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 flux 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 at 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. 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.

翻译：本文提出了一种新颖的高阶半隐式混合有限体积/虚拟元数值格式，用于求解Voronoi剖分上的可压缩流动。该方法基于将可压缩Navier-Stokes方程通量分裂为三个子系统：采用有限体积（FV）格式显式求解的对流子系统，以及借助虚拟元方法（VEM）进行隐式离散的粘性子系统与压力子系统。因此，整体算法的时间步长限制仅取决于平均流速，而与快速压力波或粘性特征值无关。由此，所提方法非常适用于求解全雷诺数范围内的低马赫数流动。此外，该格式被证明具有全局能量守恒特性，从而在高马赫数流动中能保持激波捕捉能力。为达到时间与空间上的高阶精度，本文采用IMEX Runge-Kutta时间推进策略，并结合基于CWENO多项式与虚拟元空间基函数的高阶空间重构。所选离散技术允许使用一般多边形网格，这在处理复杂区域构型时是一个实用工具。通过大量流体动力学经典算例，新格式在不可压缩极限与高马赫数区域均得到细致验证，从而评估了其鲁棒性与精确性。