(Manuscript received 3 March 2001, in final form 10 January 2002) ... and without making the Boussinesq approximation in the continuity equation, correspond very closely with the hydrostatic ..... 1997 measures) and acts as an additional advective te
TECHNOLOGY ADMINISTRATION. Robert M. White, Under Secretary for Technology ... Many of the techniques developed by the CFD .... P + 0, then we recover the Boussinesq equation for the density: 3F. ~(Po+P), dcj - 0. - at ... cold wall BC.
xUxx + 2b0(UtUxx + 2UxUxt) â. (5.4). 4b2UxUxx + 2b3Uxx + 4b0b2Uxt â 3b2. 0Uyy = 0. Remember that the Boussinesq higher order equation represents how ...
Feb 27, 2013 - the R package ''geotopbricks'' freely available under GPL on CRAN ... d'appel variable de l'hydrologie du bassin versant, Hydrol. Sci. Bull.,.
house made 6oz certified angus beef burger with side caesar salad and hand cut french fries. (all burgers dressed with l
Apr 8, 2016 - Boussinesq Energy Conservation. William K. Dewar 1,*, Joseph Schoonover 1, Trevor McDougall 2 and Rupert Klein 3. 1. Department of Earth ...
Apr 16, 2013 - AP] 16 Apr 2013. THE OBERBECK-BOUSSINESQ APPROXIMATION IN CRITICAL. SPACES. RAPHAÃL DANCHIN AND LINGBING HE.
systems provide a much more precise approximation than the KP equation and ... This limits severely its applicability as a realistic model for long water- waves.
Aug 23, 2018 - Boussinesq system, Arab Journal of Basic and Applied Sciences, 25:2, 85-91, DOI: ... These interesting exact solutions may be useful in the study of some phenomena appeared ..... of nonlinear PDEs in mathematical physics.
obtained by the Wronskian formulation and a detailed discussion on their ... Keywords: Hirota's bilinear method, Soliton equation, Boussinesq equation.
NY cheesecake spiced with cinnamon and brown sugar and topped with caramel. FOUR LAYER CHOCOLATE CAKE four layers of dec
Mar 22, 2009 - [25] H. Triebel: Theory of function spaces. (Leipzig 1983). ... 35 042 Rennes cedex, France. E-mail address: [email protected].
Jun 22, 2009 - bar-tilde and bar-hat versions of (1.2), which can be derived from (1.3a). Consider now the cube of Figure 1, where F stands for the three ...
formed in Section 4 on larger spatial intervals and with special initial data that yield nearly one-way .... Application
Boussinesq equations, Global existence, Vortex stretching, Fluid .... Multiplying both sides of this equation by Ï and integrating over R2, we get. 1. 2 d dt. â«. R2.
such that the velocity field is given by v = ∇ ... ∂z. = 0, z = −h,. ∂t ζ + ∂x. ∂xζ + ∂y. ∂yζ = ∂z. , z = ζ(t,x,y),. ∂t. + 1 ... 3 This constraint is due to a singular approximation of the dispersion relation of .... For all 1 ⩽ p ⩽ ∞, the usual Lp(R
Feb 7, 2014 - From here on we discuss periodic domains for which there are .... chy is denoted P2G, so named because it adds vortical-wave-wave interactions to the ..... For a first test of the models described in Section 3 and Table 1, we consider t
Mar 22, 2016 - assessing the viability of such approximation during nonlinear stability ... Accordingly a 3-D computational model of a rectangular loop is ... Stability appraisal of single-phase natural circulation loops ..... tion system in rolling
Oct 31, 2018 - We construct a weakly-nonlinear d'Alembert-type solution ... The solution is applied to study interactions of radiating solitary waves. Keywords: ...
Aug 7, 2009 - Department of Mathematics - IMECC/UNICAMP ... Concerning the LWP question for the initial value problem (IVP), several results ... In this paper, we also consider the periodic setting and improve this last result by establishing the LWP
involving runup at a plane beach and overtopping of a laboratory seawall. ... and first order dispersion, there has been considerable progress made in ex-.
FINITE ELEMENTS FOR THE BOUSSINESQ WAVE EQUATIONS. HANS PETTER LANGTANGEN AND GEIR PEDERSEN. Mechanics Division, Department of ...
to Eq. (6), which are equivalent to applying the approximate symmetry perturbation method and approximate direct method to Eq. (4), respectively. Section IV ...
Feb 19, 2015 - Title Analytic Solutions for (ground-water) Boussinesq Equation ... empirical coefficient to estimate hydraulic diffusivity D = ks/(s â (p â h1 +.
Package ‘boussinesq’ February 19, 2015 Maintainer Emanuele Cordano License GPL (>= 2) Title Analytic Solutions for (ground-water) Boussinesq Equation Type Package Depends R (>= 2.10) Author Emanuele Cordano Description This package is a collection of R functions implemented from published and available analytic solutions for the One-Dimensional Boussinesq Equation (ground-water). In particular, the function ``beq.lin'' is the analytic solution of the linearized form of Boussinesq Equation between two different head-based boundary (Dirichlet) conditions; ``beq.song'' is the non-linear power-series analytic solution of the motion of a wetting front over a dry bedrock (Song at al, 2007, see complete reference on function documentation). Bugs/comments/questions/collaboration of any kind are warmly welcomed. Version 1.0.3 Repository CRAN Date 2013-04-18 URL http://onlinelibrary.wiley.com/doi/10.1002/wrcr.20072/abstract Collate 'beq.lin.dimensionless.R' 'beq.lin.R' 'beq.song.dimensionless.R' 'beq.song.R' 'boussinesq-package.R' 'coefficient.song.solution.R' NeedsCompilation no Date/Publication 2013-04-19 16:29:04
Analytic exact solution for One-Dimensional Boussinesq Equation in a two-bounded domain with two constant-value Dirichlet Condition
Description Analytic exact solution for One-Dimensional Boussinesq Equation in a two-bounded domain with two constant-value Dirichlet Condition Usage beq.lin(t = 0, x = seq(from = 0, to = L, by = by), h1 = 1, h2 = 1, L = 100, ks = 0.01, s = 0.4, big = 10^7, by = L/100, p = 0.5)
beq.lin
3
Arguments t
time coordinate.
x
spatial coordinate. Default is seq(from=0,to=L,by=by).
big
maximum level of Fourier series considered. Default is 10^7.
by
see seq
L
length of the domain.
h1
water surface level at x=0. Left Dirichlet Bounday Condition.
h2
water surface level at x=L. Right Dirichlet Bondary Condition.
ks
Hydraulic conductivity
s
drainable pororosity (assumed to be constant)
p
empirical coefficient to estimate hydraulic diffusivity D = ks/(s ∗ (p ∗ h1 + (1 − p) ∗ h2)). It ranges between 0 and 1.
Value Solutions for the indicated values of x and t. Author(s) Emanuele Cordano
