Mesh Dispersion Minimization Algorithms Within Explicit Finite-Difference Schemes to Calculate Transient Wave Processes in Elastic Media and Composite Structures

Abstract

Precise calculation of wave fronts and high-gradient components is always of utmost importance for problems of numerical simulation of wave processes in media and composite structures. The usage mesh algorithms come across specific obstacles, which do not allow to accurately calculate such disturbances localized at the loading area or propagated with time. One of such obstacles (notably in the problems with singularities) is the spurious effect caused by the mesh dispersion responsible for the emergence of high-frequency "parasite" oscillations damaged the computer solution. In this work, advanced numerical algorithms within the explicit finite-difference scheme are developed exactly for very purpose -to precisely calculate wave processes with singularities. The algorithms are constructed with the condition that dependence domains are the same (or maximally closed) in differential and difference equations corresponding to continual and discrete models, respectively. In the designed algorithms, the influence of spurious effects of numerical dispersion is suppressed (or essentially minimized) that allows discontinuities in fronts and high-gradient components to be accurately calculated. A set of examples of computer simulations of linear and nonlinear wave processes are presented. Among them are (a) impact propagation in a waveguide resting on an elastic foundation, (b) cylindrical and spherical waves, and (c) wave propagation and fracture pattern in a unidirectional composite. Comparison of results calculated by conventional and developed algorithms clearly shows the advantage of the latter. To this end, precise numerical solutions (in mesh points of the discrete space) are obtained for the problems listed above.