Skip to main content
SpringerLink
Log in

Upwind local differential quandrature method for solving coupled viscous flow and heat transfer equations

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The differential quadrature method (DQM) has been applied successfully to solve numerically many problems in the fluid mechanics. But it is only limited to the flow problems in regular regions. At the same time, here is no upwind mechanism to deal with the convective property of the fluid flow in traditional DQ method. A local differential quadrature method owning upwind mechanism (ULDQM) was given to solve the coupled problem of incompressible viscous flow and heat transfer in an irregular region. For the problem of flow past a contraction channel whose boundary does not parallel to coordinate direction, the satisfactory numerical solutions were obtained by using ULDQM with a few grid points. The numerical results show that the ULDQM possesses advantages including well convergence, less computational workload and storage as compared with the low-order finite difference method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bellman R, Casti J. Differential quadrature and long-term integration[J].J Math Anal Appl, 1971,34:235–238.

    Article  MATH  MathSciNet  Google Scholar 

  2. Bellman R, Kashef G, Casti J. Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations[J].J Comput Phys, 1972,10(1):40–52.

    Article  MATH  MathSciNet  Google Scholar 

  3. Bert C W, Malik M. The differential quadrature method for irregular domains and application to plate vibration[J].Internat J Mech Sci, 1996,38(6):589–606.

    Article  MATH  Google Scholar 

  4. Lam S S. Application of the differential quadrature method to two-dimensional problems with arbitrary geometry[J].Compu Struct, 1993,47(3):459–464.

    Article  Google Scholar 

  5. Han J B, Liew K M. An eight-node curvilinear differential quadrature formulation for reissner/mindlin plates[J].Compu Methods Appl Mech Engrg, 1997,141(3/4):265–280.

    Article  MATH  Google Scholar 

  6. Wang X W, Guh Z. Static analysis of frame structures by the differential quadrature element method [J].Internat J Numer Methods Engrg, 1997,40(4):759–772.

    Article  MATH  Google Scholar 

  7. Chen W, Alfred G, Bert C W. A new approach to the differential quadrature method for fourth-order equation[J].Internat J Numer Methods Engrg, 1997,40(11):1941–1956.

    Article  MATH  Google Scholar 

  8. Shu C, Chen W, Du H. Free vibration analysis of curvilinear quadrilateral plates by the differential quadrature method[J].J Comput Phys, 2000,163(2):452–466.

    Article  MATH  Google Scholar 

  9. Shu C, Xue H, Zhu Y D. Numerical study of natural convection in an eccentric annulus between a square outer cylinder and a circular inner cylinder using DQ method[J].Internat J Heat and Mass Transfer, 2001,44(17):3321–3333.

    Article  MATH  Google Scholar 

  10. Shu C. Application of differential quadrature method to simulate natural convection in a concentric annulus[J].Internat J Numer Methods Fluids, 1999,30(8):977–993.

    Article  MATH  Google Scholar 

  11. Shu C, Xue H. Comparison of two approaches for implementing stream function boundary conditions in DQ simulation of natural convection in a square cavity[J].Internat J Heat and Fluid Flow, 1998,19(1):59–68.

    Article  Google Scholar 

  12. Liaqat A, Baytas A C. Conjugate natural convection in a square enclosure containing volumetric sources[J].Internat J Heat and Mass Transfer, 2001,44(17):3273–3280.

    Article  MATH  Google Scholar 

  13. Papanicolaou E, Belessioties V. Transient natural convection in a cylindrical enclosure at high Rayleigh numbers[J].Internat J Heat and Mass Transfer, 2002,45(7):1425–1444.

    Article  MATH  Google Scholar 

  14. Lin W X, Armfield S W. Natural convection cooling of rectangular and cylindrical containers[J].Internat J Heat and Fluid Flow, 2001,22(1):72–81.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072, Shanghai, P. R. China

    A. S. J. Al-Saif Doctor & Zhu Zheng-you Professor

  2. Department of Mathematics, Shanghai University, 200436, Shanghai, P. R. China

    Zhu Zheng-you Professor

  3. Department of Mathematics, University of Basrah, Iraq

    A. S. J. Al-Saif Doctor

Authors
  1. A. S. J. Al-Saif Doctor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhu Zheng-you Professor
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhu Zheng-you Professor.

Additional information

Communicated by ZHOU Zhe-wei

Foundation item: the Municipal Key Subject Programs of Shanghai

Biographies: A. S. J. Al-Saif (1964 ~)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Al-Saif, A.S.J., Zheng-you, Z. Upwind local differential quandrature method for solving coupled viscous flow and heat transfer equations. Appl Math Mech 25, 1130–1138 (2004). https://doi.org/10.1007/BF02439865

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02439865

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation