Principal Investigator Ahmed Ghoniem
Project Website http://web.mit.edu/rgd/www/ScientificComputing/scientificComputing.html
A motivation for the development of the multi-purpose treecode was the possibility to perform more efficient simulations using Passive Scalar Transport for two reasons.
First, we observe in the curl-form of Navier-Stokes equation using Boussinesq approximation , that we do not need the value of the temperature field, but only the value of the gradient of the temperature, in order to compute the baroclinic generation of vorticity. In terms of Passive Scalar Transport, this means that we can use elements carrying the gradient of the temperature, instead of Conserved Scalar Elements, carrying the temperature information. In fact, with Conserved Scalar Elements, we solve the Energy equation, then we need to differentiate the temperature field to obtain the temperature gradient, using finite differences for example. This takes more CPU time and we may loose accuracy. Now that we developed the adaptive treecode algorithm, we are able to solve the energy equation in its gradient form (which requires the gradient of the velocity for each particle). In other words, we will compute the evolution of the temperature gradient, instead of the temperature field.
The second reason is that the support may be smaller since we only need to cover the support of gradients, and not the whole field as it is done with Conserved Scalar Elements, which results in less elements. As a consequence, we have a faster simulation.