Coupled physical modelling for the analysis of groundwater systems. We examine variable density flows and the corresponding transport of solute and heat. The mathematical model comprises three nonlinear coupled partial differential equations for pressure, solute concentration and temperature. We study numerically Henry’s and Elder’s problems by using different codes – ROCKFLOW and FEFLOW. Based on the verified simulators, more complex problems are tackled. In this way we consider thermohaline convection and mixed convection in thermoelastic fractures. Finally, an example of a three-dimensional Bénard convection is presented.