针对 Voronoi 网格上可压缩粘性流的全马赫数半隐式有限体积/虚拟元素混合方法

IF 6.9 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Computer Methods in Applied Mechanics and Engineering Pub Date : 2024-11-01 DOI:10.1016/j.cma.2024.117502
Walter Boscheri , Saray Busto , Michael Dumbser
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引用次数: 0

摘要

我们提出了一种新颖的高阶半隐式混合有限体积/虚元数值方案,用于求解沃罗诺网格上的可压缩流。该方法依靠算子将可压缩纳维-斯托克斯方程拆分为三个子系统:使用有限体积(FV)方案显式求解的对流子系统,以及借助虚拟元素方法(VEM)隐式离散的粘性和压力子系统。因此,整个算法的时间步长限制只取决于平均流速,而不取决于快速压力波或粘性特征值。因此,所提出的方法非常适合解决所有雷诺数下的低马赫数流动问题。此外,该方案被证明是全局能量守恒的,因此在高马赫数流动中可以检索到冲击捕捉特性,同时在时间上只是线性隐含的。为了在时间和空间上达到高阶精度,采用了 IMEX Runge-Kutta 时间步进策略,以及 CWENO 多项式和虚拟元素空间基函数的高阶空间重构。所选择的离散化技术允许使用通用多边形网格,这是在处理复杂领域配置时的有用工具。在不可压缩极限和高马赫数条件下,通过大量流体动力学经典基准,对新方案进行了仔细验证,以评估其稳健性和准确性。
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An all Mach number semi-implicit hybrid Finite Volume/Virtual Element method for compressible viscous flows on Voronoi meshes
We present a novel high order semi-implicit hybrid finite volume/virtual element numerical scheme for the solution of compressible flows on Voronoi tessellations. The method relies on the operator splitting of the compressible Navier–Stokes equations into three sub-systems: a convective sub-system solved explicitly using a finite volume (FV) scheme, and the viscous and pressure sub-systems which are discretized implicitly with the aid of a virtual element method (VEM). Consequently, the time step restriction of the overall algorithm depends only on the mean flow velocity and not on the fast pressure waves nor on the viscous eigenvalues. As such, the proposed methodology is well suited for the solution of low Mach number flows at all Reynolds numbers. Moreover, the scheme is proven to be globally energy conserving so that shock capturing properties are retrieved in high Mach number flows while being only linearly implicit in time. To reach high order of accuracy in time and space, an IMEX Runge–Kutta time stepping strategy is employed together with high order spatial reconstructions in terms of CWENO polynomials and virtual element space basis functions. The chosen discretization techniques allow the use of general polygonal grids, a useful tool when dealing with complex domain configurations. The new scheme is carefully validated in both the incompressible limit and the high Mach number regime through a large set of classical benchmarks for fluid dynamics, assessing robustness and accuracy.
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来源期刊
CiteScore
12.70
自引率
15.30%
发文量
719
审稿时长
44 days
期刊介绍: Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.
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