Achieving high-order convergence rates with deforming basis functions

SIAM Journal on Scientific Computing

Volumn 26, Issue 3, 2005, Pages 885-906

  Rossi, Louis F ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

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

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; DEFORMATION; DIFFUSION; FUNCTIONS; HEAT CONVECTION; INCOMPRESSIBLE FLOW; LAGRANGE MULTIPLIERS; ROTATION;

BASIS FUNCTIONS; CONVECTION-DIFFUSION; DEFORMING BLOBS; PARTICLE METHODS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 19644388175     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827503425286     Document Type: Article

References (35)

1. J. T. BEALE AND A. MAJDA, Rates of convergence for viscous splitting of the Navier-Stokes equations, Math. Comp., 37 (1981), pp. 243-259.
2. J. T. BEALE AND A. MAJDA, Vortex methods II: Higher order accuracy in two and three dimensions, Math. Comp., 39 (1982), pp. 29-52.
3. J. T. BEALE AND A. MAJDA, High order accurate vortex methods with explicit kernels, J. Comput. Phys., 58 (1985), pp. 188-205.
4. G.-H. COTTET AND P. D. KOUMOUTSAKOS, Vortex Methods: Theory and Practice, Cambridge University Press, Cambridge, UK, 2000.
5. A. GHARAKHANI, A Higher Order Vorticity Redistribution Method for 3-D Diffusion in Free Space, Technical report SAND2000-2505, Sandia National Laboratories, Albuquerque, NM, 2000.
6. A. GHARAKHANI, Grid-Free Simulation of 3-D Vorticity Diffusion by a High-Order Vorticity Redistribution Method, Technical report AIAA-2001-2640, American Institute of Aeronautics and Astronautics, 2001.
7. C. GREENGARD, The core spreading vortex method approximates the wrong equation, J. Comput. Phys., 61 (1985), pp. 345-348.
8. L. GREENGARD AND V. ROKHLIN, A fast algorithm for particle simulations, J. Comput. Phys., 73 (1987), pp. 325-348.
9. T. KIDA, Theoretical and numerical results of a deterministic two-dimensional vortex method, Sādhanā, 23 (1998), pp. 419-441.
10. T. KIDA AND T. NAKAJIMA, Core spreading vortex methods in two-dimensional viscous flows, Comput. Methods Appl. Mech. Engrg., 160 (1998), pp. 273-298.
11. T. KIDA, T. NAKAJIMA, AND H. SUEMITSU, Second order core spreading vortex method in two-dimensional viscous flows, JSME Internat. J. Fluids &: Therm. Engrg. B, 41 (1998), pp. 441-446.
12. A. LEONARD, Vortex methods for flow simulation, J. Comput. Phys., 37 (1980), pp. 289-335.
13. A. LEONARD, AIAA 97-0204: Large-eddy simulation of chaotic convection and beyond, in Proceedings of the 35th Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, 1997, pp. 1-8.
14. P. LINZ, Theoretical Numerical Analysis, John Wiley, New York, 1979.
15. J. S. LOWENGRUB AND M. J. SHELLEY, Smooth grid methods for the vorticity formulation of the Euler equations, in Vortex Dynamics and Vortex Methods, Lectures Appl. Math. 28, AMS, Providence, RI, 1991, pp. 423-432.
16. J. S. LOWENGRUB, M. J. SHELLEY, AND B. MERRIMAN, High-order and efficient methods for the vorticity formulation of the Euler equations, SIAM J. Sci. Comput., 14 (1993), pp. 1107-1142.
17. Z. Y. Lu AND T. J. Ross, Diffusing-vortex numerical scheme for solving incompressible Navier-Stokes equations, J. Comput. Phys., 95 (1991), pp. 400-435.
18. 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.
19. 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.
20. P. MOELEKER AND A. LEONARD, Lagrangian methods for the tensor-diffusivity subgrid model, J. Comput. Phys., 167 (2001), pp. 1-21.
21. J. J. MONAGHAN, Why particle methods work, SIAM J. Sci. Statist. Comput., 3 (1982), pp. 422-433.
22. J. J. MONAGHAN, Smoothed particle hydrodynamics, Ann. Rev. Astron. Astrophys., 30 (1992), pp. 543-574.
23. A. OJIMA AND K. KAMEMOTO, Numerical simulation of unsteady flow around three dimensional bluff bodies by an advanced vortex method, JSME Int. J. Fluids & Therm. Mixing B, 43 (2000), pp. 127-135.
24. T. A. PRICKETT, T. G. NAYMIK, AND C. G. LONNQUIST, A "random walk" solute transport model for selected groundwater quality evaluations, Illinois Water Survey Bull., 65 (1981), p. 103.
25. 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.
26. L. F. ROSSI, Merging computational elements in vortex simulations, SIAM J. Sci. Comput., 18 (1997), pp. 1014-1027.
27. 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.
28. 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.
29. D. SHIELS, Simulation of Controlled Bluff Body Flow with a Viscous Vortex Method, Ph.D. thesis, California Institute of Technology, Pasadena, CA, 1998.
30. J. C. STRIKWERDA, Finite Difference Schemes and Partial Difference Equations, Wadsworth and Brooks/Cole Advanced Books and Software, New York, 1989.
31. Z.-H. TENG, Elliptic-vortex method for incompressible flow at high Reynolds number, J. Comput. Phys., 46 (1982), pp. 54-68.
32. Z.-H. TENG, Variable-elliptical-vortex method for incompressible flow simulation, J. Comput. Math., 4 (1986), pp. 255-262.
33. 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.
34. X.-H. WEN AND C.-S. KUNG, Implementation of the constant displacement scheme in random walk, Computers & Geosciences, 22 (1996), pp. 369-377.
35. G. S. WINCKLEMANS AND A. LEONARD, Contributions to vortex particle methods for the computation of three-dimensional incompressible unsteady flows, J. Comput. Phys., 109 (1993), pp. 247-273.