A multigrid procedure for three‐dimensional flows on non‐orthogonal collocated grids

K. M. Smith, W. K. Cope, S. P. Vanka

Research output: Contribution to journalArticlepeer-review


The development of a multigrid solution algorithm for the computation of three‐dimensional laminar fully‐elliptic incompressible flows is presented. The procedure utilizes a non‐orthogonal collocated arrangement of the primitive variables in generalized curvilinear co‐ordinates. The momentum and continuity equations are solved in a decoupled manner and a pressure‐correction equation is used to update the pressures such that the fluxes at the cell faces satisfy local mass continuity. The convergence of the numerical solution is accelerated by the use of a Full Approximation Storage (FAS) multigrid technique. Numerical computations of the laminar flow in a 90° strongly curved pipe are performed for several finite‐volume grids and Reynolds numbers to demonstrate the efficiency of the present numerical scheme. The rates of convergence, computational times, and multigrid performance indicators are reported for each case. Despite the additional computational overhead required in the restriction and prolongation phases of the multigrid cycling, the superior convergence of the present algorithm is shown to result in significantly reduced overall CPU times.

Original languageEnglish (US)
Pages (from-to)887-904
Number of pages18
JournalInternational Journal for Numerical Methods in Fluids
Issue number10
StatePublished - Nov 30 1993


  • Collocated grids
  • Finite‐volume
  • Multigrid
  • Non‐orthogonal co‐ordinates

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics


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