Abstract The present paper extends the conservative finite element convective scheme proposed by Charnyi et al.(Journal of Computational Physics 337, 2017, 289–308) originally formulated for incompressible flows to the low Mach regime. Similar to Lehmkuhl et al.(Journal of Computational Physics 390, 2019, 51–65) stabilisation is only introduced for the continuity equation by means of a non-incremental fractional-step method, modified in order to account for variable density flows. The final scheme preserves momentum and angular momentum for variable density flows. The error of kinetic energy conservation is of order O ( δ t h k + 1 ) , thus dissipation is limited. Standard stabilised finite elements are used for the scalars. Time integration is carried out by means of an explicit third order Runge-Kutta scheme for all equations. The proposed strategy is tested on a set of relevant cases with available reference data using large-eddy simulations. First, an anisothermal turbulent channel flow is assessed. Later, a technically premixed turbulent flame in a swirl-stabilized configuration is considered. And finally, a turbulent jet diffusion flame in a low-velocity co-flow has been studied. In all cases the performance of the presented low Mach formulation is fairly good, showing better accuracy than skew-symmetric like strategies.

中文翻译：

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低马赫数反应流的低耗散有限元策略

摘要 本文将 Charnyi 等人（Journal of Computational Physics 337, 2017, 289–308）最初为不可压缩流动制定的保守有限元对流方案扩展到低马赫数区域。与 Lehmkuhl 等人（Journal of Computational Physics 390, 2019, 51-65）相似，仅通过非增量分步法为连续性方程引入稳定性，并进行修改以考虑可变密度流。最终方案保留了可变密度流的动量和角动量。动能守恒误差为O (δ thk + 1 ) 级，因此耗散是有限的。标准稳定有限元用于标量。时间积分是通过所有方程的显式三阶 Runge-Kutta 格式进行的。所提出的策略使用大涡模拟在一组相关案例上进行了测试，并具有可用的参考数据。首先，评估非等温湍流通道流动。后来，考虑了在涡流稳定配置中技术上预混的湍流火焰。最后，研究了低速协流中的湍流射流扩散火焰。在所有情况下，所提出的低马赫公式的性能都相当好，显示出比偏斜对称策略更好的准确性。