Modelling Residence Time as Advection- Diffusion with Zero-order Reaction Kinetics

As an alternative to the particle tracking-based residence time calculations, a finite difference approach using the conventional advection-diffusion-reaction kinetics equation for describing the evolution of the residence time field is derived. Advection and mixing of water masses is accompanied with their ageing following a simple zero-order kinetics rule. The governing equations are solved by finite differences with special attention to the approximation of the advective terms. To reduce numerical errors in the presence of sharp gradients robust upwind schemes are implemented. The sample applications demonstrate the main features of the approach including steady-state flow in a channel with groins and aquatic vegetation patches, reservoir through-flow with superimposed wind effect, and time-periodic flow in a bay.