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Lagrangian modelling of multi-dimensional advection-diffusion with space-varying diffusivities: theory and idealized test cases

Spivakovskaya, Darya;Heemink, Arnold W.;Deleersnijder, Eric
(2007) Ocean Dynamics : theoretical, computational oceanography and monitoring — Vol. 57, n° 3, p. 189-203 (2007)

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Abstract
To efficiently simulate the advection-diffusion processes along and across density surfaces, we need to deal with a diffusivity tensor containing off-diagonal elements (Redi, J Phys Oceanogr, 12:1154-1158, 1982). In the present paper, the Lagrangian model, in case of a space-varying diffusivity tensor, is developed. This random walk model is applied for two idealized test cases for which the analytical solutions are known. Results of the testing show that the Lagrangian approach provides accurate and effective solutions of advection-diffusion problems for general diffusivity tensor.
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Spivakovskaya, D., Heemink, A. W., & Deleersnijder, E. (2007). Lagrangian modelling of multi-dimensional advection-diffusion with space-varying diffusivities: theory and idealized test cases. Ocean Dynamics : theoretical, computational oceanography and monitoring, 57(3), 189-203. https://doi.org/10.1007/s10236-007-0102-9 (Original work published 2007)