Ground sources energy systems, such as open-loop systems, have been widely employed in recent years due to their economic and environmental benefits compared to conventional heating and cooling systems. Numerical modelling of such geothermal system requires solving a coupled thermo-hydraulic problem which is characterised by a convection-dominated heat transfer which can be challenging for the Galerkin finite element method (GFEM). This paper first presents the coupled thermo-hydraulic governing formulation as well as the coupled thermo-hydraulic boundary condition, which can be implemented into a finite element software. Subsequently, the stability condition of the adopted time marching scheme for coupled thermo-hydraulic analysis is established analytically. The behaviour of highly convective problems is then investigated via a series of analyses where convective heat transfer along a soil bar is simulated, with recommendations on the choice of an adequate discretisation with different boundary conditions being provided to avoid oscillatory solutions. Finally, the conclusions from the analytical and numerical studies are applied to the simulation of a boundary value problem involving an open-loop system, with the results showing good agreement with an approximate solution. The main objective of this paper is to demonstrate that the GFEM is capable of dealing with highly convective geotechnical problems.