Do we need non-linear corrections? On the boundary Forchheimer equation in acoustic scattering

2021 ◽  
Vol 495 ◽  
pp. 115905
Author(s):  
Matthew J. Colbrook ◽  
Lorna J. Ayton
2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 943-951
Author(s):  
Pei-Tao Qiu ◽  
Zhan-Qing Chen ◽  
Hai Pu ◽  
Jiong Zhu

Studying the seepage properties of broken rock is important for understanding the behavior of engineering projects and preventing seepage disasters from occurring. Therefore, a test system was developed to test the seepage properties of broken rock under different porosities and particle sizes. A non-linear seepage equation of broken rock was developed based on the Forchheimer equation and the theories of fraction calculus. The influence of the coupling mechanism of the porosity and particle size on the seepage properties of broken rock was analyzed. The results show that the non-linear seepage equation can describe the non-linear seepage properties of broken rock well. The relations between the permeability and the porosity and particles size can all be represented through an exponential function. It is thought that watercourses are developed in broken rock with high porosity and large particle size, which shows a stronger hydraulic conductivity capability. However, the inertial potential energy of a non-Darcy flow is relatively small.


1967 ◽  
Vol 28 ◽  
pp. 105-176
Author(s):  
Robert F. Christy

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)


Optimization ◽  
1975 ◽  
Vol 6 (4) ◽  
pp. 549-559
Author(s):  
L. Gerencsér

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