This work presents the face-centred finite volume (FCFV) paradigm for the simulation of compressible flows. The FCFV method defines the unknowns at the face barycentre and uses a hybridisation procedure to eliminate all the degrees of freedom inside the cells. In addition, Riemann solvers are defined implicitly within the expressions of the numerical fluxes. The resulting methodology provides first-order accurate approximations of the conservative quantities, i.e. density, momentum and energy, as well as of the viscous stress tensor and of the heat flux, without the need of any gradient reconstruction procedure. Hence, the FCFV solver preserves the accuracy of the approximation in presence of distorted and highly stretched cells, providing a solver insensitive to mesh quality. In addition, FCFV is capable of constructing non-oscillatory approximations of sharp discontinuities without resorting to shock capturing or limiting techniques. For flows at low Mach number, the method is robust and is capable of computing accurate solutions in the incompressible limit without the need of introducing specific pressure correction strategies. A set of 2D and 3D benchmarks of external flows is presented to validate the methodology in different flow regimes, from inviscid to viscous laminar flows, from transonic to subsonic incompressible flows, demonstrating its potential to handle compressible flows in realistic scenarios.
翻译:这项工作展示了模拟压缩流的以面为核心的有限量范式(FCFV)模式; FCFV方法界定了面部甘蓝中心的未知数,并使用混合程序消除细胞内所有自由度;此外,在数字通量的表达方式中隐含了Riemann解答器的定义;由此得出的方法提供了保守数量(即密度、动力和能量)的第一阶准确近似值,以及粘性应力阵列和热通量,而无需采用任何梯度重建程序;因此,FCFV解解答器在扭曲和高度拉伸的细胞存在的情况下保存近似值的准确性,提供对网状质量不敏感的解答器; 此外,FCFCFV有能力在不诉诸休克捕捉或限制技术的情况下,构建不连续不连续不测的不精确近似近似值; 对于低马赫数字的流动,该方法是稳健的,并且能够在不需引入具体的压力校正战略的情况下,在可压缩的极限范围内计算出准确的解决方案; 在从扭曲的外部流动中,从一个2D和3D基准流到从可逆流到可逆流,在对流中演示的动态中,在不同的次压流中演示流中,在不同的次流中演示中,在从可逆流中演示中,在不同的流向分流向分流向分流中演示流向分流中演示的方法是论证方法。