JANOS JOZSA, TAMAS KRAMER Budapest University of Technology and Economics Department of Hydraulic and Water Resources Engineering Műegyetem rkp. 3. Kmf. 8., H-1111 Budapest, Hungary Phone: +36 1 463 1164, Fax: +36 1 463 1879 E-mail: jozsa@vit.bme.hu, kramer@vit.bme.hu, http://www.vit.bme.hu ABSTRACT: 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. 1 INTRODUCTION Residence time is an important issue in environmental flows with implication for sedimentation, hydro-chemistry and biology. Traditional calculation methods consist of determining residence time along flow paths (see e.g. Pollock, 1988; Shafer-Perini and Wilson, 1991; Glasgow et al., 1996). In a velocity field given on a grid, the nodal values of residence time distribution due to advection can be calculated by reversing the velocity field in which particles are then released from the nodes and tracked until they reach an open boundary. This method is in fact satisfactory for advection-dominated problems. When the role of mixing is also important, random walk particle tracking methods can be applied, by means of which the effect of turbulent diffusion on the trajectories, thus on the residence time can be taken into account. Both a forward and backward time version can be formulated based on the two alternative forms of the corresponding Kolmogorov stochastic differential equation (Uffink, 1991). The more traditional forward time version is a stochastic equivalent of the deterministic advection-diffusion equation (Arnold, 1974; van Kampen, 1981), whereas the backward time version does not have any physical equivalent due to the irreversibility of the diffusion process. When the residence time has to be evaluated at few selected sites only, the backward time version provides an efficient technique by means of calculating the breakthrough-curves at open boundaries for particles injected at the selected site in the