A finite difference technique for simulating unsteady viscoelastic free surface flows

S. McKee, A. Castelo, J.A. Cuminato, M.F. Tomé, N. Mangiavacchi

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This work is concerned with the development of a numerical method capable of simulating viscoelastic free surface flow of an Oldroyd-B fluid. The basic equations governing the flow of an Oldroyd-B fluid are considered. A novel formulation is developed for the computation of the non-Newtonian extra-stress components on rigid boundaries. The full free surface stress conditions are employed. The resulting governing equations are solved by a finite difference method on a staggered grid, influenced by the ideas of the marker-and-cell (MAC) method. Numerical results demonstrating the capabilities of this new technique are presented for a number of problems involving unsteady free surface flows.
Original languageEnglish
Pages (from-to)61-106
Number of pages45
JournalJournal of Non-Newtonian Fluid Mechanics
Issue number2-3
Publication statusPublished - 2002



  • viscoelastic flow
  • Oldroyd-B
  • finite difference
  • constitutive equations
  • computational physics
  • numerical analysis

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