Solution of fully-coupled shallow water equations and contaminant transport using a primitive-variable Riemann method

A Riemann-solver scheme, using primitive variables rather than conserved variables, is configured and tuned for the solution of the fully-coupled two-dimensional shallow water and contaminant transport equations. This scheme is based on the unstructured finite volume discretization using primitive-variable Roe-flux approximation with an entropy fix. The primitive-variable flux associated with the exact source-term balancing is well-behaved and well-balanced for both still-water and dry regions with arbitrary bed topography. Second-order accuracy is used in space and time. The present study uses a nonlinear implicit scheme based on Newton-iterative algorithm for the time integration. In order to show the accuracy of the scheme, numerical results are verified by different test cases for contaminant advection and diffusion. A scenario of contaminant transport in a complex geometry with wet and dry elements is also simulated to demonstrate that the present work can be implemented on practical applications involving flooding and contaminant transport.