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Source Panel Method: Circular Cylinder

Here we are. We finally have all the mathematical information needed to code up the source panel method. In this video, we take the code we had from the panel method geometry video, and add in the following: computation of the source panel strengths, computation of the panel tangential velocities and pressure coefficients, and computation of the grid X and Y velocities (for streamline plotting). This video uses a circular cylinder geometry because it is a convenient test case where we can compare the pressure coefficients on the panels to an analytical solution. If your code doesn't work with a circular cylinder, it's not a good idea to move on to harder geometries. ===== WHERE ARE WE GOING? ===== → The next video will be very similar to this one; the source panel method solution for airfoil geometries. → We will see some limitations in the SPM which will motivate the need for the vortex panel method (VPM). → I will need to go through the derivations for the geometric integrals for the VPM (which are similar to the SPM derivations). → We will then implement the VPM and see some of its limitations. These limitations will motivate the need for a more robust implementation of the VPM. → I will derive the combined SPM/VPM formulation and code it to show how good we can get the results for a pretty simple implementation. → We can finally extend the SPM/VPM formulation to multiple separate airfoil elements. This will be the last video in the series. ===== CODE ===== ► My website http://www.joshtheengineer.com/2020/0... ► GitHub https://github.com/jte0419/Panel_Methods ===== RELEVANT VIDEOS ===== ► Panel Methods Playlist    • How To: Run XFoil from MATLAB   ► Panel Method Geometry    • Panel Method Geometry   ► Building More Complex Flows    • Building More Complex Potential Flows...   ► Flow Around an Airfoil    • Flow Around an Airfoil: Panel Methods   ► Normal Velocity Geometric Integral [I(ij)]    • Source Panel Method: Normal Velocity ...   ► Tangential Velocity Geometric Integral [J(ij)]    • Source Panel Method: Tangential Veloc...   ► Streamline Geometric Integral SPM [Mx(ij) and My(ij)]    • Streamline Geometric Integral SPM [Mx...   ► Solving the System of Equations    • Source Panel Method: System of Equations   ===== NOTES ===== → I forgot to add the pop filter in front of my microphone for this video, so I apologize in advance. ===== ERRORS ===== → If you see an error in the video, please let me know and I will include it here. ===== REFERENCES ===== Note: the links are Amazon affiliate links. If you do happen to want to buy the book and use the link below, it helps me out a little. ► Fundamentals of Aerodynamics, Anderson https://amzn.to/3emVuXU ► Foundations of Aerodynamics, Kuethe and Chow https://amzn.to/2yMg1Vi ► Theory of Wing Sections, Abbott and Doenhoff https://amzn.to/2wvZyUt