Multipurpose Adaptive Tree Code

Fluid simulations using Lagrangian vortex methods are interesting in many ways. Since they are grid-free methods, the distribution of computational elements is adaptive, and the simulation is performed only over the support covered by vorticity. The vortical structures, which are important for understanging the dynamics of many interesting fluid systems, are readily identified, since the computational elements represent vorticity. The mechanical deformation of each vortical structures can be easily correlated to the important phenomena such as mixing and transition.

Recently, these methods become even more efficient by implementing fast-multipole type approaches to compute pairwise interactions of vortex elements. Our parallel adaptive tree-code has provided an efficient way to deal these pairwise interactions, for computing the local velocity induced by vortex elements. However, velocity evaluation is not the only place where pairwise particle interaction occurs. For many applications, we need velocity gradients from vortex elements, expansion velocity from a nontrivial divergence field, and recovery of scalar properties from distributed particles.

In this study, an extension of our previous tree-code to a multipurpose tree-code is made. A single universal set of expansion coefficients is recombined in a different ways to compute expansion for various quantities. Our multipurpose tree-code forms an essential part for multiphysics simulations, such as reacting flow simulations.