Curvature-compensated convective transport: Smart, a new boundedness- preserving transport algorithm.

*(English)*Zbl 0668.76118The 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.

##### Keywords:

higher order; finite difference; approximating the convection term; steady-state transport equations; polynomial-based discretization; curvature compensation; convective transport approximation; third-order accurate; linear scalar transport problems; boundedness of solutions; ADI pentadiagonal solver; multi-dimensional fluid flows
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\textit{P. H. Gaskell} and \textit{A. K. C. Lau}, Int. J. Numer. Methods Fluids 8, No. 6, 617--641 (1988; Zbl 0668.76118)

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