An unfitted discontinuous Galerkin method for pore-scale simulations of solute transport. (English) Zbl 1309.76120
Summary: For the simulation of transport processes in porous media effective parameters for the physical processes on the target scale are required. Numerical upscaling, as well as multiscale approaches can help where experiments are not possible, or hard to conduct.
In 2009, P. Bastian and C. Engwer [Int. J. Numer. Methods Eng. 79, No. 12, 1557–1576 (2009; Zbl 1176.65131)] proposed an Unfitted Discontinuous Galerkin (UDG) method for solving PDEs in complex domains, e.g. on the pore scale. We apply this method to a parabolic test problem. Convergence studies show the expected second-order convergence. As an application, example solute transport in a porous medium at the pore scale is simulated.
Macroscopic breakthrough curves are computed using direct simulations. The method allows finite element meshes which are significantly coarser then those required by standard conforming finite element approaches. Thus it is possible to obtain reliable numerical results for macroscopic parameter already for a relatively coarse grid.
In 2009, P. Bastian and C. Engwer [Int. J. Numer. Methods Eng. 79, No. 12, 1557–1576 (2009; Zbl 1176.65131)] proposed an Unfitted Discontinuous Galerkin (UDG) method for solving PDEs in complex domains, e.g. on the pore scale. We apply this method to a parabolic test problem. Convergence studies show the expected second-order convergence. As an application, example solute transport in a porous medium at the pore scale is simulated.
Macroscopic breakthrough curves are computed using direct simulations. The method allows finite element meshes which are significantly coarser then those required by standard conforming finite element approaches. Thus it is possible to obtain reliable numerical results for macroscopic parameter already for a relatively coarse grid.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76S05 | Flows in porous media; filtration; seepage |
| 76R99 | Diffusion and convection |
Keywords:
numerical upscaling; convection-diffusion-problem; parabolic equation; second-order convergenceCitations:
Zbl 1176.65131Software:
DUNEReferences:
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