(untitled) (Archives of Mechanics - Test, 2017)
The eigenvalues and eigenfunctions of the Helmholtz equation with Neumann conditions are obtained for the stadium-shaped domain. The variational Ritz method is found to be accurate and efficient in determining these eigenvalues and eigenfunctions. The eigenfunctions show the evolution and switching of mode shapes from a long rectangular strip to a circle. These new results are applied to the sloshing of a liquid in a tank, and to the onset of thermo-convective stability in a confined porous layer.