A mesh-adaptive collocation technique for the simulation of advection-dominated single- and multiphase transport phenomena in porous media
- Florida State Univ., Tallahasse, FL (United States)
A new mesh-adaptive 1D collocation technique has been developed to efficiently solve transient advection-dominated transport problems in porous media that are governed by a hyperbolic/parabolic (singularly perturbed) PDE. After spatial discretization a singularly perturbed ODE is obtained which is solved by a modification of the COLNEW ODE-collocation code. The latter also contains an adaptive mesh procedure that has been enhanced here to resolve linear and nonlinear transport flow problems with steep fronts where regular FD and FE methods often fail. An implicit first-order backward Euler and a third-order Taylor-Donea technique are employed for the time integration. Numerical simulations on a variety of high Peclet-number transport phenomena as they occur in realistic porous media flow situations are presented. Examples include classical linear advection-diffusion, nonlinear adsorption, two-phase Buckley-Leverett flow without and with capillary forces (Rapoport-Leas equation) and Burgers` equation for inviscid fluid flow. In most of these examples sharp fronts and/or shocks develop which are resolved in an oscillation-free manner by the present adaptive collocation method. The backward Euler method has some amount of numerical dissipation is observed when the time-steps are too large. The third-order Taylor-Donea technique is less dissipative but is more prone to numerical oscillations. The simulations show that for the efficient solution of nonlinear singularly perturbed PDE`s governing flow transport a careful balance must be struck between the optimal mesh adaptation, the nonlinear iteration method and the time-stepping procedure. More theoretical research is needed with this regard.
- OSTI ID:
- 198204
- Report Number(s):
- CONF-9307220-Vol.75; TRN: 96:001696-0016
- Resource Relation:
- Conference: Modeling, mesh generation and adaptive numerical methods for partial differential equations program, Minneapolis, MN (United States), 6-23 Jul 1993; Other Information: PBD: 1995; Related Information: Is Part Of Modeling, mesh generation, and adaptive numerical methods for partial differential equations; Babuska, I. [ed.] [Univ. of Maryland, College Park, MD (United States). Inst. for Physical Science and Technology]; Henshaw, W.D. [ed.] [Los Alamos National Lab., NM (United States)]; Oliger, J.E. [ed.] [Research Inst. for Advanced Computer Science, Moffet Field, CA (United States)]; Flaherty, J.E. [ed.] [Rensselaer Polytechnic Inst., Troy, NY (United States)]; Hopcroft, J.E. [ed.] [Cornell Univ., Ithaca, NY (United States). Coll. of Engineering]; Tezduyar, T. [ed.] [Army High Performance Computing Research Center, Minneapolis, MN (United States)]; PB: 501 p.
- Country of Publication:
- United States
- Language:
- English
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