2D Inviscid Vortex Simulations

The following 3 videos are results from the code I produced for my master’s thesis work. One key piece to the validation of a new simulation code is comparing it’s output with references that are known to be correct. The videos show two different test cases by Strain and Koumoutsakos that were used.

The first two videos show the evolution of several interacting vortex patches and the third shows the evolution of an elliptical vortex. The simulation code is a “high-order” code; the computational domain is split into many elements, but the representation of the solution on any one element is actually composed of high-order interpolating function. This means that when one wants increased fidelity, increasing the number of elements used actually increases the fidelity proportional to a power function (where the power is proportional to the order of accuracy of the code).

In order to accurately simulate the evolution of the vortices, it is critical that the velocity field is computed accurately. The velocity was computed with an Integral method which has certain advantages, but is challenging because of singularities present in the computation.
This is a similar simulation to the above, but with different initial conditions. Additionally the order of accuracy here is sufficiently higher compared to the first video to capture the transient small scale behavior as the vortices merge.
The identifying feature of this test case is that the vortex is initially elliptical, but that it never becomes symmetric. Many vortex configurations become circular over time, but this test case was constructed so that did not happen. This is an excellent test case to examine the dissipative characteristics of the simulation method, as dissipation will tend to reduce the ellipticity of the vortex over time. Compared to the original published data the results obtained indicate my approach was actually less dissipative.