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Streamline upwind/full Galerkin method for solution of convection dominated solute transport problems


A new streamline method for the solution of convection-dominated transport problems is introduced. First, an analysis is made of the nature of classic streamline upwinding from the perspective of space and spacetime solution domains, as they pertain to the nature of the problems. From this analysis emerges a rigorous logic for upwinding, which can easily be implemented in the full (spacetime) Galerkin formulation of the transport equation. Comparative performance testing of this technique, in solving a number of examples, proves it to be robust and versatile. The advantage of this method resides in its applicability to a wider range of Courant numbers.

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  1. Bouloutas, E. T. and Celia, M. A., 1991, An improved cubic Petrov-Galerkin method for simulation of transient advection-diffusion processes in rectangularly decomposable domains,Comp. Meth. Appl. Mech. Eng. 92, 289–308.

  2. Brooks, A. N. and Hughes, T. J. R., 1982, Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stocks equations,Comp. Meth. Appl. Mech. Eng. 32, 199–259.

  3. Cantekin, M. E. and Westerink, J. J., 1990, Non-diffusiveN + 2 degree Petrov-Galerkin method for two-dimensional transient transport computations,Int. J. Num. Meth. Eng. 30, 397–418.

  4. Donea, J., Quarlapelle, L., and Selmin, V., 1987, An analysis of time discretization in the finite element solution of hyperbolic problems,J. Comp. Phys. 70, 463–499.

  5. Heinrich, J. C., Huyakorn, P. S., Zienkiewicz, O. C., and Mitchell, A. R., 1977, An upwind finite element scheme for two-dimensional convective-transport equation,Int. J. Num. Meth. Eng. 11, 131–143.

  6. Leonard, B. P., 1979, A survey of finite differences of opinion on numerical modelling of incomprehensible defective confusion equation, in T. J. R. Hughes, (ed.),Finite Element Methods for Convection Dominated Flows, AMD, 34.

  7. Noorishad, J., Tsang, C. F., Perochet, P., and Musy, A., 1992, A perspective on the numerical solution of the convection dominated transport problem. A price to pay for the easy way out, accepted for publication inWater Resour. Res.

  8. Van Genuchten, M. T., 1980, Predicting the hydraulic conductivity of unsaturated soils,Soil Sci. Soc. Am. 44(5), 892–898.

  9. Varoglu, E., 1982, A finite element model for the diffusion-convection equation with application to air pollution problems,Adv. Water Resour. 5, 35–41.

  10. Westerink, J. J. and Shea, D., 1989, Consistent higher degree Petrov-Galerkin methods for the solution of the transient convection-diffusion equation,Int. J. Num. Meth. Eng. 28, 1077–1101.

  11. Yu, C. C. and Heinrich, J. C., 1986, Petrov-Galerkin methods for the time-dependent, convective transport equations,Int. J. Num. Meth. Eng. 23, 883–901.

  12. Yu, C. C. and Heinrich, J. C., 1987, Petrov-Galerkin methods for multidimensional, time-dependent, convection-diffusion equations,Int. J. Num. Meth. Eng. 24, 2201–2215.

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Noorishad, J., Tsang, C.F., Perrochet, P. et al. Streamline upwind/full Galerkin method for solution of convection dominated solute transport problems. Transp Porous Med 16, 53–74 (1994).

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Key words

  • Space-time finite element methods
  • convection dominated transport
  • full Petrov/Galerkin