A Multidomain Pseudospectral Formulation for the Simulation of Elastic Wave Scattering
Abstract
In many areas of acoustical imaging, such as ultrasonic non-destructive evaluation (NDE), a realistic calculation of ultrasonic field parameters and associated elastic wave scattering requires the treatment of discontinuous, layered solids in complex geometries. These facts suggest the need for an accurate and geometrically flexible numerical approach for the simulation of the ultrasonic field, rather than reliance on semi-analytic solutions. In this paper we present an approach for solving the elastic wave equation in discontinuous layered materials in general complex geometries. The approach, based on a direct pseudospectral solution of the time-domain elastodynamic equations consists of five steps. The first step decomposes the global computational domain into a number of subdomains adding the required geometrical flexibility to the method. Moreover, this decomposition allows for efficient parallel computations, hence decreasing the computational time. The second step in the method maps every subdomain onto the unit square using transfinite blending functions. With this curvilinear mapping the elastodynamic equations can be solved to spectral accuracy, and furthermore, complex interfaces can be approximated smoothly, thus avoiding staircasing. The third step of the method deals with the evaluation of spatial derivatives on Chebyshev-Gauss-Lobatto nodal points within each subdomain, by means of a pseudospectral approach, while the fourth step reconstruct a global solution from the local solutions using properties of the equations of elastodynamics. In a final step, the global solution is advanced in time using a fourth order Runge-Kutta scheme. Several examples of elastic wave scattering related to ultrasonic NDE are presented as evidence of the accuracy and flexibility of the proposed computational method.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 15, 2001
- Accession Number
- ADA462237
Entities
People
- Jan S. Hesthaven
- Steen A. Nielsen