Fundamental Solutions

2014 ◽  
pp. 33-57
Author(s):  
Petia Dineva ◽  
Dietmar Gross ◽  
Ralf Müller ◽  
Tsviatko Rangelov
Keyword(s):  
Fundamental Solutions

Improved geometric modeling using the method of fundamental solutions

2021 ◽  
Vol 130 ◽  
pp. 49-57
Author(s):  
C.S. Chen ◽  
Lionel Amuzu ◽  
Kwesi Acheampong ◽  
Huiqing Zhu
Keyword(s):  
Geometric Modeling ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions

scholarly journals Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows

1975 ◽  
Vol 67 (4) ◽  
pp. 787-815 ◽  
Author(s):  
Allen T. Chwang ◽  
T. Yao-Tsu Wu
Keyword(s):  
Exact Solutions ◽  
Stokes Flow ◽  
Fundamental Solutions ◽  
The Body ◽  
Circular Cylinders ◽  
Geometrical Parameters ◽  
Flow Problems ◽  
Singularity Method ◽  
Wide Range ◽  
Body Shapes

The present study further explores the fundamental singular solutions for Stokes flow that can be useful for constructing solutions over a wide range of free-stream profiles and body shapes. The primary singularity is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives other fundamental singularities can be obtained, including rotlets, stresslets, potential doublets and higher-order poles derived from them. For treating interior Stokes-flow problems new fundamental solutions are introduced; they include the Stokeson and its derivatives, called the roton and stresson.These fundamental singularities are employed here to construct exact solutions to a number of exterior and interior Stokes-flow problems for several specific body shapes translating and rotating in a viscous fluid which may itself be providing a primary flow. The different primary flows considered here include the uniform stream, shear flows, parabolic profiles and extensional flows (hyper-bolic profiles), while the body shapes cover prolate spheroids, spheres and circular cylinders. The salient features of these exact solutions (all obtained in closed form) regarding the types of singularities required for the construction of a solution in each specific case, their distribution densities and the range of validity of the solution, which may depend on the characteristic Reynolds numbers and governing geometrical parameters, are discussed.

scholarly journals Influence of fish backbone model geometrical features on the numerical target strength of swimbladdered fish

2020 ◽  
Author(s):  
I Pérez-Arjona ◽  
L Godinho ◽  
V Espinosa
Keyword(s):  
Atlantic Salmon ◽  
Salmo Salar ◽  
Sparus Aurata ◽  
Fundamental Solutions ◽  
Sea Bream ◽  
Method Of Fundamental Solutions ◽  
Target Strength ◽  
Simplified Models ◽  
Geometrical Features ◽  
Proper Estimation

Abstract The method of fundamental solutions has been applied to evaluate the influence of fish models geometrical features on the target strength (TS) directivity and TS frequency response of swimbladdered fish. Simplified models were considered for two fish species: gilt-head sea bream (Sparus aurata, Linnaeus 1758) and Atlantic salmon (Salmo salar, Linnaeus 1758), and different geometrical details of their morphology were studied, such as backbone presence, and its curvature or the inclusion of vertebrae modulation. Swimbladder shape and tilt, together with the inclusion of backbone (and its realistic curvature) for dorsal measurements were the most important features for proper estimation of mean TS. The estimation of mean TS is considered including the effect of fish tilt, the echosounder frequency, and the fish-to-transducer distance.

scholarly journals Fundamental solutions for non-divergence form operators on stratified groups

2003 ◽  
Vol 356 (7) ◽  
pp. 2709-2737 ◽  
Author(s):  
Andrea Bonfiglioli ◽  
Ermanno Lanconelli ◽  
Francesco Uguzzoni
Keyword(s):  
Fundamental Solutions ◽  
Divergence Form ◽  
Stratified Groups
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