TUMBLE Project Links:
Todd Phillips (tp517 at andrew.cmu.edu)
Mark J. Olah (mjo at andrew.cmu.edu)
Thus not only does TUMBLE deal with moving elements, but also with elements with a non-linear geometry. The concepts involved with moving (Lagrangian) meshes, and curved (Bezier) elements are relatively new and untested. Accordingly, the main use of the TUMBLE package is as a testbed for new algorithms and techniques relating to Lagrangian meshes, and meshes with Bezier elements.
The ultimate goals of the authors of TUMBLE are:
In this light, we will attempt to provide links to relevant papers, which describe the theoretical results on which TUMBLE is based. The reader will see that nearly every data-structure and algorithm employed by the TUMBLE package is extensible to three dimensions, and also to a parallel computing framework. The main reason for the existence of TUMBLE is that while many algorithms and techniques useful for Lagrangian meshing are known, their relationship within a complete and general meshing framework is not clear. TUMBLE will demonstrate the feasibility of the techniques in two-dimensions, where prototyping and computational costs are less, yet it will not loose sight of the ultimate, three dimensional goal.
For more information see the Detailed Introduction to TUMBLE.
One of the main advantages of working in a Lagrangian environment is that it is much more natural to solver certain problems in such a framework. In particular fluid simulations are very natural to solve with Lagrangian techniques, as the elements in the mesh represent regions of fluid. Thus, the Lagrangian techniques are able to explicitly track fluid interfaces as they move and deform over time. In addition the Navier-Stokes equations which govern the dynamics of Newtonian Fluids, require solving a non-linear system, when formulated as an Eulerian problem. But in the Lagrangian framework, Navier-Stokes reduces to a linear problem.
The primary application for which TUMBLE is used at this time is the simulation of blood flow at a microscopic level. Traditionally this is an extraordinarily ddifficult problem, as the interfaces between fluid and cells are dynamic and not well understood. The ability of TUMBLE to formulate the problem in a Lagrangian framework greatly simplifies many of the difficulties.