Transient solutions by a least-squares finite-element method and Jacobi conjugate gradient technique

Li Q. Tang, Tate T.H. Tsang

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We present a least-squares finite-element method that can provide implicit, fully coupled transient solutions for time-dependent incompressible fluid flows and thermal convection. The algorithm consists of the Crank-Nicolson scheme for time discretization, Newton's method for linearization, and a matrix-free Jacobi conjugate gradient method as an iterative solver for the symmetric, positive-definite linear system of equations. The combined algorithm is first validated by two-dimensional flows: flows in a square cavity with a periodically oscillating lid and mixed convection in a driven cavity. Then the algorithm is used to obtain transient solutions of a three-dimensional lid-driven cavity flow for Re = 400 Copyright.

Original languageEnglish
Pages (from-to)183-198
Number of pages16
JournalNumerical Heat Transfer, Part B: Fundamentals
Issue number2
StatePublished - Sep 1995

Bibliographical note

Funding Information:
Received 26 October 1994; accepted 12 April 1995. This work was partially supported by the National Science Foundation (grant no. ASC-8811171; NSF/KY EPSCoR program). We would like to thank Dr. B. N. Jiang of NASA's Lewis Research Center for useful discussion. Dr Li. Q. Tang's present address is Design & Manufacturing Institute, Stevens Institute of Technology, Hoboken, NJ 07030, USA. Address correspondence to Dr. Tate T. H. Tsang, Department of Chemical and Materials Engineering, University of Kentucky, 163 Anderson Hall, Lexington, KY 40506-0046, USA.

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Condensed Matter Physics
  • Mechanics of Materials
  • Computer Science Applications


Dive into the research topics of 'Transient solutions by a least-squares finite-element method and Jacobi conjugate gradient technique'. Together they form a unique fingerprint.

Cite this