Enriched Galerkin finite element method for locally mass conservative simulation of coupled hydromechanical problems

Abstract

Numerical simulation of coupled hydromechanical processes is crucial to address many problems in geotechnical engineering. Conventionally, the seepage flow equation in a hydromechanical model is solved by the continuous Galerkin (CG) finite element method. However, the CG method does not ensure mass conservation in a local (element-wise) manner, which may be a critical drawback in a number of situations. Here we introduce an enriched Galerkin (EG) finite element method that allows locally mass conservative simulation of coupled hydromechanical problems. The major advantage of the EG method is that its computational cost is appreciably less than that of the discontinuous Galerkin (DG) method. We describe the proposed method’s key idea and demonstrate its performance and significance through an example simulation of wetting collapse of a heterogeneous unsaturated soil.