I am collaborating with Karim Shariff at NASA Ames on an investigation of the code RBV2.
Check back soon for more details on the manuscript Investigation of a Vorticity-preserving Scheme for the Euler Equations (Seligman & Shariff submitted).
The fidelity with which RBV2 maintains a skewed shear flow on a square grid. The initial conditions for the simulations are shown in the left panel. The color scale in the image corresponds to the x velocity, u(y). The overlaid arrows give a visual representation of the velocity field. In the right panel, the initial, analytic solution is shown in the solid lines, and the numerical solution evolved for t~15 sound crossing times is shown in dots. The different colors represent different y cross sections of the grid. We initialize the simulation on a 64x64 zone grid. The amplitude of the shear flow is A=.1, the sound speed is $c_s=1.0$ and the domain length is L_x,L_y=sqrt 2\pi. It is evident that the scheme is maintaining the analytic solution.