[1] |
Steger J L, Warming R F.Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods[J].J Comp Phys,1981,40(2):263-293. doi: 10.1016/0021-9991(81)90210-2
|
[2] |
Chung T J.Finite Element Analysis in Fluid Dynamics[M].New York: McGraw-Hill Publ, 1978.
|
[3] |
Baker A J, Kim J W.A Taylor weak-statement algorithm for hyperbolic conservation laws[J].Internat J Numer Methods Fluids,1987,7(5):489-520. doi: 10.1002/fld.1650070505
|
[4] |
Patankar S V. Numerical Heat Transfer and Fluid Flow[M].Washington D C: Hemisphere, 1980.
|
[5] |
Wang Z J, Srinivasan K.An adaptive Cartesian grid generation method for ‘dirty' geometry[J].Internat J Numer Methods Fluids, 2002,39(8):703-717. doi: 10.1002/fld.344
|
[6] |
Monaghan J J. An introduction to SPH[J].Comput Physics Communications,1988,48(1):89-96. doi: 10.1016/0010-4655(88)90026-4
|
[7] |
Aluru N R, Li G.Finite cloud method: a true meshless technique based on a fixed reproducing kernel approximation[J]. Internat J Numer Methods Engrg,2001,50(10):2373-2410. doi: 10.1002/nme.124
|
[8] |
Liu W K, Jun S, Zhang Y F.Reproducing kernel particle methods[J].Internat J Numer Methods Fluids, 1995, 30(8/9):1081-1106.
|
[9] |
Nayroles B, Touzot G, Villon P.Generalizing the FEM: diffuse approximation and diffuse elements[J].Computational Mechanics,1992,10(5):307-318. doi: 10.1007/BF00364252
|
[10] |
Belytschko T, Lu Y Y, Gu L.Element-free Galerkin methods[J].Internat J Numer Methods Engrg,1994,37(2):229-256. doi: 10.1002/nme.1620370205
|
[11] |
Duarte C A, Oden J T.A hp adaptive method using clouds[J]. Comput Methods Appl Mech Engrg,1996, 139(1/4):237-262. doi: 10.1016/S0045-7825(96)01085-7
|
[12] |
Kansa E J.Multiquadrics —a scattered data approximation scheme with applications to computational fluid-dynamics —Ⅰ surface approximations and partial derivative estimates[J].Computers Math Appl,1990, 19(8/9):127-145.
|
[13] |
Kansa E J.Multiquadrics —a scattered data approximation scheme with applications to computational fluid-dynamics —Ⅱ solutions to parabolic, hyperbolic, and elliptic partial differential equations[J]. Computers Math Appl,1990,19(8/9):147-161.
|
[14] |
Shu C, Ding H, Yeo K S.Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations[J].Comput Methods Appl Mech Engrg,2003,192(7/8):941-954. doi: 10.1016/S0045-7825(02)00618-7
|
[15] |
Li J.A radial basis meshless method for solving inverse boundary value problems[J].Comm Num Meth Eng,2004, 20(1):51-61.
|
[16] |
Ding H, Shu C, Yeo K S,et al.Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method[J].Comput Methods Appl Mech Engrg,2004,193(9/11):727-744. doi: 10.1016/j.cma.2003.11.002
|
[17] |
Ding H, Shu C,Yeo K S,et al.Development of least-square-based two-dimensional finite-difference schemes and their application to simulate natural convection in a cavity[J]. Computers & Fluids, 2004,33(1):137-154.
|
[18] |
Balakrishann N, Deshpande S M.Reconstruction on unstructured meshes with upwind solvers[A].In:Hui W H, Kwok Y K, Chasnov J R,Eds.Proc of the First Asian CFD Conference[C].Hong Kong:Hong Kong University of Science and Technology,1995,359-364.
|
[19] |
Luo D, Joseph D B, Lhner R.A comparison of reconstruction schemes for compressible flows on unstructured grids[A]. In: Hui W H, Kwok Y K, Chasnov J R,Eds.Proc of the First Asian CFD Conference[C].Hong Kong:Hong Kong University of Science and Technology,1995,365-370.
|
[20] |
蔡庆东.各种网络上统一的数值离散方法[J].力学学报,2004,36(4):393-400.
|
[21] |
Schnauer W, Adolph T.How we solve PDEs[J].J Comp Appl Math,2001,131(1/2):473-492. doi: 10.1016/S0377-0427(00)00255-7
|
[22] |
Sridar D, Balakrishnan N.An upwind finite difference scheme for meshless solvers[J].J Comp Phys,2003,189(1): 1-29. doi: 10.1016/S0021-9991(03)00197-9
|
[23] |
Ding H, Shu C, Yeo K S,et al.Numerical simulation of flows around two circular cylinders by mesh-free least square-based finite difference methods[J].Internat J Numer Methods Fluids,2007,53(2):305-332. doi: 10.1002/fld.1281
|
[24] |
Wu W X, Shu C, Wang C M.Computation of modal stress resultants for completely free vibrating plates by LSFD method[J].Journal of Sound and Vibration,2006, 297(3/5):704-726. doi: 10.1016/j.jsv.2006.04.019
|
[25] |
Wang C M, Wu W X, Shu C,et al.LSFD method for accurate vibration modes and modal stress-resultants of freely vibrating plates that model VLFS[J].Computers and Structures,2006,84(31/32): 2329-2339. doi: 10.1016/j.compstruc.2006.08.055
|
[26] |
Wu W X, Shu C,Wang C M.Mesh-free least-squares-based finite difference method for large amplitude free vibration analysis of arbitrarily shaped thin plates[J].Journal of Sound and Vibration, 2008,317(3/5): 955-974. doi: 10.1016/j.jsv.2008.03.050
|