AdvectionDiffusionModels

Advection Diffusion Models

The advection-diffusion models consist of two-dimensional kinematic fluid velocity fields which can be used to advect particles with a specified diffusivity. This project also contains code to estimate kinematic model parameters from a given set of particles.

Table of contents

1. Quick start
2. Kinematic models

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Quick start

Start by initializing and visualizing a kinematic model,

jet = MeanderingJet();
figure
jet.plotStreamfunction(), hold on
jet.plotVelocityField()

This meandering jet example is bounded in the y-direction, and periodic in the x-direction.

Now that we have a KinematicModel initialized, we can use that in the AdvectionDiffusionIntegrator.

kappa = 1e3;
integrator = AdvectionDiffusionIntegrator(jet,kappa);

Let's choose appropriate time scales to integrate

T = 5*jet.Lx/jet.U;
dt = 864;

and place particles throughout the valid domain

x = linspace(min(jet.xlim),max(jet.xlim),6);
y = linspace(min(jet.ylim),max(jet.ylim),6);
[x0,y0] = ndgrid(x,y);

Finally, we now use the integrator to generate some trajectories

[t,x,y] = integrator.particleTrajectories(x0,y0,T,dt);

figure
jet.plotVelocityField(), hold on
jet.plotTrajectories(x,y)

Kinematic models

A kinematic model (in this context) is a parametric two-dimensional fluid velocity field which may or may not be time-dependent.