scholarly journals Gradient estimates in non-linear potential theory

2009 ◽  
pp. 179-190
Author(s):  
Giuseppe Mingione ◽  
Frank Duzaar
Keyword(s):  
Potential Theory ◽  
Gradient Estimates ◽  
Linear Potential ◽  
Non Linear ◽  
Linear Potential Theory

scholarly journals Non-Linear Motion Characteristics of a Shallow Draft Cylindrical Barge Type Floater for a FOWT in Waves

2021 ◽  
Vol 9 (1) ◽  
pp. 56
Author(s):  
Hideyuki Suzuki ◽  
Yuta Sakai ◽  
Yasuo Yoshimura ◽  
Hidetaka Houtani ◽  
Lucas H. S. Carmo ◽  
...  
Keyword(s):  
Potential Theory ◽  
Water Surface ◽  
Linear Potential ◽  
Viscous Damping ◽  
Linear Motion ◽  
Floating Offshore Wind Turbines ◽  
Hydrodynamic Phenomenon ◽  
Non Linear ◽  
Motion Characteristics ◽  
Linear Potential Theory

A shallow draft cylindrical barge type floater with footing close to the water surface was experimentally evaluated in waves to investigate non-linear motion characteristics. The floater was designed to be used as an option for FOWT—floating offshore wind turbines. The non-linear mechanism can be promoted due to the viscous force that acts on the footing edges and the footing interaction with the free surface. In general, the observed non-linear viscous damping is modeled as a force proportional to the square of the relative velocity between the floater and the water. Therefore, the viscous damping levels is expected to increase, and the response in waves, to decrease. However, an increase in motion responses was observed for a broad range of wave periods. An attempt was made to clarify the hydrodynamic mechanism by comparing wave tank experiments, numerical calculations by CFD—computational fluid dynamics codes, and linear potential theory codes. Regular wave tests for three different wave height conditions were carried out, including free decay tests in still waters. For CFD simulations, the OpenFOAM code was selected. For potential theory simulations, the WAMIT code was chosen. As a result of the research, three points could be highlighted and discussed: first, the hydrodynamic phenomenon that contributed to the non-linear motion of the floater was identified; second, the increase and coupling of the motions response of heave and pitch motions; and finally, the phenomenon that the footing held water mass and lifted it to the water surface. The CFD calculations were able to get good qualitative results compared with the experiments and confirmed the use of CFD as a useful tool to capture the non-linear hydrodynamic phenomenon. The linear potential theory was not able to capture the phenomenon discussed herein.

NON-LINEAR POTENTIAL THEORY

1972 ◽  
Vol 27 (6) ◽  
pp. 71-148 ◽  
Author(s):  
V G Maz'ya ◽  
V P Khavin
Keyword(s):  
Potential Theory ◽  
Linear Potential ◽  
Non Linear ◽  
Linear Potential Theory

Linear potential theory of steady internal supersonic flow with quasi-cylindrical geometry. Part 1. Flow in ducts

1994 ◽  
Vol 281 ◽  
pp. 159-191 ◽  
Author(s):  
Andreas Dillmann
Keyword(s):  
Supersonic Flow ◽  
Potential Theory ◽  
Broad Class ◽  
Three Dimensional ◽  
Double Series ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linear Potential ◽  
Linear Potential Theory ◽  
Initial Boundary Value

Based on linear potential theory, the general three-dimensional problem of steady supersonic flow inside quasi-cylindrical ducts is formulated as an initial-boundary-value problem for the wave equation, whose general solution arises as an infinite double series of the Fourier–Bessel type. For a broad class of solutions including the general axisymmetric case, it is shown that the presence of a discontinuity in wall slope leads to a periodic singularity pattern associated with non-uniform convergence of the corresponding series solutions, which thus are unsuitable for direct numerical computation. This practical difficulty is overcome by extending a classical analytical method, viz. Kummer's series transformation. A variety of elementary flow fields is presented, whose complex cellular structure can be qualitatively explained by asymptotic laws governing the propagation of small perturbations on characteristic surfaces.

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