Lagrangian Transport

Abstract

Lagrangian techniques are introduced to show how to calculate the internal motion of a convecting fluid in a box. Two types of flows are tested, (i) a rigid rotation of the space and (ii) a more complex thinning flow that stretches shapes. Emphasis is given to prevent the errors may appear and quickly build up when calculating the trajectory of the Lagrangian particles. Three projections from the grid to the particles are illustrated, based on a different weights. It is particularly illustrated how to implement these functions very efficiently in order to prevent lack of scalability and also use NumPy functions at their best. It is finally shown how to scale the projection up to a large number of particles and how to project back the field (Temperature, composition) from the particles to the mesh.