Modification of QUICK Scheme for Unstructured Grid Finite Volume Method

비정렬 유한체적법을 위한 QUICK법의 수정

  • 강동진 (영남대학교 기계공학부) ;
  • 배상수 (영남대학교 기계공학부)
  • Published : 2000.09.01


The QUICK scheme for convection terms is modified for unstructured finite volume method by using linear reconstruction technique and validated through the computation of two well defined laminar flows. It uses two upstream grid points and one downstream grid point in approximating the convection terms. The most upstream grid point is generated by considering both the direction of flow and local grid line. Its value is calculated from surrounding grid points by using a linear construction method. Numerical error by the modified QUICK scheme is shown to decrease about 2.5 times faster than first order upwind scheme as grid size decreases. Computations are also carried out to see effects of the skewness and irregularity of grid on numerical solution. All numerical solutions show that the modified QUICK scheme is insensitive to both the skewness and irregularity of grid in terms of the accuracy of solution.



  1. Connell, S. D., and Holmes, D. G., 1994,'Three Dimensional Unstructured Adaptive Multigrid Scheme for the Euler Equations,' AIAA J., Vol. 32, No.8, pp. 1626-1632
  2. Mavripilis, D. J., 1991, 'Three Dimensional Unstructured Multigrid for the Euler equations,' AIAA Paper 91-1549
  3. Lohner, R., 1989, 'Adaptive H-Refinement on 3D Unstructured Grids for Transient Problems,' AIAA Paper 89-0365
  4. Jiang, Y., Wang, Z. J., and Przekwas, A. J., 1996, 'Pressure Based High Order Accuracy Flow Solver on Adaptive, Mixed Type Unstructured Grids,' AIAA Paper 96-0417
  5. Thomadakis, M, and Leschziner, M., 1996, 'A Pressure Correction Method for the Solution of Incompressible Viscous Flows on Unstructured Grids,' Int. J. Nume, Methd. in Fluids, Vol. 22, pp. 581-601
  6. Leonard, B. P., 1979, 'A Stable and Accurate Convective Modelling Procedure Based on Quadratic Interpolation,' Comp. Methods Appl. Mech. Eng. Vol. 19, pp 59-98
  7. 강동진, 배상수, 1996, '일반 비직교 표면좌표계에서의 비압축성 점성유동의 수치해석 : Hybrid법과 QUICK법의 비교,' 대한기계학회논문집, 제20권 제5호, pp. 1613-1623
  8. Pan, D., Lu, C., and Cheng, J., 1994, 'Incompressible Flow Solution on Unstructured Triangular Meshes,' Numerical Heat Transfer, Part B, Vol. 26, pp. 207-224
  9. Baliga, B. R., and Patankar, S. V., 1980, 'A New Finite Element Formulation for Convection Diffusion Problems,' Numerical Heat Transfer, Vol. 3, pp. 393-409
  10. Hookey, N. A., Baliga, B. R., and Prakash, C., 1988, 'Evaluation and Enhancements of Some Control Volume Finite Element Methods- Part 1 : Convection-Diffusion Problems,' Numerical Heat Transfer, Vol. 14, pp. 255-272
  11. Saabas, H. J., and Baliga, B. R., 1994, 'Co-Located Equal-Order Control Volume Finite Element Method for Multi-Dimensional, Incompressible, Fluid Flow-Part 1 : Formulation,' Numerical Heat Transfer, Part B, Vol. 26, pp. 381-407
  12. Anderson, W. Kyle, and Bonhaus, D. L., 1994, 'An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids,' Computers Fluids Vol. 23 No. 1, pp. 1-21
  13. Aftosmis, M., Gaitonde, D., and Tavares, T. S., 1995, 'Behavior of Linear Reconstuction Techniques on Unstructured Meshes,' AIAA J., Vol. 33 No. 11, pp. 2038-2049
  14. 강동진, 배상수, 주상우, 1998, '비압축성 점성유동의 수치해석을 위한 유한 체적법,' 대한기계학회논문집, 제22권 제10호, pp. 1410-1421
  15. Barth, T. J., and Frederickson, P.O., 1993, 'Higher Order Solution of the Euler Equations on Unstructured Grids Using Quadratic Reconstruction,' AIAA Paper 93-0668
  16. Shen, C., Y., Reed, H., and Foley, T., 1993, 'Shepard's Interpolation for Solution Adaptive Methods,' J. Comp. Phys., Vol. 106, pp. 52-61
  17. Ghia, U., Ghia, K. N., and Shin, C. T., 1982, 'High Resolutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method,' Journal of Computational Physics, Vol. 48, pp. 387-411