An Unfitted Discontinuous Galerkin method for pore-scale simulations of solute transport

作者：Bastian Peter; Engwer Christian^*; Fahlke Jorrit; Ippisch Olaf

来源：Mathematics and Computers in Simulation, 2011, 81(10): 2051-2061.

DOI：10.1016/j.matcom.2010.12.024

• Discontinuous Galerkin method
• Higher order
• Unfitted finite elements
• Numerical upscaling
• Flows in porous media
• Convection-diffusion-problems
• Parabolic equations

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, Bastian and Engwer proposed an Unfitted Discontinuous Calerkin (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.

• 出版日期2011-6