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A semi-staggered finite volume approach applied to two- and three-dimensional flow in channels with gradual expansions
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-06-15 , DOI: 10.1002/fld.5024 Adyllyson Nascimento 1 , Gustavo Rodrigues 2 , José Ricardo Figueiredo 1
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-06-15 , DOI: 10.1002/fld.5024 Adyllyson Nascimento 1 , Gustavo Rodrigues 2 , José Ricardo Figueiredo 1
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Two- and three-dimensional computations have been performed to study incompressible laminar flow of viscous fluids in symmetric channels with gradual expansions. The divergent form advective and viscous terms of Navier–Stokes equations are discretized by means of the UNIFAES scheme, which has been showing unpaired accuracy. Explicit time-wise integration allows continuity to be imposed via the Poisson equation for the pressure, solved iteratively with several iterations per velocity step in order to ensure mass conservation throughout the transient regime. The proposed finite volume approach uses the semi-staggered mesh structure, in which pressure is put at the center of the continuity cell and the velocity components at the cell vertexes. Comparative studies have shown this mesh to be highlighted by accuracy, in relation to the traditional, staggered and collocated meshes. Furthermore, it was observed that the semi-staggered mesh allowed to treat a plane diverging channel in entirely regular fashion without losing accuracy, by appropriate choice of the aspect ratio of the numerical cell, providing geometrical flexibility that does not exist in more common meshes, such as staggered and collocated structures. The present proposal explored the geometric flexibility of the semi-staggered mesh to solve with simplicity a relevant problem of a channel with gradual expansion. Overall, good agreement was observed against experimental and numerical results in the literature, therefore, it illustrates the capability of the semi-staggered approach to easily handle flat surfaces nonparallel to the coordinates axes.
中文翻译：
一种半交错有限体积法应用于渐扩通道中的二维和三维流动
已执行二维和三维计算来研究粘性流体在逐渐膨胀的对称通道中的不可压缩层流。Navier-Stokes 方程的发散形式平流项和粘性项通过 UNIFAES 方案进行离散化，该方案已显示出无与伦比的准确性。显式的按时间积分允许通过压力的泊松方程施加连续性，通过每个速度步长多次迭代迭代求解，以确保整个瞬态状态的质量守恒。所提出的有限体积方法使用半交错网格结构，其中压力位于连续单元的中心，而速度分量位于单元顶点。比较研究表明，与传统的网格相比，这种网格的准确性突出，交错和并置的网格。Furthermore, it was observed that the semi-staggered mesh allowed to treat a plane diverging channel in entirely regular fashion without losing accuracy, by appropriate choice of the aspect ratio of the numerical cell, providing geometrical flexibility that does not exist in more common meshes,例如交错和并置的结构。本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。it was observed that the semi-staggered mesh allowed to treat a plane diverging channel in entirely regular fashion without losing accuracy, by appropriate choice of the aspect ratio of the numerical cell, providing geometrical flexibility that does not exist in more common meshes, such as交错和并置的结构。本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。it was observed that the semi-staggered mesh allowed to treat a plane diverging channel in entirely regular fashion without losing accuracy, by appropriate choice of the aspect ratio of the numerical cell, providing geometrical flexibility that does not exist in more common meshes, such as交错和并置的结构。本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。by appropriate choice of the aspect ratio of the numerical cell, providing geometrical flexibility that does not exist in more common meshes, such as staggered and collocated structures. 本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。by appropriate choice of the aspect ratio of the numerical cell, providing geometrical flexibility that does not exist in more common meshes, such as staggered and collocated structures. 本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。
更新日期：2021-06-15
中文翻译：
一种半交错有限体积法应用于渐扩通道中的二维和三维流动
已执行二维和三维计算来研究粘性流体在逐渐膨胀的对称通道中的不可压缩层流。Navier-Stokes 方程的发散形式平流项和粘性项通过 UNIFAES 方案进行离散化，该方案已显示出无与伦比的准确性。显式的按时间积分允许通过压力的泊松方程施加连续性，通过每个速度步长多次迭代迭代求解，以确保整个瞬态状态的质量守恒。所提出的有限体积方法使用半交错网格结构，其中压力位于连续单元的中心，而速度分量位于单元顶点。比较研究表明，与传统的网格相比，这种网格的准确性突出，交错和并置的网格。Furthermore, it was observed that the semi-staggered mesh allowed to treat a plane diverging channel in entirely regular fashion without losing accuracy, by appropriate choice of the aspect ratio of the numerical cell, providing geometrical flexibility that does not exist in more common meshes,例如交错和并置的结构。本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。it was observed that the semi-staggered mesh allowed to treat a plane diverging channel in entirely regular fashion without losing accuracy, by appropriate choice of the aspect ratio of the numerical cell, providing geometrical flexibility that does not exist in more common meshes, such as交错和并置的结构。本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。it was observed that the semi-staggered mesh allowed to treat a plane diverging channel in entirely regular fashion without losing accuracy, by appropriate choice of the aspect ratio of the numerical cell, providing geometrical flexibility that does not exist in more common meshes, such as交错和并置的结构。本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。by appropriate choice of the aspect ratio of the numerical cell, providing geometrical flexibility that does not exist in more common meshes, such as staggered and collocated structures. 本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。by appropriate choice of the aspect ratio of the numerical cell, providing geometrical flexibility that does not exist in more common meshes, such as staggered and collocated structures. 本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。本提案探索了半交错网格的几何灵活性，以简单地解决逐渐扩展的通道的相关问题。总体而言，在文献中观察到与实验和数值结果的良好一致性，因此，它说明了半交错方法可以轻松处理与坐标轴不平行的平面的能力。
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