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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A characteristics strategy for solving advection equations in 2D steady flows containing recirculating areas
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A characteristics strategy for solving advection equations in 2D steady flows containing recirculating areas

机译：求解包含回流区域的二维稳流中对流方程的特征策略

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摘要

Numerical modelling of non-Newtonian flows usually involves the coupling between equations of motion characterized by an elliptic character, and the fluid constitutive equation, which defines an advection problem linked to the fluid history. There are different numerical techniques to treat the hyperbolic character of advection equations. In non-recirculating flows, Eulerian discretisations can give an accurate mesh size dependent solution within a short computing time. However, the existence of steady recirculating flow areas induces additional difficulties. Actually, in these flows neither boundary conditions nor initial conditions are known. In a former paper we have proved that in such flows Eulerian techniques lead to solutions with significant deviations from the exact one. These deviations obviously decrease as the mesh density increases. In other paper, the authors have proved that some linear advection equations modelling non-Newtonian fluid behaviors have only one solution in steady recirculating flows. This solution is found imposing the solution periodicity along the closed streamlines, where the equation is integrated by the method of characteristics. In this paper we propose a characteristics algorithm for solving advection equations in general steady flows, which may contain recirculating areas.
机译：非牛顿流的数值建模通常涉及以椭圆特征为特征的运动方程与流体本构方程之间的耦合，流体本构方程定义了与流体历史有关的对流问题。有不同的数值技术来处理平流方程的双曲特性。在非循环流中，欧拉离散化可以在短计算时间内提供准确的网格尺寸相关解决方案。然而，稳定的循环流动区域的存在引起了额外的困难。实际上，在这些流中，既不知道边界条件也不知道初始条件。在以前的一篇论文中，我们证明了在这样的流中，欧拉技术导致与精确解有很大偏差的解。随着网格密度的增加，这些偏差明显减小。在其他论文中，作者证明了一些模拟非牛顿流体行为的线性对流方程在稳定的循环流中只有一个解。发现该解决方案沿封闭的流线强加了解决方案周期性，其中方程式通过特征方法进行了积分。在本文中，我们提出了一种特征算法，用于求解一般稳定流中的平流方程，该平流方程可能包含再循环区域。

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