Disk self-gravity force calculation in protoplanet simulations (with Shengtai Li, LANL, Summer 2006)

The discovery of about 170 extrasolar planets over the past decade has raised many fundamental questions about the basic processes that determine planet-system evolution. Numerical simulations have revealed a rich variety of subtle, sometimes competing physical processes on protoplanets' dynamical evolution. In the protoplanet simulations studied here, we model the planet as a discrete point mass embedded in a disk of rotating mass, modeled as a gas. The compressible gas flow equations are solved on the disk with an external force term due to gravity from the planet, while the planet is evolved due to gravitational forces from the disk. Disk self-gravity forces are usually either neglected or crudely approximated (as having only radial dependence, for example), in spite of their physical importance. This is because computing them exactly is very computationally expensive, slowing down simulations by more than 1000 times on highly resolved grids.

Above: Snapshot of the density profile of the gaseous disk with embedded protoplanet using our code.

My research goal was to develop a parallel fast force summation algorithm to compute disk self-gravity forces in 2D proto-planet simulations. To accomplish this, I wrote and parallelized (using MPI) a hierarchical tree-code specifically tailored and optimized for our disk geometry. Also, I modeled the 3D effects of finite disk height to compute an effective 2D force law.  Although these efforts led to a 300-fold speedup over direct methods, the self-gravity calculation still remained a bottleneck in the simulations.  We followed up this work with an investigation into a Green's function FFT method, which turned out to be much faster (an additional 100 times) and is now being used to study proto-planet dynamics.

Here is a 2-page summary describing the parallel tree-code and the 3D interaction force model.

To see a detailed presentation describing the parallel tree-code and the 3D interaction force model, click here.

To see a preprint of the article to be submitted to Astrophysics Journal, click here.

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