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
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; ..View full abstract
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
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).