Numerical damping of spurious oscillations using the explicit dissipative Tchamwa-Wielgosz algorithm
Résumé
The use of Finite Element and Finite Difference methods of spatial and temporal discretization for solving structural dynamics problems gives rise to purely numerical errors. Among the many numerical methods used to damp out the spurious oscillations occurring in the high frequency domain, it is proposed here to analyse and compare the Bulk Viscosity method which modifies the stresses calculations and a method recently presented by Tchamwa and Wielgosz (Rio, Soive, Grolleau, Adv. in Eng. Soft., vol. 36(4), 2005), which is based on a modification of an explicit time integration algorithm. The first method can be seen like a perturbation of the local behavior equation while the second appears like a perturbation of the global balance equation. The first method has been widely used in numerous engineering works, and is regarded as reference to smooth the spurious oscillations whereas the second, recently appeared, provides also a powerful tool for smoothing high frequencies, without loss of accuracy. In this study, the Central Differences schemes, the Bulk Viscosity method and the Tchamwa scheme are first defined in the FEM context. The damping efficiency of these methods is studied throughout an accuracy analysis and theoretical evidence is presented showing the sensitivity of each method to the size of time step, the mesh size, the type of strain field and the behavioral parameters of the material. Numerical examples provide 1-D and 3-D examples of this sensitivity.