Particle-Based Simulation of Transport in Heterogeneous Coupled Hydrosystems

The computational costs of reactive-transport simulations based on spatially explicit, three-dimensional, Eulerian discretization methods are so high that stochastic analysis, requiring multiple model runs, become prohibitive. Therefore, the stochastic framework for reactive transport on the catchment scale envisioned in CRC CAMPOS relies on reactive-transport simulations on trajectories, using travel times, exposure times, and the cumulative relative reactivity. These methods require accurate particle-tracking methods for the coupled flow model HydroGeoSphere used within CAMPOS, which is based on standard finite element discretization.

Accurate particle tracking requires conforming, mass-conservative velocity fields, implying that the velocity component normal to an element interface is identical in the neighbouring elements. While finite volume methods (FVM) yield such fields by definition, this is not the case for standard finite element methods (FEM), like the P1 Galerkin FEM. Standard FEM are often used nonetheless because they can easily handle unstructured grids and anisotropy, and yield a continuous approximation of the pressure heads.

A projection will be defined, which maps the non-conforming, element-wise given velocity field of an FEM solution, representing non-mass-conservative flow, onto a conforming velocity field in lowest-order Raviart-Thomas-Nédélec (RTN0) space. The target velocity space ensures continuity of the normal velocity component on element-boundaries, zero-divergence of the element-wise velocity field for non-divergent flow, and element-wise mass conservation. The projector will be coupled to HydroGeoSphere (HGS) as a postprocessing code. With this, particle tracking can be conducted analogously to Pollock's method.

In next steps, the particle tracking will be considered in domains where subdomains of different dimensionality (i.e. 3-D subsurface domain, 2-D overland-flow domain, 1-D river domain) are coupled. The overall goal is to provide an accurate and reliable particle tracker for catchment-scale reactive-transport solutions using an integrated flow simulator based on an FEM.