panelmethoden

Panelmethoden is a numerical technique used in computational fluid dynamics and potential flow theory to solve for the velocity and pressure fields around objects. It is particularly effective for external flow problems where the fluid is assumed to be inviscid and incompressible. The core idea is to discretize the surface of the object into a series of small, flat panels. Each panel is then assigned a singularity, such as a source or a doublet, of unknown strength.

The strength of these singularities is determined by solving a system of linear equations. These equations are derived from the boundary condition that the fluid flow must be tangent to the surface of the object. By imposing this condition at a representative point on each panel, a set of equations is created where the unknowns are the strengths of the singularities on each panel. Once these strengths are known, the velocity and pressure at any point in the flow field can be calculated by summing the contributions from all the panels.

Panel methods are computationally efficient compared to full Navier-Stokes solvers for certain types of problems, especially when viscosity effects are negligible. They are widely used in aerodynamics for calculating lift and drag on wings and fuselages, and in naval hydrodynamics for analyzing ship hulls. The accuracy of the method depends on the number and distribution of panels used, with more panels generally leading to higher accuracy but also increased computational cost. Variations of the panel method exist, including source-panel methods and vortex-panel methods, each suited to different flow characteristics.