A novel non-upwind, interconnected, multi-grid, overlapping numerical procedure for problems involving fluid flow

Mohsen M M Abou-Ellail, Yuan Li, Wai Cheung Timothy Tong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


A novel numerical procedure for heat, mass and momentum transfer in fluid flow is presented. The new scheme is passed on a non-upwind, interconnected, multi-grid, overlapping (NIMO) finite-difference algorithm. In 2D flows, the NIMO algorithm solves finite-difference equations for each dependent variable on four overlapping grids. The finite-difference equations are formulated using the control-volume approach, such that no interpolations are needed for computing the convective fluxes. For a particular dependent variable, four fields of values are produced. The NIMO numerical procedure is tested against the exact solution of two test problems. The first test problem is an oblique laminar 2D flow with a double step abrupt change in a passive scalar variable for infinite Peclet number. The second test problem is a rotating radial flow in an annular sector with a single step abrupt change in a passive scalar variable for infinite Peclet number. The NIMO scheme produced essentially the exact solution using different uniform and non-uniform square and rectangular grids for 45 and 30° angle of inclination. All other schemes were unable to capture the exact solution, especially for the rectangular and non-uniform grids. The NIMO scheme was also successful in predicting the exact solution for the rotating radial flow, using a uniform cylindrical-polar coordinate grid.
Original languageEnglish
Pages (from-to)1669-1694
Number of pages26
JournalInternational Journal for Numerical Methods in Fluids
Issue number11
Publication statusPublished - 20 Aug 2008
Externally publishedYes


  • Fluid flow
  • Higher-order scheme
  • Interconnected
  • Multi-grid
  • Non-upwind
  • Overlapping

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Safety, Risk, Reliability and Quality
  • Applied Mathematics
  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computational Mechanics
  • Mechanics of Materials

Cite this