An iterative substructuring method for the $p$ -version of the boundary element method for hypersingular integral operators in three dimensions

1998 ◽  
Vol 79 (3) ◽  
pp. 371-396 ◽  
Author(s):  
Norbert Heuer
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Integral Operators ◽  
Three Dimensions ◽  
Hypersingular Integral ◽  
Iterative Substructuring ◽  
Element Method

Numerical Simulations of Large Deep Water Waves: The Application of a Boundary Element Method

2006 ◽  
Author(s):  
Caroline H. Hague ◽  
Chris Swan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Deep Water ◽  
Water Waves ◽  
Physical Space ◽  
Wave Model ◽  
Three Dimensions ◽  
Fully Nonlinear ◽  
Highly Nonlinear ◽  
Element Method

This paper concerns the description of extreme surface water waves in deep water. A fully nonlinear numerical wave model in three dimensions is presented, based on the Boundary Element Method (BEM), and is applied to nonlinear focusing of wave components with varying frequency and direction of propagation to form highly nonlinear groups. By using multiple fluxes at corners and edges of the numerical domain the “corner problem” associated with BEM-based models in physical space is overcome. A two-dimensional version of the method is also employed to model unidirectional cases, and examples presented include the focusing of Top Hat spectra in deep water to form highly nonlinear wave groups at or close to their breaking limit. The ability of the model to accurately simulate these sea states is highlighted by comparison to the fully nonlinear model of Bateman, Swan and Taylor (2001, 2003).

Toward Large Scale Simulations of Emulsion Flows in Microchannels Using Fast Multipole and Graphics Processor Accelerated Boundary Element Method

2012 ◽  
Author(s):  
Yulia A. Itkulova ◽  
Olga A. Solnyshkina ◽  
Nail A. Gumerov
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Experimental Studies ◽  
Three Dimensions ◽  
Graphics Processors ◽  
Fast Multipole ◽  
Two Phase ◽  
Droplet Dynamics ◽  
Element Method

Several interesting effects discovered recently, such as “dynamic blocking” and “jamming” of emulsion flows in microchannels require in depth theoretical, computational, and experimental studies. The present study is dedicated to development of efficient computational methods and tools to understand the behavior of complex two-phase Stokesian flows. Application of the conventional boundary element method is frequently limited by the computational and memory complexity. The fast multipole methods provide O(N) type algorithms, which can further be accelerated by utilization of graphics processors. We developed efficient codes, which enable direct simulation of systems of tens of thousands of deformable droplets in three dimensions or several droplets with very high discretization of the interface. Such codes can be used for detailed visualization and studies of the structure of droplet flows in channels. Example computations include droplet dynamics in shear flows and in microchannels. We discuss results of simulations and details of the algorithm. We also consider that the present work is a step towards more realistic modeling of the microchannel dispersed flows as further development of the model is required to account for properties of thin films between the droplets, processes of coalescence, etc.

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