A GPU based model for multi-layer scalar transport in open channels

Scalar transport models derived from the two-dimensional depth averaged shallow water equations are frequently applied to a wide range of environmental flow conditions. A scalar may represent a dissolved solute, a pollutant, or fine sediment transported in river channels, estuaries, or ocean waters. However, these depth-averaged scalar transport models do not provide detailed information about the vertical distribution of the solute. The vertical distribution of a scalar could be computed from the 3D shallow water equations but is complex to compute numerically. One possible approach is to implement a multi-layer transport system, in which exchanges between layers determine the vertical concentration distribution of the transported scalar depending on the velocity of deposition, vertical eddy viscosity, and flow velocity.

The model presented is a GPU-based multi-layer scalar transport model implemented in C++/CUDA and coupled with an existing two-dimensional shallow water (SWE-2D) model. The SWE-2D framework is designed to handle three types of mesh topology: structured quadrilateral meshes, structured triangular meshes, and unstructured triangular meshes. The multi-layer system is implemented using an implicit scheme that accounts for interlayer exchanges. The layers are uniformly distributed in the vertical direction, with the total water depth divided by the number of layers, however, layer thickness varies in time and space with the water depth. Flux exchanges between layers depend on the vertical eddy viscosity, flow velocity, and the scalar deposition (settling) velocity. Different types of vertical eddy viscosity models have been developed (linear and constant), and the vertical flow velocity model implemented is a simple logarithmic wall low model.

To assess the viability of the multi-layer model, a series of synthetic channel test cases are implemented, in which the vertical eddy viscosity and the settling velocity are systematically varied but the vertical velocity considered as constant in depth. In addition, an experimental study by García J.A, Latorre B. et al., investigating the vertical concentration distribution of a passive solute in unsteady laboratory channel flow, is reproduced using the multi-layer framework. Results from the laboratory experiments and the numerical model are first compared using depth-averaged concentrations and, secondly, using the multi-layer system with a depth-varying vertical velocity profile. The model demonstrates a good representation of the horizontal solute distribution. Vertically, when the flow velocity varies with depth, the multi-layer system captures the solute global distribution, however , the lack of precision is due to the flow velocity and eddy viscosity vertical models that must be adapted to the specific flow conditions and environmental context.