The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity
- 1Department of Mathematical Physics, Delft Institute of Applied Mathematics (DIAM), Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
- 2Université catholique de Louvain, G. Lemaitre Institute of Astronomy and Geophysics (ASTR) & Centre for Systems Engineering and Applied Mechanics (CESAME), Avenue G. Lemaitre 4, 1348 Louvain-la-Neuve, Belgium
Abstract. Random walk models are a powerful tool for the investigation of transport processes in turbulent flows. However, standard random walk methods are applicable only when the flow velocities and diffusivity are sufficiently smooth functions. In practice there are some regions where the rapid but continuous change in diffusivity may be represented by a discontinuity. The random walk model based on backward Îto calculus can be used for these problems. This model was proposed by LaBolle et al. (2000). The latter is best suited to the problems under consideration. It is then applied to two test cases with discontinuous diffusivity, highlighting the advantages of this method.