Use of the all-Russian mathematical portal Math-Net.Ru implies that you have read and agreed to these terms of use http://www.mathnet.ru/eng/agreement Download details: IP: 52.36.4.81 May 12, 2018, 09:52:56 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2017, vol. 21, no. 2, pp. 362-375 ISSN: 2310-7081 (online), 1991 http://doi.
AbstractThe stable stationary solutions of the test problem of hydrodynamics and heat transfer in a plane channel with the backward-facing step have been considered in the work for extremely high Reynolds numbers and expansion ratio of the stream ER. The problem has been solved by numerical integration of the 2D Navier-Stokes equations in 'velocity-pressure' formulation and the heat equation in the range of Reynolds number 500Re 3000 and expansion ratio Introduction. Permanent improvement of numerical techniques for modeling fluid dynamics and heat transfer requires adequate methods to assess their effectiveness. For these purposes, consideration of well-known test problems which solutions have all main features of real fluid flows is the best approach. On the one hand, for these problems the huge volume of experimental and theoretical results is saved up that provides their maximum reliability. On the other hand the critical parameters are unambiguously determined for them. The 'intensification' of these parameters increases the complexity of the problems. The efficiency evaluation of a new computing technology follows from this: the more critical parameters of the problem are 'intense', the more the technology is effective. The well-known example of such problem of hydrodynamics of incompressible viscous liquids is the classical lid-driven cavity problem. Reynolds number is the critical parameter for this problem.The problem of separated flow in a 2D channel with backward-facing step is one more such a problem [1]. The problem is characterized by a simple geometry. Its solution, in general, depends on two parameters: Reynolds number Re and expansion ratio ER, where ER is defined as the ratio of the full height of the channel to the height of its inlet segment. Prandtl number Pr is added when heat transfer is taken into account. Change of these few input parameters allows to receive radically various solutions of the problem-namely, separated flow patterns, which are characterized by the quantity, form, size, and position of the vortices. Furthermore, they can have a very complex structure. The maximum value of Reynolds number (Re = 3000 at ER = 2) was reached in the article [2], and expansion ratio (ER = 4 at Re 300) was reached in the works [3,4].Further increase in these parameters causes computational instability which, in particular, is discussed in [2]. E. Erturk recommends to reduce a mesh step for overcoming this instability (see, for example, [5]). But in this case, the systems of the linear algebraic equations (SLAE) with huge number of unknowns are generated, and more effective methods are needed to solve the...