# Simulations

1. Worcester Polytechnic Institute (PI: Prof. Trygvasson), The fluid in a box problem with a moving viscous surface has been done repeatedly throughout the Computational Fluid Dynamics (CFD) community to demonstrate a mastery of the art of writing code, as well as testing basic limitations of computational resources. These two animations show the transient problem as a Scalar Function (ink loop) diffuses through the moving fluid in a box.

The above figure represents the diffusion of a loop of ink within the box of fluid as the fluid is mixed by the transfer of momentum at the top surface of the box due to viscosity.

The above figure represents velocity (red arrows) and vorticity (gradient contours) of the fluid as momentum is propagated through the box of fluid due to the effects of viscosity.

2. Worcester Polytechnic Institute (PI: Prof. Trygvasson), I wrote code that simulated and analyzed a shock tube with Lex-Wendrof flux vector splitting, a technique that resolves a shock wave within one grid element effectively eliminating any diffusion-based artifacts in the solution.
3. Worcester Polytechnic Institute (PI: Prof. Sullivan), I simulated the radiation of a tumor in a abdomen utilizing point source techniques (such as radioactive pellets) and a radiating boundary condition. The constraints of the system where to denature the cancerous tissue so that the body would mark it for destruction without damaging surrounding non-cancerous tissue. This code verified a researcher’s code used at Dana-Farber Cancer Institute.
4. University of Notre Dame (PI: Prof. Cheng), I wrote code which simulated the instability of an airfoil suspended by two spring constants in a turbulent flow. The following animation is an example of an unstable region on the / plot below.
The above plot shows regions where , the torque spring constant, and , the vertical spring constant, have different regions of stability. This graph was determined through trial and error. Basically region I is unconditionally stable, since both spring constants are stiff enough to lead to a stable aerodynamic configuration. Regions II through V have different behavior which will not be discussed here. However, the following animation represents region III: unconditionally stable with oscillations.

The above animation represents an unstable condition of an airfoil suspended by two springs: one along the vertical axis connected to the quarter chord point of the airfoil, and a torque spring at the same point. This particular configuration is unstable with oscillations.