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Original Articles

A novel three-level time-split MacCormack scheme for two-dimensional evolutionary linear convection-diffusion-reaction equation with source term

Pages 47-74 | Received 26 Jul 2019, Accepted 01 Feb 2020, Published online: 16 Feb 2020

References

  • F.A. Anderson, R.H. Pletcher, and J.C. Tannehill, Computational Fluid Mechanics and Heat Transfer, 2nd ed., Taylor and Francis, New York, 1997.
  • R. Codina and J. blasco, Analysis of a stabilized finite element approximation of the transcient convective-diffusive-reactive equation using orthogonal subscales, Comput. Vis. Sci. 4 (2002), pp. 167–174. doi: 10.1007/s007910100068
  • M.J. Crochet, A.R. Davies, and K. Walters, Numerical Simulations of Non-Newtonian Flow, Elsevier, New York, 1984.
  • J. Douglas and T.F. Russell, Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Numer. Anal. 19 (1982), pp. 871–885. doi: 10.1137/0719063
  • J. Frutos, A.B. Garcia, and J. Novo, Local error estimates for the SUPG method applied to evolutionary convection-reaction-diffusion equations, J. Sci. Comput. 66 (2016), pp. 528–554. doi: 10.1007/s10915-015-0035-2
  • I. Harari and T.J.R. Hughes, Finite element methods for the Helmholtz equation in an exterior domain: Model problem, Comput. Methods Appl. Mech. Eng. 87 (1991), 59 pages. doi: 10.1016/0045-7825(91)90146-W
  • A. Huerta and J. Donea, Time-accurate solution of stabilized convection-reaction-diffusion equations, Commun. Numer. Methods Eng. 18 (2002), pp. 565–573. doi: 10.1002/cnm.517
  • V. John and J. Novo, On (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations, J. Comput. Phys. 231 (2012), pp. 1570–1585. doi: 10.1016/j.jcp.2011.10.025
  • P.D. Lax and B. Wendroff, Systems of conservation laws, Comm. Pure Appl. Math. 13 (1960), pp. 217–237. doi: 10.1002/cpa.3160130205
  • L. Leboucher, Monotone scheme and boundary conditions for finite volume simulation of magnetohynamic internal flows at high Hartmann number, J. Comput. Phys. 150 (1999), p. 181. doi: 10.1006/jcph.1998.6170
  • Q. Lingzhi, C. Huiping, G. Rui, and F. Xinlong, The characteristic variational muliscale method for convection-dominated convection-diffusion-reaction problems, Int. J. Heat Mass Transf. 572 (2014), pp. 461–469.
  • R.W. MacCormack, An efficient numerical method for solving the time-dependent compressible Navier-Stokes equations at high Reynolds numbers, NASA TM, 1976, pp. 73–129.
  • R.W. MacCormack, A numerical method for solving the equations of compressible viscous-flows, AIAA Paper 81-0110, St. Louis, Missouri, 1981.
  • R.W. MacCormack and A.J. Paullay, Computational efficiency achieved by time splitting of finite difference operators, AIAA Paper 72-154, San Diego, California, 1972.
  • C. Man and C.W. Tsai, A high order predictor-corrector scheme for two-dimensional advection-diffusion equation, Int. J. Numer. Methods Fluids 56(4) (2008), pp. 401–418. doi: 10.1002/fld.1528
  • F.T. Namio, E. Ngondiep, R. Ntchantcho, Mathematical models of complete shallow water equations with source terms, stability analysis of Lax-Wendroff scheme. J. Theor. Comput. Sci. 2(132) (2015), pp. 1–10. doi:10.4172/2376-130X.1000132.
  • E. Ngondiep, Asymptotic growth of the spectral radii of collocation matrices approximating elliptic boundary problems, Int. J. Appl. Math. Comput. 4 (2012), pp. 199–219, 20 pages.
  • E. Ngondiep, Long time stability and convergence rate of MacCormack rapid solver method for nonstationary Stokes-Darcy problem, Comput. Math. Appl. 75 (2018), pp. 3663–3684, 22 pages. doi: 10.1016/j.camwa.2018.02.024
  • E. Ngondiep, A three-level explicit time-split MacCormack method for 2D nonlinear reaction-diffusion equations, preprint (2019). Available at http://arxiv.org/abs/1903.10877.
  • E. Ngondiep, Error estimate of MacCormack rapid solver method for 2D incompressible Navier-Stokes problems, preprint (2019). Available at http://arxiv.org/abs/1903.10857.
  • E. Ngondiep, Long time unconditional stability of a two-level hybrid method for nonstationary incompressible Navier-Stokes equations, J. Comput. Appl. Math. 345 (2019), pp. 501–514, 14 pages. doi: 10.1016/j.cam.2018.05.023
  • E. Ngondiep, Stability analysis of MacCormack rapid solver method for evolutionary Stokes-Darcy problem, J. Comput. Appl. Math. 345 (2019), pp. 269–285, 17 pages. doi: 10.1016/j.cam.2018.06.034
  • E. Ngondiep, An efficient three-level explicit time-split method for solving 2D heat conduction equations, submitted for publication.
  • E. Ngondiep, Analysis of stability and convergence rate of a three-level time-split method for two-dimensional unsteady convection-diffusion equation, submitted for publication.
  • E. Ngondiep, R. Alqahtani, and J.C. Ntonga, Stability analysis and convergence rate of MacCormack scheme for complete shallow water equations with source terms, preprint (2019). Available at http://arxiv.org/abs/1903.11104.
  • T.E. Tezduyar, Y.J. Park, and H.A. Deans, Finite element procedures for time-dependent convection-diffusion-reaction systems, Int. J. Numer. Methods Fluids 7 (1987), pp. 1013–1033. doi: 10.1002/fld.1650071003

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