View source: R/beq.song.dimensionless.R
beq.song.dimensionless | R Documentation |
Dimensionless solution for one-dimensional derived equation from scaling Boussinesq Equation (Song et al, 2007)
beq.song.dimensionless(xi, xi0, a)
xi |
dimensionless coordinate (see |
xi0 |
displacement of wetting front expressed as dimensionless coordinate (see |
a |
vector of coefficient returned by |
the dimesioneless solution, i.e. the variable H
The expession for the dimensionless coordinate (Song at al., 2007) is \xi=x (\frac{2 \, s }{\eta_1 \, K_s \, t^{\alpha+1} } )^{1/2}
and the solution for the dimensionless equation derived by Boussinesq Equation is:
H = \sum_{n=0}^{\infty} a_n (1-\frac{\xi}{\xi_0} )^n
for \xi<\xi_0
, otherwise is 0 .
Emanuele Cordano
Song, Zhi-yao;Li, Ling;David, Lockington. (2007), "Note on Barenblatt power series solution to Boussinesq equation",Applied Mathematics and Mechanics, https://link.springer.com/article/10.1007/s10483-007-0612-x ,\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10483-007-0612-x")}
beq.song
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