergence of the variable-elliptic-vortex method for Euler equations, SIAM J. Numer. Anal., 32 (1995), pp. 754-774.
25. L. N. TREFETHEN, Spectral Methods in MATLAB, SIAM, Philadelphia, 2000.