A Boundary Integral Approach for Three-Dimensional Underwater Explosion Bubble Dynamics

1992 ◽  
Author(s):  
Stephen Wilkerson
Keyword(s):  
Bubble Dynamics ◽  
Three Dimensional ◽  
Underwater Explosion ◽  
Boundary Integral ◽  
Integral Approach

A Boundary Integral Method for Examining Underwater Explosion Bubble Dynamics

1991 ◽  
Author(s):  
Stephen Wilkerson
Keyword(s):  
Bubble Dynamics ◽  
Free Field ◽  
Three Dimensional ◽  
Underwater Explosion ◽  
Boundary Integral ◽  
Integral Formulation ◽  
Boundary Integral Method ◽  
Spherically Symmetric ◽  
First Order ◽  
Boundary Integral Formulation

Abstract A boundary integral formulation for the numerical calculation of an underwater explosion bubble’s expansion and collapse is presented. The formulation makes use of first-order three-dimensional panels and adapts the methodology specifically for the simulation of an underwater explosion bubble. These simulations include a free field bubble as well as a bubble’s interaction with a nearby fixed surface. A number of explosion bubble codes have been written using the boundary integral formulation and are discussed throughout the three-dimensional formulation. Specifically, a spherically symmetric code, an axisymmetric code for simple geometries, and a first-order three-dimensional code was developed. The validity of the three-dimensional code presented is established through direct comparisons with the previously validated axisymmetric code (Wilkerson, 1989).

A three-dimensional magnetostatics computer code for insertion devices

1998 ◽  
Vol 5 (3) ◽  
pp. 481-484 ◽  
Author(s):  
Oleg Chubar ◽  
Pascal Elleaume ◽  
Joel Chavanne
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Object Oriented ◽  
Computer Code ◽  
Boundary Integral ◽  
Integral Approach ◽  
Registered Trademark ◽  
Cpu Time ◽  
Analytical Formulae ◽  
Field Integral

RADIA is a three-dimensional magnetostatics computer code optimized for the design of undulators and wigglers. It solves boundary magnetostatics problems with magnetized and current-carrying volumes using the boundary integral approach. The magnetized volumes can be arbitrary polyhedrons with non-linear (iron) or linear anisotropic (permanent magnet) characteristics. The current-carrying elements can be straight or curved blocks with rectangular cross sections. Boundary conditions are simulated by the technique of mirroring. Analytical formulae used for the computation of the field produced by a magnetized volume of a polyhedron shape are detailed. The RADIA code is written in object-oriented C++ and interfaced to Mathematica [Mathematica is a registered trademark of Wolfram Research, Inc.]. The code outperforms currently available finite-element packages with respect to the CPU time of the solver and accuracy of the field integral estimations. An application of the code to the case of a wedge-pole undulator is presented.

A Three-Dimensional Modeling of Multidirectional Random Wave Interactions by Multiple Rectangular Submarine Pits

2004 ◽  
Author(s):  
Hong Sik Lee ◽  
A. Neil Williams ◽  
Sung Duk Kim
Keyword(s):  
Numerical Model ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integral Approach ◽  
Random Wave ◽  
Random Surface ◽  
Directional Spectrum ◽  
Practical Applications ◽  
Three Dimensional Modeling

A three-dimensional numerical model is presented to predict the interactions of multidirectional random surface waves with one or more rectangular submarine pits. The water depth in the fluid region exterior to the pits is taken to be uniform. The three-dimensional Green function in the boundary integral equation, obtained by Green’s second identity, has been used for the solution of the velocity potential and its derivative in fluid interface between regions, and also a form of the Fourier expansion is utilized for the solution of the velocity potential in the interior region. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. The present method is based on the cumulative superposition of linear diffraction solutions obtained by a three-dimensional boundary integral approach. The results of the present model have been compared with those of previous theoretical studies for both regular and random wave diffraction by single or multiple pits. Reasonable agreement was consistently obtained in all cases. In accordance with good agreement from these comparisons, it is concluded that the present numerical model may accurately be utilized to predict the three-dimensional wave field around multiple submarine pits or navigation channels in many practical applications.

Boundary Element Crystal Plasticity Method

2017 ◽  
Vol 08 (03n04) ◽  
pp. 1740003
Author(s):  
Ivano Benedetti ◽  
Vincenzo Gulizzi ◽  
Vincenzo Mallardo
Keyword(s):  
Grain Boundary ◽  
Boundary Element ◽  
Crystal Plasticity ◽  
Boundary Integral Equations ◽  
Voronoi Tessellation ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integral Approach ◽  
Rate Dependent ◽  
Individual Grains

A three-dimensional (3D) boundary element method for small strains crystal plasticity is described. The method, developed for polycrystalline aggregates, makes use of a set of boundary integral equations for modeling the individual grains, which are represented as anisotropic elasto-plastic domains. Crystal plasticity is modeled using an initial strains boundary integral approach. The integration of strongly singular volume integrals in the anisotropic elasto-plastic grain-boundary equations are discussed. Voronoi-tessellation micro-morphologies are discretized using nonstructured boundary and volume meshes. A grain-boundary incremental/iterative algorithm, with rate-dependent flow and hardening rules, is developed and discussed. The method has been assessed through several numerical simulations, which confirm robustness and accuracy.

Wave propagation through an interface between dissimilar media with a doubly periodic array of arbitrary shaped planar delaminations

2017 ◽  
Vol 24 (2) ◽  
pp. 483-498 ◽  
Author(s):  
Mikhail V Golub ◽  
Olga V Doroshenko
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Elastic Waves ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Periodic Array ◽  
Integral Approach ◽  
Galerkin Scheme ◽  
Scattering Of Elastic Waves ◽  
Doubly Periodic Array

This paper considers the scattering of elastic waves by a doubly periodic array of three-dimensional planar delaminations at the interface between two dissimilar media. The delaminations are modelled in terms of the spring boundary conditions, which are employed to formulate a boundary integral equation. The problem is solved using the Bubnov–Galerkin scheme and the integral approach, taking into account geometrical periodicity. The effects of distribution and shape of periodic delaminations on wave transmission and diffraction are analysed. The specific phenomenon of pass-bands or an ‘opening’ interface for wave propagation by a periodic array of delaminations is revealed.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

scholarly journals The Numerical Analysis of the Flow on the Smooth and Nonsmooth Boundaries by IBEM/DBIEM

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Gang Xu ◽  
Guangwei Zhao ◽  
Jing Chen ◽  
Shuqi Wang ◽  
Weichao Shi
Keyword(s):  
Boundary Value ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Tangential Velocity ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Surface Shape ◽  
Normal Vector ◽  
Computational Domain ◽  
Nonsmooth Boundary

The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.

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