Simple high-accuracy resolution program for convective modelling of discontinuities.(English)Zbl 0667.76125
For steady multi-dimensional convection, the QUICK scheme has several attractive properties. However, for highly convective simulation of step profiles, QUICK produces unphysical overshoots and a few oscillations, and this may cause serious problems in non-linear flows. Fortunately, it is possible to modify the convective flux by writing the ‘normalized’ convected control-volume face value as a function of the normalized adjacent upstream node value, developing criteria for monotonic resolution without sacrificing formal accuracy. This results in a non- linear functional relationship between the normalized variables, whereas standard methods are all linear in this sense. The resulting Simple High- Accuracy Resolution Program (SHARP) can be applied to steady multi- dimensional flows containing thin shear or mixing layers, shock waves and other frontal phenomena. This represents a significant advance in modelling highly convective flows of engineering and geophysical importance. SHARP is based on an explicit, conservative, control-volume flux formulation, equally applicable to one-, two-, or three-dimensional elliptic, parabolic, hyperbolic or mixed-flow regimes. Results are given for the bench-mark purely convective oblique-step test. The monotonic SHARP solutions are compared with the diffusive first-order results and the non-monotonic predictions of second- and third-order upwinding.
Keywords:
third-order upwinding;high convection;resolution of discontinuities;steady multi-dimensional convection;QUICK scheme;monotonic resolution;Simple High-Accuracy Resolution Program;thin shear or mixing layers;shock waves;frontal phenomena;convective oblique-step testCite
Full Text:DOI
References:
| [1] | Warming, AIAA J. 14 pp 1241– (1976) |
| [2] | Leonard, Comput. Methods Appl. Mech. Eng. 19 pp 59– (1979) |
| [3] | and , ’Calculation of recirculating flows’, Report No. HTS/74/2, Department of Mechanical Engineering, Imperial College, London, 1974. |
| [4] | Castro, Int. j. numer. methods fluids 7 pp 793– (1987) |
| [5] | , and , ’The implementation of a finite difference method for predicting incompressible flows in complex geometries’, in et al. (eds), Numerical Methods in Laminar and Turbulent Flow, vol. 5, Pineridge Press, Swansea, 1987, pp. 339-350. |
| [6] | Huang, Comput. Methods Appl. Mech. Eng. 48 pp 1– (1985) |
| [7] | Han, Comput. Methods Appl. Mech. Eng. 29 pp 81– (1981) |
| [8] | Humphrey, J. Fluid Mech. 154 pp 357– (1985) |
| [9] | Beier, Numer. Heat Transfer 6 pp 283– (1983) |
| [10] | Azzola, J. Fluids Eng. 108 pp 214– (1986) |
| [11] | Phillips, Numer. Heat Transfer 8 pp 25– (1985) |
| [12] | Rhode, J. Fluids Eng. 108 pp 19– (1986) |
| [13] | Aggarwal, Numer. Heat Transfer 11 pp 143– (1987) |
| [14] | and , ’Improved numerical codes for solving three-dimensional unsteady flows’, in et al. (eds), Numerical Methods in Laminar and Turbulent Flow, vol. 5, Pineridge Press, Swansea, 1987, 12-22. |
| [15] | ’Error estimates and convergence acceleration of different discretization schemes’, in et al. (eds), Numerical Methods in Laminar and Turbulent Flow, vol. 5, Pineridge Press, Swansea, 1987, pp. 91-101. |
| [16] | and , ’Two efficient solution strategies for use with high order discretisation schemes, in the simulation of fluid flow problems’, in et al. (eds), Numerical Methods in Laminar and Turbulent Flow, vol. 5, Pineridge Press, Swansea, 1987, pp. 210-220. |
| [17] | and , ’A numerical-experimental study of confined unsteady laminar flow around a squared obstacle’, in et al. (eds), Numerical Methods in Laminar and Turbulent Flow, vol. 5, Pineridge Press, Swansea, 1987, pp. 261-272. |
| [18] | and , ’Effect of shaft rotation on the incompressible flow in a labyrinth seal’, in et al. (eds), Numerical Methods in Laminar and Turbulent Flow, vol. 5, Pineridge Press, Swansea, 1987, pp. 508-520. |
| [19] | ’A numerical method for three-dimensional compressible turbulent boundary-layer flows’, in et al. (eds), Numerical Methods in Laminar and Turbulent Flow, vol. 5, Pineridge Press, Swansea, 1987, pp. 1421-1435. |
| [20] | and , ’On the influence of the numerical approximation of convection in the computation of 3D jet injection into an IC-engine combustion-chamber model’, in et al. (eds), Numerical Methods in Laminar and Turbulent Flow, vol. 5, Pineridge Press, Swansea, 1987, pp. 1436-1447. |
| [21] | and , ’Assessment of discretization schemes to reduce numerical diffusion in th calculation of complex flows’, Paper No. AIAA-85-0441, AIAA 23rd Aerospace Sciences Meeting, Reno; Nevada, January 1985. |
| [22] | Department of Mechanical Engineering and Engineering Mechanics, Michigan Technological University, personal communication. |
| [23] | Leschziner, J. Fluids Eng. 103 pp 352– (1981) |
| [24] | Goodman, Math. Comput. 45 pp 15– (1985) |
| [25] | ’Elliptic systems: finite-difference method IV’, in et al. (eds), Handbook of Numerical Heat Transfer, Wiley, New York, 1988, Ch. 9, pp. 347-378. |
| [26] | Leonard, Appl. Math. Modelling 4 pp 401– (1980) |
| [27] | Paollucci, J. Comput. Phys. 47 pp 489– (1982) |
| [28] | Gaskell, Int. J. Numer. Methods Fluids 8 pp 617– (1988) |
| [29] | Sweby, SIAM J. Numer. Anal. 21 pp 995– (1984) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
