High-fidelity numerical simulation of the dynamic beam equation
A high-fidelity finite difference approximation of the dynamic beam equation is derived. Different types of well-posed boundary conditions are analysed. The boundary closures are based on the summation-by-parts (SBP) framework and the boundary conditions are imposed using a penalty (SAT) technique, to guarantee linear stability. The resulting SBPSAT approximation leads to fully explicit time integration. The accuracy and stability properties of the newly derived SBPSAT approximations are demonstrated for both 1-D and 2-D problems.
dynamic beam equation stability finite difference methods high-order derivative high-order accuracy boundary treatment