beq.song.dimensionless {boussinesq}

Dimensionless solution for one-dimensional derived equation from scaling Boussinesq Equation (Song et al, 2007)

Description

Dimensionless solution for one-dimensional derived equation from scaling Boussinesq Equation (Song et al, 2007)

Usage

beq.song.dimensionless(xi, xi0, a)

Arguments

xi

dimensionless coordinate (see Note)

xi0

displacement of wetting front expressed as dimensionless coordinate (see Note)

a

vector of coefficient returned by coefficient.song.solution

Value

the dimesioneless solution, i.e. the variable H

Note

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 .

Author(s)

Emanuele Cordano

References

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 ,doi:10.1007/s10483-007-0612-x

See Also

beq.song