Computational and Applied Mathematics

, Volume 36, Issue 2, pp 903–913 | Cite as

Well-posed initial conditions and numerical methods for one-dimensional models of liquid dynamics in a horizontal capillary



In this paper, we undertake a mathematical and numerical study of liquid dynamics models in a horizontal capillary. In particular, we prove that the classical model is ill-posed at initial time, and we recall two different approaches in order to define a well-posed problem. Moreover, for an academic test case, we compare the numerical approximations, obtained by an adaptive initial value problem solver based on an one-step one-method approach, with new asymptotic solutions. This is a possible way to validate the adaptive numerical approach for its application to real liquids.


Well-posed initial conditions Horizontal capillary Asymptotic solutions Adaptive numerical method 

Mathematics Subject Classification

34A12 65L05 76D45 



The first author gratefully thanks Chris Budd for fruitful discussions concerning the asymptotic solutions while he was visiting the Department of Mathematics, University of Bath, United Kingdom. This work was supported by the University of Messina and by the GNCS (Computational Science National Group) of the INDAM (Italian Institute of High Mathematics).


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2015

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of MessinaMessinaItaly

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