The goal of the present paper is to understand the impact of numerical schemes for the reconstruction of data at cell faces in finite-volume methods, and to assess their interaction with the quadrature rule used to compute the average over the cell volume. Here, third-, fifth- and seventh-order WENO-Z schemes are investigated. On a problem with a smooth solution, the theoretical order of convergence rate for each method is retrieved, and changing the order of the reconstruction at cell faces does not impact the results, whereas for a shock-driven problem all the methods collapse to first-order. Study of the decay of compressible homogeneous isotropic turbulence reveals that using a high-order quadrature rule to compute the average over a finite volume cell does not improve the spectral accuracy and that all methods present a second-order convergence rate. However the choice of the numerical method to reconstruct data at cell faces is found to be critical to correctly capture turbulent spectra. In the context of simulations with finite-volume methods of practical flows encountered in engineering applications, it becomes apparent that an efficient strategy is to perform the average integration with a low-order quadrature rule on a fine mesh resolution, whereas high-order schemes should be used to reconstruct data at cell faces.
翻译:本文的目的是要了解以有限容量方法重建单元格面部数据的数字办法的影响,并评估其与计算细胞体积平均值所用的二次规则的相互作用。在这里,对三、五、七级WENO-Z方案进行调查。关于一种顺利解决办法的问题,检索了每种方法的理论趋同率,改变细胞面部重建顺序并不影响结果,而对于冲击驱动的问题,所有方法都崩溃到第一级。对可压缩同质同质异位波动衰变的研究显示,使用高阶二次规则计算某一有限体积单元格平均值不会提高光谱精度,所有方法都显示第二级趋同率。然而,选择细胞面数据重建的数字方法被认为对于正确捕捉扰动光谱至关重要。在模拟工程应用中遇到的、实际流的有限量方法时,显然有效的战略是执行与低级同级平流平均集法,而在使用高阶的单元格面图上,应当采用高分辨率规则。