Modelling of Potential Flow using PDE Toolbox (Partial Differential Equation Toolbox)

1- study the concept of 2D steady ideal fluid flow and the significance of the velocity potential and stream function;
2- study the derivation of Laplace`s equation for both the velocity potential and the stream function and identify the boundary conditions that need to be imposed in each case;
3- study the construction of the solution for ideal fluid flow over some simple geometric shapes, such as the Rankine body and the circular cylinder, by using superposition of some fundamental solutions;
4- study the application of the PDE Toolbox to the solution of Laplace`s equation, including refining the mesh to improve the solution quality;
5- determine the MATLAB statements required to enable the relevant information may be extracted from the PDE Toolbox so as to allow access to other quantities of physical interest, such as the velocity components or the pressure over a prescribed surface;
6- validate the procedure by comparing the exact solution for the pressure distribution over a circular cylinder in a potential flow with the solution from the PDE Toolbox;
7- use the procedure developed to predict the pressure distribution over a number of bodies of different shape located in a steady 2D ideal fluid flow.

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