Aerodynamic potential-flow code
In fluid dynamics, aerodynamic potential flow codes or panel codes are used to determine the fluid velocity, and subsequently the pressure distribution, on an object. This may be a simple two-dimensional object, such as a circle or wing, or it may be a three-dimensional vehicle. A series of singularities as sources, sinks, vortex points and doublets are used to model the panels and wakes. These codes may be valid at subsonic and supersonic speeds. History. Early panel codes were developed in the late 1960s to early 1970s. Advanced panel codes, such as Panair (developed  by Boeing), were first introduced in the late 1970s, and gained popularity as computing speed increased. Over time, panel codes were replaced with higher order panel methods and subsequently CFD (Computational Fluid Dynamics). However, panel codes are still used for preliminary aerodynamic analysis as the time required for an analysis run is significantly less due to a decreased number of elements. Assumptions. These are the various assumptions that go into developing potential flow panel methods: However, the incompressible flow assumption may be removed from the potential flow derivation leaving: Derivation of panel method solution to potential flow problem. As Q  goes from inside V to the surface of V, For :formula_4, where the surface normal points inwards. This equation can be broken down into both a source term and a doublet term. The Source Strength at an arbitrary point Q is: The Doublet Strength at an arbitrary point Q is: The simplified potential flow equation is: With this equation, along with applicable boundary conditions, the potential flow problem may be solved. Required boundary conditions. The velocity potential on the internal surface and all points inside V (or on the lower surface S) is 0. The Doublet Strength is: The velocity  potential on the outer surface is normal to the surface and is equal to the freestream velocity. These basic equations are satisfied when the geometry is a 'watertight' geometry. If it is watertight, it is a well-posed problem. If it is not, it is an ill-posed problem. Discretization of potential flow equation. The potential flow equation with well-posed boundary conditions applied is: The continuous surface S may now be discretized into discrete panels. These panels will approximate the shape of the actual surface. This value of the various source and doublet terms may be evaluated at a  convenient point (such as the centroid of the panel). Some assumed distribution of the source and doublet strengths (typically constant or linear) are used at points other than the centroid. A single source term s of unknown strength formula_24 and a single doublet term m of unknown strength formula_24 are defined at a given point. where: These terms can be used to create a system of linear equations which can be solved for all the unknown values of formula_24. Methods for discretizing panels. Some techniques are commonly used to model surfaces. Methods of determining pressure. Once the Velocity at every  point is determined, the pressure can be determined by using one of the following formulas. All various Pressure coefficient methods produce results that are similar and are commonly used to identify regions where the results are invalid. Pressure Coefficient is defined as: The Isentropic Pressure Coefficient is: