Comparative study of numerical explicit time integration algorithms

The aim of this research is to make a comparative study of numerical explicit time integration algorithms used in the domain of shock and impact. Numerical simulation of such problems, with explicit algorithms for time integration, involves very small time steps for reasons of stability. Thus, very high numerical frequencies can be found in the final solution in displacement or stress. But generally the high frequencies and mode shapes of the spatially discretized equations do not accurately represent the behavior of the original problem. It is proved that algorithms such as Chung-Lee, Zhai, HHT, Tchamwa, central difference method, are useful to solve problems including high speed phenomena. The different regions of stability, accuracy, but also the capacity of each numerical scheme to smooth very high frequencies are compared. Finally, these integration schemes are implemented in the HEREZH++ finite element code developed at the LG2M laboratory ([1]). For some simple problems the solutions obtained from HEREZH++ and the commercial code LS-DYNA are compared and discussed, For instance, following these simulations, it seems that the Tchamwa's algorithm is particularly efficient to smooth the highest frequencies.