Curvature-compensated convective transport: Smart, a new boundedness- preserving transport algorithm. (English) Zbl 0668.76118

The paper describes a new approach to approximating the convection term found in typical steady-state transport equations. A polynomial-based discretization scheme is constructed around a technique called “curvature compensation”; the resultant curvature-compensated convective transport approximation is essentially third-order accurate in regions of the solution domain where the concept of order is meaningful. In addition, in linear scalar transport problems it preserves the boundedness of solutions. Sharp changes in gradient in the dependent variable are handled particularly well. But above all, the scheme, when used in conjunction with an ADI pentadiagonal solver, is easy to implement with relatively low computational cost, representing an effective algorithm for the simulation of multi-dimensional fluid flows. Two linear test problems, for the case of transport by pure convection, are employed in order to assess the merit of the method.


76R10 Free convection
76M99 Basic methods in fluid mechanics
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[1] Computational Fluid Dynamics, Hermosa, Albuquerque, 1976.
[2] and , Difference Methods for Initial-Value Problems, Interscience, New York, 1967.
[3] Leonard, Comput. Methods Appl. Mech. Eng. 19 pp 59– (1979)
[4] ’A survey of finite differences of opinion on numerical muddling of incomprehensible defective confusion equation’, paper in ASME, Applied Mechanics Division, Winter Annual Meeting, 1979. · Zbl 0435.76003
[5] ’A third-ordcr-accurate upwind scheme for Navier-Stokcs solution at high Reynolds numbers’, Paper No. AIAA-81-0112, AIAA 19th Aerospace Science Meeting, St. Louis, 1982.
[6] ’Adjusted quadratic upstream algorithms for transient incompressible convection’, AIAA- J., 226-233 (1979).
[7] Shyy, J. Comput. Phys. 57 pp 415– (1985)
[8] and , ’An efficient solution strategy for use with high-order discretization schemes’, Report No. T40, Department of Mechanical Engineering, University of Leeds, 1986.
[9] Raithby, Comput. Methods Appl. Mech. Eng. 9 pp 153– (1976)
[10] and , ’Assessment of discretization schemes to reduce numerical diffusion in the calculation of complex flows’, Paper No. AIAA-85-0441, AIAA 23rd Aerospace Science Meeting, Reno, January 1985.
[11] and , ’An assessment of direct stress modelling for elliptic turbulent flows with the aid of a non-diffusive, boundedness preserving, discretization scheme’, Proc. 5th int. Conf. on Numerical Methods in Laminar and Turbulent Flow, Montreal, 1987.
[12] and , ’Multigrids applied to an efficient fully coupled solution technique for recirculating fluid flow problems’, Proc. IMA Conf. on the Simulation and Optimisation of Large Systems, Reading, 1986.
[13] Alias, AIAA J. 15 pp 263– (1977)
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