## CODES

Potential flow around a cylinder

The potential flow over a cylinder in the free stream is a common problem as it helps to examine numerical problem-solving techniques.  The equation describing the potential flow over an object in two-dimensional flow reduces to the Laplace partial differential equation.  Fortunately, the Laplace equation has a well-known solution and can be solved analytically.  This provides a good benchmark to gauge the accuracy of the numerical approximation.  The problem is the simplest form of Computational Fluid Dynamics, but the general algorithm forms the foundation for the higher fidelity models.

A cylinder was selected due to the availability of its analytical solution and for its simplicity. The numerical simulation was conducted by changing grid densities, calculating the order of convergence, and verifying with the exact solution

In this example, I implemented a second-order accurate potential flow solver for the flow around a cylinder using $R_{max}=10$, $R_{cyl}=0.5$, $U_{1}=1$, and $N_{r}=N_{\theta}=50$.