# Lattice Boltzmann modelling

Drawdown at groundwater abstraction boreholes is influenced by both regional and local flow processes. To predict how drawdown might change under different patterns of abstraction or recharge it is therefore essential to understand the small-scale flow processes around a borehole.

The BGS has been working with colleagues in the Department of Mathematics at the University of Leicester to develop alternative methods for modelling groundwater systems, which fully capture the complex dynamics of flow around abstraction boreholes.

## What is the lattice Boltzmann method?

Developed for modelling gases, the lattice Boltzmann method (LBM) models a fluid as a system of particles that evolve on a lattice through processes of collision and advection.

The LBM resolves the generalised Navier-Stokes equation for fluid flow, which represents both laminar and turbulent fluid behaviour. Linear and non-linear drag terms are incorporated as external forces in the Navier Stokes equation to represent the effect of flow through a porous medium.

## Why use the lattice Boltzmann method to model flow to boreholes?

The process of pumping to abstract groundwater at a borehole causes an increase in flow velocities as the fluid moves towards the borehole. This acceleration produces inertial effects in the fluid which lead to turbulent or non-linear fluid behaviour. These effects may be particularly pronounced in Chalk aquifers where flow is predominantly through fractures.

Traditional methods of groundwater modelling are based on Darcy’s law for fluid flow through a porous medium. This linear equation describes the typical nature of groundwater flow, which is slow and laminar. However it does not represent the turbulent flows that often develop around an abstraction borehole.

A new lattice Boltzmann method is being developed for modelling the complex nature of groundwater flow around an abstraction borehole during pumping. This should help us understand and simulate drawdown more accurately, which in turn will allow us to make better predictions about how drawdown might change under different conditions.