This work focuses on the application of the Lattice Boltzmann Method in natural water bodies (lakes, rivers, reservoirs) under the background of human activities and climate change. The mathematical model used is based on the two dimensional LB method (D2Q9), with shallow water formulation coupled with a water pollution dispersion routine. The LB method belongs to a new class of mesoscopic methods, based on a discretized formulation of the Boltzmann kinetic equation. The model is simple to implement, accurate andsuitabletosimulateshallowwaterbodies[Tubbs, 2012]. Moreover, thekineticapproachcorrectlysolves small scale phenomena [Biscarini, 2011] and multiphase ﬂows and also provides an eﬀortless treatment of source terms. The model is ﬁrstly validated through benchmark problems available in literature and then applied to simulate pollution dispersion in a lake. As a case study, we chose the Trasimeno Lake, which is located in Umbria Region and is the fourth biggest Italian lake, with an extension of about 121.5 km2 and an average depth of 4.3 m. The simulation of pollution dispersion takes into account the inﬂuence of seasonal level variations and of wind forces. The progressive disappearance of reed bed vegetation (Phragmites australis) near the lakeshore also aﬀects boundary conditions in terms of lakeshores roughness and nutrients concentration, thus diﬀerent scenarios are simulated. The topic appears remarkable in order to save the ecological balance of the Trasimeno Lake that is aﬀected by the increased concentration of dissolved salts and pollutants during the dry period.

### Lattice Boltzmann pollution dispersion in a shallow water body: the case of Trasimeno Lake

#### Abstract

This work focuses on the application of the Lattice Boltzmann Method in natural water bodies (lakes, rivers, reservoirs) under the background of human activities and climate change. The mathematical model used is based on the two dimensional LB method (D2Q9), with shallow water formulation coupled with a water pollution dispersion routine. The LB method belongs to a new class of mesoscopic methods, based on a discretized formulation of the Boltzmann kinetic equation. The model is simple to implement, accurate andsuitabletosimulateshallowwaterbodies[Tubbs, 2012]. Moreover, thekineticapproachcorrectlysolves small scale phenomena [Biscarini, 2011] and multiphase ﬂows and also provides an eﬀortless treatment of source terms. The model is ﬁrstly validated through benchmark problems available in literature and then applied to simulate pollution dispersion in a lake. As a case study, we chose the Trasimeno Lake, which is located in Umbria Region and is the fourth biggest Italian lake, with an extension of about 121.5 km2 and an average depth of 4.3 m. The simulation of pollution dispersion takes into account the inﬂuence of seasonal level variations and of wind forces. The progressive disappearance of reed bed vegetation (Phragmites australis) near the lakeshore also aﬀects boundary conditions in terms of lakeshores roughness and nutrients concentration, thus diﬀerent scenarios are simulated. The topic appears remarkable in order to save the ecological balance of the Trasimeno Lake that is aﬀected by the increased concentration of dissolved salts and pollutants during the dry period.
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2015
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11391/1396749`
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