Modified interpolation kernels for treating diffusion and remeshing in vortex methods

Journal of Computational Physics - Tập 213 - Trang 239-263 - 2006
Daehyun Wee1, Ahmed F. Ghoniem1
1Massachusetts Institute of Technology, Department of Mechanical Engineering, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA

Tài liệu tham khảo

Barba, 2005, Advances in viscous vortex methods—meshless spatial adaption based on radial basis function interpolation, International Journal for Numerical Methods in Fluids, 47, 387, 10.1002/fld.811 Chapra, 1988 Chatelain, 2002, Face-centred cubic lattices and particle redistribution in vortex methods, Journal of Turbulence, 3, 1 Chin, 1978, A dispersive analysis for difference schemes: tables of generalized Airy functions, Mathematics of Computation, 32, 1163, 10.1090/S0025-5718-1978-0494982-6 Chorin, 1973, Numerical study of slightly viscous flow, Journal of Fluid Mechanics, 57, 785, 10.1017/S0022112073002016 Cottet, 2000 Cottet, 2000, Vortex methods with spatially varying cores, Journal of Computational Physics, 162, 164, 10.1006/jcph.2000.6531 Cottet, 1990, A particle method to solve the Navier–Stokes system, Numerische Mathematik, 57, 805, 10.1007/BF01386445 Degond, 1989, The weighted particle method for convection–diffusion equations, Part 1: The case of an isotropic diffusion, Mathematics of Computation, 53, 485 Degond, 1989, The weighted particle method for convection–diffusion equations, Part 2: The anisotropic case, Mathematics of Computation, 53, 509 Degond, 1990, A deterministic approximation of diffusion-equations using particles, SIAM Journal on Scientific and Statistical Computing, 11, 293, 10.1137/0911018 Friedlander, 1998 A. Gharakhani, A higher order vorticity redistribution method for 3-D diffusion in free space, Sandia Report, SAND2000-2505, 2000. Ghoniem, 1988, Numerical simulation of a thermally stratified shear layer using the vortex element method, Journal of Computational Physics, 79, 135, 10.1016/0021-9991(88)90008-3 Kida, 1991, Collision of two vortex rings, Journal of Fluid Mechanics, 230, 583, 10.1017/S0022112091000903 Knio, 1990, Numerical study of a three-dimensional vortex method, Journal of Computational Physics, 86, 75, 10.1016/0021-9991(90)90092-F Knio, 1991, Three-dimensional vortex simulation of rollup and entrainment in a shear layer, Journal of Computational Physics, 97, 172, 10.1016/0021-9991(91)90044-L Koumoutsakos, 1997, Inviscid axisymmetrization of an elliptical vortex, Journal of Computational Physics, 138, 821, 10.1006/jcph.1997.5749 Koumoutsakos, 1994, Boundary conditions for viscous vortex methods, Journal of Computational Physics, 113, 52, 10.1006/jcph.1994.1117 Ladyženskaja, 1968 Lakkis, 2003, Axisymmetric vortex method for low Mach number, diffusion-controlled combustion, Journal of Computational Physics, 184, 435, 10.1016/S0021-9991(02)00030-X LeVeque, 1992 Lindsay, 2001, A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow, Journal of Computational Physics, 172, 879, 10.1006/jcph.2001.6862 Lu, 1991, Diffusing-vortex numerical scheme for solving incompressible Navier–Stokes equations, Journal of Computational Physics, 95, 400, 10.1016/0021-9991(91)90283-Q Majda, 2002 Marzouk, 2005, k-means clustering for optimal partitioning and dynamic load balancing of parallel hierarchical N-body simulations, Journal of Computational Physics, 207, 493, 10.1016/j.jcp.2005.01.021 Ploumhans, 2002, Vortex methods for direct numerical simulation of three-dimensional bluff body flows: application to the sphere at Re=300, 500, and 1000, Journal of Computational Physics, 178, 427, 10.1006/jcph.2002.7035 Rosen, 1979, Nonlinear heat conduction in solid H2, Physical Review B, 19, 2398, 10.1103/PhysRevB.19.2398 Rossi, 1996, Resurrecting core spreading vortex methods: a new scheme that is both deterministic and convergent, SIAM Journal of Scientific Computing, 17, 370, 10.1137/S1064827593254397 Rott, 1993, Vortex drift. I: Dynamic interpretation, Physics of Fluids A, 5, 1443, 10.1063/1.858581 Russo, 1992, A deterministic vortex method for the Navier–Stokes equations, Journal of Computational Physics, 108, 84, 10.1006/jcph.1993.1165 S. Shankar, Grid-free redistribution methods for axisymmetric and anisotropic diffusion, Internal Report, Reacting Gas Dynamics Laboratory, Massachusetts Institute of Technology, 1999. Shankar, 1996, A new diffusion procedure for vortex methods, Journal of Computational Physics, 127, 88, 10.1006/jcph.1996.0160 Shariff, 1992, Vortex rings, Annual Review of Fluid Mechanics, 24, 235, 10.1146/annurev.fl.24.010192.001315 S.K. Stanaway, B.J. Cantwell, P.R. Spalart, Navier–Stokes simulations of axisymmetric vortex rings, AIAA Technical Paper, AIAA-88-0318, 1988. S.K. Stanaway, B.J. Cantwell, P.R. Spalart, A numerical study of viscous vortex rings using a spectral method, NASA Technical Memorandum, NASA TM 101041, 1988. Strichartz, 1994 Strikwerda, 1989 Thirifay, 2002, Development of a Lagrangian method for combustion and application to the planar methane air jet diffusion flame, Journal of Turbulence, 3, 1 Trac, 2003, A primer on Eulerian computational fluid dynamics for astrophysics, Publications of the Astronomical Society of the Pacific, 115, 303, 10.1086/367747 Winckelmans, 1993, Contributions to vortex particle methods for the computation of three-dimensional incompressible unsteady flows, Journal of Computational Physics, 109, 247, 10.1006/jcph.1993.1216 Winckelmans, 1996, Application of fast parallel and sequential tree codes to computing three-dimensional flows with the vortex element and boundary element methods, ESAIM Proceedings: Vortex Flows and Related Numerical Methods II, 1, 225, 10.1051/proc:1996039