Journal article

A numerical method for the multiphase viscous flow equations

James M Osborne, Jonathan P Whiteley

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | ELSEVIER SCIENCE SA | Published : 2010

Abstract

A numerical technique is developed for the solution of the equations that govern multiphase viscous flow. We demonstrate that the equations can be written as a coupled system of Partial Differential Equations (PDEs) comprising: (i) first order hyperbolic PDEs for the volume fraction of each phase; (ii) a generalised Stokes flow for the velocity of each phase; and (iii) elliptic PDEs for the concentration of nutrients and messengers. Furthermore, the computational domain may vary with time for some applications. Appropriate numerical methods are identified for each of these subsystems. The numerical technique developed is then demonstrated using two exemplar applications: tissue engineering; ..

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University of Melbourne Researchers

Grants

Awarded by Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom through the Life Sciences Interface Doctoral Training Centre at the University of Oxford


Funding Acknowledgements

This research was enabled by a studentship from the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom awarded through the Life Sciences Interface Doctoral Training Centre at the University of Oxford (Grant No. EP/E501605/1).