Thermohaline convection of subsurface fluids strongly influences heat and mass fluxes within the Earth's crust. The most effective hydrothermal systems develop in the vicinity of magmatic activity and can be important for geothermal energy production and ore formation. As most parts of these systems are inaccessible to direct observations, numerical simulations are necessary to understand and characterize fluid flow. Here, we present a new numerical scheme for thermohaline convection based on the control volume finite element method (CVFEM), allowing for unstructured meshes, the representation of sharp thermal and solute fronts in advection-dominated systems and phase separation of variably miscible, compressible fluids. The model is an implementation of the Complex Systems Modelling Platform CSMP++ and includes an accurate thermodynamic representation of strongly nonlinear fluid properties of salt water for magmatic-hydrothermal conditions (up to 1000°C, 500 MPa and 100 wt% NaCl). The method ensures that all fluid properties are taken as calculated on the respective node using a fully upstream-weighted approach, which greatly increases the stability of the numerical scheme. We compare results from our model with two well-established codes, HYDROTHERM and TOUGH2, by conducting benchmarks of different complexity and find good to excellent agreement in the temporal and spatial evolution of the hydrothermal systems. In a simulation with high-temperature, high-salinity conditions currently outside of the range of both HYDROTHERM and TOUGH2, we show the significance of the formation of a solid halite phase, which introduces heterogeneity. Results suggest that salt added by magmatic degassing is not easily vented or accommodated within the crust and can result in dynamic, complex hydrologies.