Flow modelling in a straight rigid-walled duct with two rectangular axisymmetric narrowings. Part 2. An alternative approach
Abstract
A second-order technique is suggested to study fluid motion in a two-dimensional hard-walled duct with two abrupt constrictions. In this technique, the governing relationships are integrated via their rewriting in a non-dimensional form, deriving their integral analogues, performing a discretization of the derived integral relationships, simplifying the obtained (after making the discretization) coupled non-linear algebraic equations, and final solving the resulting (after making the simplification) uncoupled linear ones. The discretization consists of the spatial and temporal parts. The first of them is performed with the use of the total variation diminishing scheme and the two-point scheme of discretization of the spatial derivatives, whereas the second one is made on the basis of the implicit three-point non-symmetric backward differencing scheme. The noted uncoupled linear algebraic equations are solved by an appropriate iterative method.
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Ferziger J. H., Peri´c M. Computational methods for fluid dynamics, 3rd ed. Berlin: Springer, 2002. 424 p. https://link.springer.com/book/10.1007/978-3-642-56026-2
Waterson N. P., Deconinck H. Design principles for bounded higher-order convection schemes – a unified approach. Journal of Computational Physics. 2007. Vol. 224. P. 182–207. https://www.sciencedirect.com/science/article/pii/S002199910700040X
Issa R. I. Solution of implicitly discretised fluid flow equations by operator-splitting. Journal of Computational Physics. 1986. Vol. 62. P. 40–65. https://www.sciencedirect.com/science/article/pii/0021999186900999
Versteeg H. K., Malalasekera W. An introduction to computational fluid dynamics, 2nd ed. Harlow: Pearson Education Ltd, 2007. 503 p. http://ftp.demec.ufpr.br/disciplinas/TM702/Versteeg_Malalasekera_2ed.pdf
Anderson J. D., Jr. Computational fluid dynamics. The basics with applications. New York: Mc.Graw-Hill, 1995. 547 p. https://www.airloads.net/Downloads/Textbooks/Computational-Fluid-Dynamics-the-Basics-With-Applications-Anderson-J-D.pdf
Barrett R. et al. Templates for the solution of linear systems: Building blocks for iterative methods, 2nd ed. Philadelphia: SIAM, 1994. 107 p. https://www.netlib.org/templates/templates.pdf
Van Der Vorst H.A. Iterative Krylov methods for large linear systems. Cambridge: Cambridge Univ. Press, 2003. 221 p. https://www.cambridge.org/core/books/iterative-krylov-methods-for-large-linear-systems/FFB93854B3C47699F045AC396C0A208F
Van Der Vorst H. A. Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM Journal of Scientific and Statistical Computing. 1992. Vol. 13 (2). P. 631–644. https://epubs.siam.org/doi/10.1137/0913035
