Keywords: local discontinuous Galerkin, coupled analysis, unsaturated flow, chemical transport, unsaturated porous media.

The local discontinuous Galerkin (LDG) method offers many advantages over conventional finite element solutions for transport and mechanics problems in soils, namely more accurate simulation of sharp fronts, easier representation of domain discontinuities, algorithms that are more suited to h and p adaptivities and better mass balances between elements. The LDG method has been applied to a large number of problems in soils, saturated and unsaturated, including Richard's equation, the diffusion-advection equation and elastic as well as non-elastic mechanics. Multiphase thermo-chemo-hydro-mechanical problems occur frequently in problems of waste management and groundwater quality. However, few studies have applied the LDG method to such coupled problems. In this paper, an LDG solution is presented for the coupled unsaturated flow and chemical transport (diffusion only) problem in porous media. Also presented is an analytical solution for these problems in a one-dimensional domain for a one-layer Gardner soil to validate the new numerical model. The performance of the CG and the LDG method are compared in terms of accuracy and processing time. The processing time are the average of running each problem for 100 times. This is to ensure that the CPU measurements are not overly affected by variable factors related to other jobs that the computer may be performing. As expected, the processing time for both methods increases for higher accuracy and density of nodes. The LDG method performs significantly better for larger problems, while the CG method requires less computation time for low density problems. More generally, the growth of CPU requirements with meshing refinement appears to be quasi-exponential for the CG method and linear for the LDG method. The graph also reveals that the execution time for the CG method is less sensitive to the required level of accuracy than for the LDG method. It was found that the LDG method achieves better performance than the CG method in solving this coupled problem for refined meshes with a higher number of nodes. This is an encouraging preliminary finding as the aim of the authors' research is to incorporate the advective and reactive terms of the diffusion-advection equation in the solution and extend the method to deformable soils, i.e. chemo-hydro-mechanical couplings in multiple dimensions.

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