×

A mesh-adaptive collocation technique for the simulation of advection-dominated single- and multiphase transport phenomena in porous media. (English) Zbl 0843.76062

Babuska, Ivo (ed.) et al., Modeling, mesh generation, and adaptive numerical methods for partial differential equations. Based on the proceedings of the 1993 IMA summer program held at IMA, University of Minnesota, Minneapolis, MN, USA. New York, NY: Springer-Verlag. IMA Vol. Math. Appl. 75, 307-346 (1995).
The paper deals with a new mesh-adaptive one-dimensional collocation technique for solving transient advection-dominated transport problems in porous media which are governed by a hyperbolic/parabolic singularly perturbed partial differential equation. After the phenomenological description of the transport problems in porous media, the author presents the fundamental equation and a new error-minimizing numerical method. After the spatial discretization, a singularly perturbed ordinary differential equation is obtained, and implicit first-order backward Euler and third-order Taylor-Donea techniques are employed for the time integration of this equation. Numerical examples include classical linear advection-diffusion, nonlinear adsorption, two-phase Buckley-Leverett flow, and Burgers’ equation for inviscid fluid flow. The method appears to be suitable for solving complex nonlinear transport problems in porous media in the presence of sharp fronts or even shocks.
For the entire collection see [Zbl 0822.00013].

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76S05 Flows in porous media; filtration; seepage
76T99 Multiphase and multicomponent flows
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

Software:

COLNEW; PDE2D
PDFBibTeX XMLCite