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The Performance Evaluation of an Improved Finite Volume Method for Solving the Navier Stokes Equation

机译：改进的有限体积法求解Navier Stokes方程的性能评估

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One of the most important goals of this research effort is to improve the efficiencies of computational fluid dynamic (CFD) tools by focusing on the development of a robust and accurate numerical framework capable of solving the Navier-Stokes Equations under a wide variety of initial and boundary conditions. The new scheme, which was initially described in Ref. 1 and referred to as the Integro-Differential Scheme (IDS), has a number of favorable qualities. For instance, the scheme is developed on the basis of a unique combination of the differential and integral forms of the Navier-Stokes Equations (NSE). In this paper, the differential form of the NSE is used for explicit time marching and the integral form is used for spatial flux evaluations. As such, the scheme has the potential to accurately capture the complex physics of fluid flows. In addition, the Method of Consistent Averages (MCA) numerical procedure directly provides continuity of the numerical flux quantities rather than manipulating the primitive flowfield variables to ensure continuity. Coupled temporal and spatial analyses of the mass, momentum, and energy fluxes are considered at two major locations; namely, at the center of the numerical control volume, and at each of the surface making up an elementary control volume. It is also of interest to note that the IDS procedure developed herein is based on two fundamental types of control volumes. This paper elaborates on the development of the IDS procedure and presents the results of its implementation on three established fundamental high Reynolds number fluid dynamic problems. The problems of interest to this study are the supersonic rearward facing step and the supersonic cavity flow problems. A careful analysis of the results generated from the use of the IDS procedure confirms its predictive capability and supports its potential to solve a variety of fluid dynamics problems.
机译：这项研究工作的最重要目标之一是通过专注于开发能够在各种初始值和初始值下解决Navier-Stokes方程的稳健而精确的数值框架的开发，从而提高计算流体动力学（CFD）工具的效率。边界条件。新方案，最初在参考文献1中进行了描述。图1的系统称为整数微分方案（IDS），具有许多良好的品质。例如，该方案是基于Navier-Stokes方程（NSE）的微分形式和积分形式的独特组合而开发的。在本文中，NSE的微分形式用于显式时间行进，而积分形式用于空间通量评估。因此，该方案具有准确捕获流体流动复杂物理现象的潜力。另外，一致性平均方法（MCA）数值过程直接提供了数值通量的连续性，而不是操纵原始流场变量来确保连续性。在两个主要位置考虑了对质量，动量和能量通量的时间和空间耦合分析。即，在数控体积的中心以及构成基本控制体积的每个表面上。还需要注意的是，本文开发的IDS程序基于两种基本类型的控制量。本文详细阐述了IDS程序的发展，并提出了在三个已建立的基本高雷诺数流体动力学问题上实施该程序的结果。该研究感兴趣的问题是超音速后向台阶和超音速腔流动问题。对使用IDS程序产生的结果进行的仔细分析证实了其预测能力，并支持其解决各种流体动力学问题的潜力。

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