Highly accurate space-time coupled least-squares finite element framework in studying wave propagation

Abstract

Simulation of stress wave propagation through solid medium is commonly carried using Galerkin weak-form cast over decoupled space and time domains. In this paper, accuracy of this commonly utilized framework is compared to that of the variationally-consistent least-squares form of the wave equation cast over space-time domain. The two formulations are tested for numerical dispersion and numerical diffusion, through two test cases. The first case studies the dispersion in harmonic shear wave propagation through a soil column over a wide range of forcing frequencies. The second test case investigates numerical diffusion in an axial wave propagation generated by constant force; which is removed after a certain time to allow free vibration to take place. Low numerical dispersion and numerical diffusion as well as high rates of convergence are the main advantages of the coupled least-squares (CLS) computational framework; when compared to the decoupled Galerkin (DG) framework. Based on studies presented here, CLS has low dispersion; yielding errors with one to two orders of magnitude less than that of DG. Also, the numerical diffusion present in DG framework causes a %40 error in DG’s prediction of the stress-wave intensity. Furthermore, accumulative error during evolution is virtually nonexistent for CLS, whereas, the error steadily increases as the solution evolves in DG framework. It is also demonstrated that CLS feature of temporal meshing allows for faster computations.