Similarity solutions of radially symmetric two-phase flow
type: Item
instance of: scholarly article
title: Similarity solutions of radially symmetric two-phase flow
zbMATH Open document ID: 0820.76089
DOI: 10.1007/BF00952080
author: Scott W. Weeks
author: G. C. Sander
author: Ian G. Lisle
author: Nathan Parlange
author: J.-Y. Parlange
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1995-05-11T00:00:00Z
review text: When both the diffusivity \(D\) and fractional flow function \(f\) have a power law dependence on the water content \(\theta\), i.e. \(D= D_ 0 \theta^ \alpha\) and \(f= \theta^{\alpha+1}\), the nonlinear transport equation for radially symmetric two-phase flow can, in certain circumstances, be reduced to a weakly coupled system of two first order nonlinear ordinary differential equations. Numerical solutions of these equations for a constant flux boundary condition and comparison with experimental data are given. We show that the existence of some exact solutions is due to the presence of a Lagrangian symmetry.
Mathematics Subject Classification ID: 76T99
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 754590
zbMATH Keywords: diffusivity
zbMATH Keywords: fractional flow function
zbMATH Keywords: power law
zbMATH Keywords: weakly coupled system of two first order nonlinear ordinary differential equations
zbMATH Keywords: constant flux boundary condition
zbMATH Keywords: Lagrangian symmetry
MaRDI profile type: Publication
cites work: Q3953228
cites work: Similarity solutions of the nonlinear diffusion equation
cites work: On reducible non-linear differential equations occurring in mechanics
cites work: A note on some similarity solutions of the diffusion equation
cites work: Three dimensional similarity solutions of the nonlinear diffusion equation from optimization and first integrals
full work available at URL: https://doi.org/10.1007/bf00952080
OpenAlex ID: W2065343422
description: scientific article; zbMATH DE number 754590