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Original Articles

Partial semi-coarsening multigrid method based on the HOC scheme on nonuniform grids for the convection–diffusion problems

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Pages 2356-2372 | Received 11 May 2015, Accepted 27 Sep 2016, Published online: 28 Feb 2017

References

  • A. Brandt, Multi-level adaptive solutions to boundary-value problems, Math. Comput. 31 (1977), pp. 333–390. doi: 10.1090/S0025-5718-1977-0431719-X
  • G.F. Carey and W.F. Spotz, Higher-order compact mixed methods, Commun. Numer. Methods Eng. 13 (1997), pp. 553–564. doi: 10.1002/(SICI)1099-0887(199707)13:7<553::AID-CNM80>3.0.CO;2-O
  • Q.C. Chen, Z. Gao, and Z. Yang, A perturbational h4 exponential finite difference scheme for the convective diffusion equation, J. Comput. Phys. 104 (1993), pp. 129–139. doi: 10.1006/jcph.1993.1015
  • R. Dai and Y. Wang, Effects of different high order compact computations for solving boundary layer problems on non-uniform grids, J. Comput. Intell. Electron. Syst. 3 (3) (2014), pp. 200–211. doi: 10.1166/jcies.2014.1091
  • H.F. Ding and Y.X. Zhang, A new difference scheme with high accuracy and absolute stability for solving convection–diffusion equations, J. Comput. Appl. Math. 230 (2009), pp. 600–606. doi: 10.1016/j.cam.2008.12.015
  • Y. Ge, Multigrid method and fourth-order compact difference discretization scheme with unequal meshsizes for 3D Poisson equation, J. Comput. Phys. 229 (2010), pp. 6381–6391. doi: 10.1016/j.jcp.2010.04.048
  • Y. Ge and F. Cao, Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems, J. Comput. Phys. 230 (2011), pp. 4051–4070. doi: 10.1016/j.jcp.2011.02.027
  • Y. Ge and F. Cao, A High Order Compact Difference Scheme and Multigrid Method for Solving the 3D Convection Diffusion Equation on Non-uniform Grids, 2012 International Conference on Computational and Information Sciences, Chongqing, August 17–19, 2012, pp. 714–717.
  • L. Ge and J. Zhang, Accuracy, robustness, and efficiency comparison in iterative computation of convection diffusion equation with boundary layers, Numer. Methods Partial Differ. Equ. 16 (2000), pp. 379–394. doi: 10.1002/1098-2426(200007)16:4<379::AID-NUM3>3.0.CO;2-I
  • L. Ge and J. Zhang, High accuracy iterative solution of convection diffusion equation with boundary layers on nonuniform grids, J. Comput. Phys. 171 (2001), pp. 560–578. doi: 10.1006/jcph.2001.6794
  • Y. Ge, F. Cao, and J. Zhang, A transformation-free HOC scheme and multigrid method for solving the 3D Poisson equation on nonuniform grids, J. Comput. Phys. 234 (2013), pp. 199–216. doi: 10.1016/j.jcp.2012.09.034
  • M.M. Gupta and J. Zhang, High accuracy multigrid solution of the 3D convection–diffusion equation, Appl. Math. Comput. 113 (2000), pp. 249–274.
  • M.M. Gupta, R.P. Manohar, and J.W. Stephenson, A single cell high order scheme for the convection–diffusion equation with variable coefficients, Int. J. Numer. Methods Fluids 4 (1984), pp. 641–651. doi: 10.1002/fld.1650040704
  • M.M. Gupta, J. Kouatchou, and J. Zhang, Comparison of second- and fourth-order discretizations for multigrid Poisson solvers, J. Comput. Phys. 132 (1997), pp. 226–232. doi: 10.1006/jcph.1996.5466
  • M.M. Gupta, J. Kouatchou, and J. Zhang, A compact multigrid solver for convection–diffusion equations, J. Comput. Phys. 132 (1997), pp. 123–129. doi: 10.1006/jcph.1996.5627
  • W. Hackbusch and U. Trottenberg, Multigrid Methods, Springer-Verlag, Berlin, 1982.
  • J.C. Kalita, A.K. Dass, and D.C. Dalal, A transformation-free HOC scheme for steady convection–diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004), pp. 33–53. doi: 10.1002/fld.621
  • S. Karaa, High-order approximation of 2D convection–diffusion equation on hexagonal grids, Numer. Methods Partial Differ. Equ. 22 (2006), pp. 1238–1246. doi: 10.1002/num.20149
  • S. Karaa and J. Zhang, Convergence and performance of iterative methods for solving variable coefficient convection–diffusion equation with a fourth-order compact difference scheme, Comput. Math. Appl. 44 (3) (2002), pp. 457–479. doi: 10.1016/S0898-1221(02)00162-1
  • C. Liu, Multilevel adaptive methods in computational fluid dynamics, Ph.D. thesis, University of Colorado at Denver, 1989.
  • C. Liu and Z. Liu, Multigrid mapping and box relaxation for simulation of the whole process of flow transition in 3D boundary layers, J. Comput. Phys. 119 (1995), pp. 325–341. doi: 10.1006/jcph.1995.1138
  • W.A. Mulder, A new multigrid approach to convection problems, J. Comput. Phys. 83 (1989), pp. 303–323. doi: 10.1016/0021-9991(89)90121-6
  • A.C. Radhakrishna Pillai, Fourth-order exponential finite difference methods for boundary value problems of convective diffusion type, Int. J. Numer. Methods Fluids 37 (2001), pp. 87–106. doi: 10.1002/fld.167
  • W.F. Spotz and G.F. Carey, Formulation and experiments with high-order compact schemes for nonuniform grids, Int. J. Numer. Methods Heat Fluid Flow 8 (1998), pp. 288–303. doi: 10.1108/09615539810206357
  • Z.F. Tian and S.Q. Dai, High-order compact exponential finite difference methods for convection–diffusion type problems, J. Comput. Phys. 220 (2007), pp. 952–974. doi: 10.1016/j.jcp.2006.06.001
  • Z.F. Tian and Y.B. Ge, A fourth-order compact ADI method for solving two-dimensional unsteady convection–diffusion problems, J. Comput. Appl. Math. 198 (2007), pp. 268–286. doi: 10.1016/j.cam.2005.12.005
  • Y. Wang and J. Zhang, Fast and robust sixth-order multigrid computation for the three-dimensional convection–diffusion equation, J. Comput. Appl. Math. 234 (2010), pp. 3496–3506. doi: 10.1016/j.cam.2010.05.022
  • Y. Wang, S. Yu, R. Dai, and J. Zhang, A 15-point high-order compact scheme with multigrid computation for solving 3D convection diffusion equations, Int. J. Comput. Math. 92 (2) (2015), pp. 411–423. doi: 10.1080/00207160.2014.893296
  • P. Wesseling, An Introduction to Multigrid Methods, Wiley, Chichester, 1992.
  • J. Zhang, Accelerated multigrid high accuracy solution of the convection–diffusion equation with high Reynolds number, Numer. Meth. Partial Differ. Equ. 13 (1997), pp. 77–92. doi: 10.1002/(SICI)1098-2426(199701)13:1<77::AID-NUM6>3.0.CO;2-J
  • J. Zhang, An explicit fourth-order compact finite difference scheme for three-dimensional convection–diffusion equation, Commun. Numer. Methods Eng. 14 (1998), pp. 209–218. doi: 10.1002/(SICI)1099-0887(199803)14:3<209::AID-CNM139>3.0.CO;2-P
  • J. Zhang, Fast and high accuracy multigrid solution of the three dimensional Poisson equation, J. Comput. Phys. 143 (1998), pp. 449–461. doi: 10.1006/jcph.1998.5982
  • J. Zhang, On convergence and performance of iterative methods with fourth-order compact schemes, Numer. Methods Partial Differ. Equ. 14 (2) (1998), pp. 263–280. doi: 10.1002/(SICI)1098-2426(199803)14:2<263::AID-NUM8>3.0.CO;2-M
  • J. Zhang, Multigrid method and fourth-order compact scheme for 2D Poisson equation with unequal mesh-size discretization, J. Comput. Phys. 179 (2002), pp. 170–179. doi: 10.1006/jcph.2002.7049
  • J. Zhang, H.W. Sun, and J.J. Zhao, High order compact scheme with multigrid local mesh refinement procedure for convection diffusion problems, Comput. Methods Appl. Mech. Eng. 191 (2002), pp. 4661–4674. doi: 10.1016/S0045-7825(02)00398-5

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