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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >A comparison of explicit and semi-implicit finite volume schemes for viscous compressible flows in elastic pipes in fast transient regime
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A comparison of explicit and semi-implicit finite volume schemes for viscous compressible flows in elastic pipes in fast transient regime

机译：快速瞬态条件下弹性管粘性可压缩流动明确和半隐含有限体积方案的比较

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摘要

This paper compares the accuracy and computational efficiency of fully explicit and semi-implicit 1D and 2D finite volume schemes for the simulation of highly unsteady viscous compressible flows in laminar regime in axially symmetric compliant tubes. There are essentially two main classes of mathematical models that can be used to predict the pressure and velocity distribution along the tube: one class is based on the full compressible Navier-Stokes equations in an axially symmetric geometry, leading to a two-dimensional governing PDE system with moving boundaries, and the other class uses a simpler, cross-sectionally averaged version of the Navier-Stokes equations, which leads to a non-conservative PDE system in only one space dimension along the axial direction of the tube. Within the first class of models, the influence of the wall friction on the flow field is directly obtained from first principles, without any further modelling assumptions and is thus valid even for highly unsteady flows. In the second case, only averaged flow quantities are available, and it is well known from previous studies published in the literature that the correct representation of the wall friction needs to be frequency dependent, since the use of a simple steady friction model, like the classical Darcy-Weisbach law, is not sufficient to reproduce the wall friction effects in highly transient flows. For the cross-sectionally averaged Navier-Stokes equations, there are again two main classes of frequency-dependent wall friction models: convolution integral (CI) models and instantaneous acceleration (IA) models. In this paper we provide a very thorough and critical comparison of all the above-mentioned methods for the simulation of highly oscillatory flows in rigid and compliant tubes concerning accuracy and computational efficiency. From our numerical results we can conclude that the convolution integral models are significantly superior to instantaneous acceleration models concerning
机译：本文比较了完全明确和半隐式1D和2D有限体积方案的精度和计算效率，用于模拟轴对称柔顺管中的层状制度中高度不稳定的粘性可压缩流动的模拟。基本上有两个主要类数学模型，可用于预测沿管的压力和速度分布：一类基于轴对称几何中的完全可压缩Navier-Stokes方程，导致二维控制PDE具有移动边界的系统，另一类使用更简单，横截面平均版本的Navier-Stokes方程，其在沿管的轴向方向仅在一个空间尺寸中导致非保守PDE系统。在第一类模型中，壁摩擦对流场的影响是直接从第一原理获得的，而没有任何进一步的建模假设，因此即使对于高度不稳定的流动也是有效的。在第二种情况下，只有平均流量可用，并且在文献中发表的先前研究中众所周知，墙壁摩擦的正确表示需要是频率依赖性，因为使用简单稳定的摩擦模型，就像古典达西 - 韦斯巴赫法，不足以在高瞬态流动中重现墙壁摩擦效应。对于横截面平均的Navier-Stokes方程，再次有两个主要类的频率依赖壁摩擦模型：卷积积分（CI）模型和瞬时加速度（IA）模型。在本文中，我们提供了对刚性和柔顺管中的高度振荡流模拟的所有上述方法的非常彻底和致意的比较，该方法是关于精度和计算效率的刚性和柔顺的管。从我们的数值结果来看，我们可以得出结论，卷积积分模型明显优于瞬时加速模型

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