Parallel Lagrangian models for turbulent transport and chemistry

Abstract

In this thesis we give an overview of recent stochastic Lagrangian models and present a new particle model for turbulent dispersion and chemical reactions. Our purpose is to investigate and assess the feasibility of the Lagrangian approach for modelling the turbulent dispersion and chemistry interactions. We emphasise the numerical aspects and advantages of the method for the implementation on (massively) parallel computers.

In Chapter 1, a general introduction to the topic of modelling turbulent transport and chemistry is given.

Before we direct most of our attention to Lagrangian modelling, we give an overview of Eulerian models for turbulent transport and chemistry, like direct numerical, large eddy and Reynolds averaged simulations in Chapter 2.

We begin the treatment of Lagrangian modelling with a detailed survey of the stochastic Lagrangian theory (Chapter 3). In stochastic models turbulence is considered as a stochastic process.Accordingly the concentration is a stochastic function and can be modelled by its mean, its uctuations and higher statistical moments. By generating many one-particle trajectories we are able to predict the mean concentration only. The second moment of the concentration can be inferred from the statistics of particle pair trajectories. Models based on one-particle trajectories are discussed in Chapter 4. In the same chapter we give a short overview of the problems that arise if one attempts to formulate relative di usion models and present Kaplan and Dinar's model to describe the trajectories of pairs of uid particles.

There are to our knowledge only a few Lagrangian models for the turbulent transport of reactive constituents. In Chapter 5 an overview of these models is given. We also propose some improvements in these models and present a new one-particle model. We present, in Chapter 6 a new two-particle model for turbulent transport and chemistry interactions. The results of the new two-particle model for transport and chemistry are discussed in Chapter 7.

In Chapter 8 the parallel implementation aspects of Lagrangian models and of the new two-particle model in particular are discussed. Finally the conclusions from the present study are summarised in Chapter 9.