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Research Article

SUPG-YZβ computation of chemically reactive convection-dominated nonlinear models

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Pages 283-303 | Received 20 Apr 2022, Accepted 03 Aug 2022, Published online: 11 Sep 2022

References

  • B.E. Abali, Computational Reality: Solving Nonlinear and Coupled Problems in Continuum Mechanics, Springer, Singapore, 2016.
  • R.A. Adams and J.J.F. Fournier, Sobolev Spaces, 2nd ed., Pure and Applied Mathematics Vol. 140. Academic Press, Amsterdam, Boston, 2003.
  • B.R. Ahrabi, W.K. Anderson, and J.C. Newman, An adjoint-based hp-adaptive stabilized finite-element method with shock capturing for turbulent flows, Comput. Methods Appl. Mech. Eng. 318 (2017), pp. 1030–1065.
  • R. Araya, J. Aguayo, and S. Muñoz, An adaptive stabilized method for advection-diffusion-reaction equation, J. Comput. Appl. Math. 376 (2020), Article ID 112858.
  • M.I. Azis, Standard-BEM solutions to two types of anisotropic-diffusion convection reaction equations with variable coefficients, Eng. Anal. Bound. Elem. 105 (2019), pp. 87–93.
  • G.R. Barrenechea, V. John, and P. Knobloch, Finite element methods respecting the discrete maximum principle for convection-diffusion equations (2022).
  • M. Bause, Stabilized finite element methods with shock-capturing for nonlinear convection-diffusion-reaction models, in Numerical Mathematics and Advanced Applications 2009, Springer, Berlin, Heidelberg, 2010, pp. 125–133.
  • M. Bause and K. Schwegler, Analysis of stabilized higher-order finite element approximation of nonstationary and nonlinear convection-diffusion-reaction equations, Comput. Methods Appl. Mech. Eng. 209–212 (2012), pp. 184–196.
  • M. Bause and K. Schwegler, Higher order finite element approximation of systems of convection-diffusion-reaction equations with small diffusion, J. Comput. Appl. Math. 246 (2013), pp. 52–64.
  • Y. Bazilevs, V.M. Calo, T.E. Tezduyar, and T.J.R. Hughes, YZβ discontinuity capturing for advection-dominated processes with application to arterial drug delivery, Int. J. Numer. Methods Fluids 54(6-8) (2007), pp. 593–608.
  • A.N. Brooks and T.J.R. Hughes, Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations, Comput. Methods Appl. Mech. Eng. 32 (1982), pp. 199–259.
  • M.P. Bruchhäuser, K. Schwegler, and M. Bause, Numerical study of goal-oriented error control for stabilized finite element methods, in Lecture Notes in Computational Science and Engineering, Vol. 128, T. Apel, U. Langer, A. Meyer, and O. Steinbach, eds., Springer, Cham, 2019, pp. 85–106.
  • M.P. Bruchhäuser, K. Schwegler, and M. Bause, Dual weighted residual based error control for nonstationary convection-dominated equations: Potential or ballast?, in Lecture Notes in Computational Science and Engineering, Vol. 135, G. Barrenechea and J. Mackenzie, eds., Springer, Cham, 2020, pp. 1–17.
  • E. Burman and A. Ern, Nonlinear diffusion and discrete maximum principle for stabilized Galerkin approximations of the convection–diffusion-reaction equation, Comput. Methods Appl. Mech. Eng. 191(35) (2002), pp. 3833–3855.
  • V.M. Calo, A. Ern, I. Muga, and S. Rojas, An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms, Comput. Methods Appl. Mech. Eng. 363 (2020), Article ID 112891.
  • S. Cengizci, Stabilized finite element simulations of multispecies inviscid hypersonic flows in thermochemical nonequilibrium, Ph.D. thesis, Institute of Applied Mathematics, Middle East Technical University, 2022.
  • P.G. Ciarlet, Basic error estimates for elliptic problems, in Finite Element Methods (Part 1), Handbook of Numerical Analysis Vol. 2, Elsevier, Amsterdam, 1991, pp. 17–351.
  • R.J. Cier, S. Rojas, and V.M. Calo, Automatically adaptive, stabilized finite element method via residual minimization for heterogeneous, anisotropic advection-diffusion-reaction problems, Comput. Methods Appl. Mech. Eng. 385 (2021), Article ID 114027.
  • R. Codina, A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation, Comput. Methods Appl. Mech. Eng. 110(3-4) (1993), pp. 325–342.
  • A. Cohen, W. Dahmen, and G. Welper, Adaptivity and variational stabilization for convection-diffusion equations, ESAIM: Math. Model. Numer. Anal. 46(5) (2012), pp. 1247–1273.
  • J. de Frutos, B. García-Archilla, V. John, and J. Novo, An adaptive SUPG method for evolutionary convection-diffusion equations, Comput. Methods Appl. Mech. Eng. 273 (2014), pp. 219–237.
  • C. Erath and D. Praetorius, Optimal adaptivity for the SUPG finite element method, Comput. Methods Appl. Mech. Eng. 353 (2019), pp. 308–327.
  • D. Galbally, K. Fidkowski, K. Willcox, and O. Ghattas, Non-linear model reduction for uncertainty quantification in large-scale inverse problems, Int. J. Numer. Methods Eng. 81 (2010), pp. 1581–1608.
  • W. Guo, Y. Nie, W. Zhang, and X. Hu, Anisotropic mesh adaptation for steady convection-dominated problems based on bubble-type local mesh generation, Int. J. Comput. Math. 97(5) (2019), pp. 980–997.
  • T.J.R. Hughes and A.N. Brooks, A multi-dimensional upwind scheme with no crosswind diffusion, in Finite Element Methods for Convection Dominated Flows, AMD-Vol.34, T. J. R. Hughes, ed., ASME, New York, 1979, pp. 19–35.
  • T.J.R. Hughes and T.E. Tezduyar, Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations, Comput. Methods Appl. Mech. Eng. 45 (1984), pp. 217–284.
  • T.J.R. Hughes, L.P. Franca, and M. Mallet, A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems, Comput. Methods Appl. Mech. Eng. 63 (1987), pp. 97–112.
  • V. John and P. Knobloch, On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations: Part I–A review, Comput. Methods Appl. Mech. Eng. 196(17) (2007), pp. 2197–2215.
  • V. John and P. Knobloch, On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations: Part II–Analysis for P1 and Q1 finite elements, Comput. Methods Appl. Mech. Eng. 197(21-24) (2008), pp. 1997–2014.
  • V. John and E. Schmeyer, Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion, Comput. Methods Appl. Mech. Eng. 198(3) (2008), pp. 475–494.
  • V. John and E. Schmeyer, On finite element methods for 3D time-dependent convection-diffusion-reaction equations with small diffusion, in BAIL 2008 – Boundary and Interior Layers, A. Hegarty, N. Kopteva, E. O'Riordan, and M. Stynes, eds., Springer, Berlin Heidelberg, 2009, pp. 173–181.
  • D. Kuzmin, On the design of algebraic flux correction schemes for quadratic finite elements, J. Comput. Appl. Math. 218(1) (2008), pp. 79–87.
  • H.P. Langtangen and K.-A. Mardal, Introduction to Numerical Methods for Variational Problems, Springer Cham, Switzerland, 2019.
  • G.J. Le Beau and T.E. Tezduyar, Finite element computation of compressible flows with the SUPG formulation, in Advances in Finite Element Analysis in Fluid Dynamics, FED-Vol.123, ASME, New York, 1991, pp. 21–27.
  • J. Lin, S.Y. Reutskiy, and J. Lu, A novel meshless method for fully nonlinear advection-diffusion-reaction problems to model transfer in anisotropic media, Appl. Math. Comput. 339 (2018), pp. 459–476.
  • A. Logg, K.-A. Mardal, and G. Wells (eds.), Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book, Springer, Berlin Heidelberg, 2012.
  • G. Lube and G. Rapin, Residual-based stabilized higher-order FEM for advection-dominated problems, Comput. Methods Appl. Mech. Eng. 195(33) (2006), pp. 4124–4138.
  • H.-F. Peng, K. Yang, M. Cui, and X.-W. Gao, Radial integration boundary element method for solving two-dimensional unsteady convection-diffusion problem, Eng. Anal. Bound. Elem. 102 (2019), pp. 39–50.
  • F. Rispoli, A. Corsini, and T.E. Tezduyar, Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD), Comput. Fluids 36 (2007), pp. 121–126.
  • F. Shakib, Finite element analysis of the compressible Euler and Navier–Stokes equations, Ph.D. thesis, Department of Mechanical Engineering, Stanford University, 1988.
  • T.E. Tezduyar, Computation of moving boundaries and interfaces and stabilization parameters, Int. J. Numer. Methods Fluids 43 (2003), pp. 555–575.
  • T.E. Tezduyar, Determination of the stabilization and shock-capturing parameters in SUPG formulation of compressible flows, in Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 (CD-ROM), Jyvaskyla, Finland, 2004.
  • T.E. Tezduyar, Finite element methods for fluid dynamics with moving boundaries and interfaces, in Encyclopedia of Computational Mechanics.Volume 3. Stein E., De Borst R., and Hughes T. J. R., ed., Wiley, New York, 2004.
  • T.E. Tezduyar, Finite elements in fluids: Stabilized formulations and moving boundaries and interfaces, Comput. Fluids 36 (2007), pp. 191–206.
  • T.E. Tezduyar and T.J.R. Hughes, Development of time-accurate finite element techniques for first-order hyperbolic systems with particular emphasis on the compressible Euler equations, NASA Tech. Rep. NASA-CR-204772, NASA, 1982.
  • T.E. Tezduyar and T.J.R. Hughes, Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations, in Proceedings of AIAA 21st Aerospace Sciences Meeting, AIAA Paper 83-0125, Reno, Nevada, 1983, pp. 1–9.
  • T.E. Tezduyar and Y.J. Park, Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations, Comput. Methods Appl. Mech. Eng. 59(3) (1986), pp. 307–325.
  • T.E. Tezduyar and M. Senga, Stabilization and shock-capturing parameters in SUPG formulation of compressible flows, Comput. Methods Appl. Mech. Eng. 195 (2006), pp. 1621–1632.
  • T.E. Tezduyar and M. Senga, SUPG finite element computation of inviscid supersonic flows with YZβ shock-capturing, Comput. Fluids 36 (2007), pp. 147–159.
  • T.E. Tezduyar, M. Senga, and D. Vicker, Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZβ shock-capturing, Comput. Mech. 38 (2006), pp. 469–481.
  • M. Uzunca, B. Karasözen, and M. Manguoğlu, Adaptive discontinuous Galerkin methods for non-linear diffusion-convection-reaction equations, Comput. Chem. Eng. 68 (2014), pp. 24–37.
  • Z. Weng, J.Z. Yang, and X. Lu, Two-grid variational multiscale method with bubble stabilization for convection diffusion equation, Appl. Math. Model. 40 (2016), pp. 1097–1109.
  • H. Yücel, M. Stoll, and P. Benner, Discontinuous Galerkin finite element methods with shock-capturing for nonlinear convection dominated models, Comput. Chem. Eng. 58 (2014), pp. 278–287.

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