Advances in scientific computing have made modelling and simulation an important part of the decision-making process in engineering, science, and public policy. This book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations. The emphasis is placed on models that are described by partial differential and integral equations and the simulations that result from their numerical solution. The methods described can be applied to a wide range of technical fields, from the physical sciences, engineering and technology and industry, through to environmental regulations and safety, product and plant safety, financial investing, and governmental regulations. This book will be genuinely welcomed by researchers, practitioners, and decision makers in a broad range of fields, who seek to improve the credibility and reliability of simulation results. It will also be appropriate either for university courses or for independent study.

/pdf/verification-and-validation-in-scientific-computing-262w5ti0ia.pdf

Verification and Validation in Scientific Computing

Partitioned analysis of coupled mechanical systems

Non-reflecting boundary conditions

The perfectly matched layer (PML) absorbing boundary condition has proven to be very efficient from a numerical point of view for the elastic wave equation to absorb both body waves with nongrazing incidence and surface waves. However, at grazing incidence the classical discrete PML method suffers from large spurious reflections that make it less efficient for instance in the case of very thin mesh slices, in the case of sources located close to the edge of the mesh, and/or in the case of receivers located at very large offset. We demonstrate how to improve the PML at grazing incidence for the differential seismic wave equation based on an unsplit convolution technique. The improved PML has a cost that is similar in terms of memory storage to that of the classical PML. We illustrate the efficiency of this improved convolutional PML based on numerical benchmarks using a finite-difference method on a thin mesh slice for an isotropic material and show that results are significantly improved compared with the classical PML technique. We also show that, as the classical PML, the convolutional technique is intrinsically unstable in the case of some anisotropic materials.

An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation

Numerical solution of problems on unbounded domains. a review

Doubly asymptotic approximations (DAA) are differential equations for simplified analysis of the transient interaction between a flexible structure and a surrounding infinite medium. These surface interaction approximations approach exactness in the limit of low‐ and high‐frequency motions and effect a smooth transition in the intermediate frequency range. A finite‐element DAA formulation for an acoustic medium is presented herein, with attention focused on the first and second members of the DAA hierarchy. The free‐vibration and forced‐response characteristics of the first and second approximations are examined through specialization to a spherical geometry.

Doubly asymptotic approximations for transient motions of submerged structures

A model for a moderately deep underwater explosion bubble is developed that integrates the shock wave and oscillation phases of the motion. A hyperacoustic relationship is formulated that relates bubble volume acceleration to far-field pressure profile during the shock-wave phase, thereby providing initial conditions for the subsequent oscillation phase. For the latter, equations for bubble-surface response are derived that include wave effects in both the external liquid and the internal gas. The equations are then specialized to the case of a spherical bubble, and bubble-surface displacement histories are calculated for dilational and translational motion. Agreement between these histories and experimental data is found to be substantially better than that produced by previous models.

An integrated wave-effects model for an underwater explosion bubble

A method developed previously for an analysis of the two‐dimensional excitation of an elastic cylindrical shell by a transverse, transient acoustic wave is extended to three‐dimensional applicability. In addition, some fluid‐structure interaction approximations are presented that follow naturally from the rigorous development. Application to finite element analysis of the transient response of submerged structures is discussed.

Residual Potential and Approximate Methods for Three‐Dimensional Fluid‐Structure Interaction Problems

Evaluation of the Perfectly Matched Layer for Computational Acoustics

https://roadsafellc.com/NCHRP22-24/Literature/Papers/Metrics/Spectral%20elements%20and%20field%20separation%20for%20an%20acoustic.pdf

Thomas L. Geers

Papers

Doubly asymptotic approximations for transient motions of submerged structures

An integrated wave-effects model for an underwater explosion bubble

Residual Potential and Approximate Methods for Three‐Dimensional Fluid‐Structure Interaction Problems

Evaluation of the Perfectly Matched Layer for Computational Acoustics

Spectral elements and field separation for an acoustic fluid subject to cavitation