Species Transport

 

Dispersion of species is an important research area in water resources and environmental engineering.  In this context, species can refer to suspended sediment concentration, salinity, micro-organism number, or other water quality parameters.  Herein species transport in shallow waters is predicted by a 4 × 4 hyperbolic matrix system of conservation laws formed by including an extra depth-averaged species equation to the two-dimensional shallow water equations, assuming that the flow is nearly horizontal, the pressure field is hydrostatic, and the species are well-mixed in the vertical.  In such a system the species concentration is transported passively with the fluid velocity.

 

The resulting hyperbolic system is again numerically solved by a Godunov-type scheme, where the governing equations are discretised spatially using finite volumes on cell-centred collocated quadtree grids, with a slope-limited HLLC scheme used to model the inviscid flux terms.  Second-order accuracy is achieved using a MUSCL-Hancock method.  The resulting numerical model is applied to predict the advection of depth-averaged species due to wind-induced circulation in a shallow circular lake with a non-uniform bathymetry after validated against benchmark test cases.

 

 

                   

                                          (a)                                                                 (b)                                                          (c)

Pure advection of species concentration in a uniform velocity field: (a) velocity field; (b) Contours; (c) adapted quadtree grid.

 

 

                  

                                                                  (a)                                                                                           (b)

 

 

                                                          

                                                                  (c)                                                                                             (d)

Pure diffusion of species concentration: (a) surface plot; (b) contours; (c) analytical and numerically predicted concentration profiles across a diagonal of the domain; (d) adapted quadtree grid.

 

 

              

                                                                (a)                                                                                        (b)

 

 

                      

                                          (c)

 

 

                       

                                         (d)

Advection-diffusion of species concentration: (a) velocity field; (b) comparison of concentration profiles obtained using different slope limiters with the exact solutions at t = 2.8 and 3.1 s; (c) surface plot and adapted quadtree grid at t = 2.8 s; (d) surface plot and adapted quadtree grid at t = 3.1s.

 

 

         

                                                    (a)                                                       (b)                                                       (c)

 

 

         

                                                    (d)                                                       (e)                                                       (f)

Advection of species due to wind-driven circulation in a circular shallow lake: concentration contours at different output time.

 

 

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