Numerically stable formulations of convective terms for turbulent compressible flows
Numerically stable formulations of convective terms for turbulent compressible flows
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DOI：
10.1016/j.jcp.2019.01.007
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发表时间：
2018-05
期刊：
影响因子：
--
通讯作者：
G. Coppola;F. Capuano;S. Pirozzoli;L. Luca
中科院分区：
文献类型：
--
作者：
G. Coppola;F. Capuano;S. Pirozzoli;L. Luca
本文系统地分析了可压缩Navier-Stokes方程的无耗散中心差分近似的离散守恒性质。广义分裂的非线性对流项被认为是，和能量保持配方的充分特点是推导出一个两参数的家庭分裂形式。以前开发的制剂在文献中报道的是这个家庭的特定成员，新的分裂介绍和讨论。此外，能量方程（即总能量和内能，熵）的不同选择所产生的守恒性质进行了深入的分析。它示出，额外的保存量可以通过一个适当的自适应选择的分裂形式内的衍生家庭。本文还讨论了建立高精度激波捕捉方法的基本性质--准素不变量的局部守恒性。在零粘度下对泰勒-格林涡进行的数值试验充分证实了理论结果，并表明仔细选择分裂和能量公式可以提供非常鲁棒和准确的结果。
A systematic analysis of the discrete conservation properties of non-dissipative, central-difference approximations of the compressible Navier–Stokes equations is reported. A generalized splitting of the nonlinear convective terms is considered, and energy-preserving formulations are fully characterized by deriving a two-parameter family of split forms. Previously developed formulations reported in literature are shown to be particular members of this family; novel splittings are introduced and discussed as well. Furthermore, the conservation properties yielded by different choices for the energy equation (i.e. total and internal energy, entropy) are analyzed thoroughly. It is shown that additional preserved quantities can be obtained through a suitable adaptive selection of the split form within the derived family. Local conservation of primary invariants, which is a fundamental property to build high-fidelity shock-capturing methods, is also discussed in the paper. Numerical tests performed for the Taylor–Green Vortex at zero viscosity fully confirm the theoretical findings, and show that a careful choice of both the splitting and the energy formulation can provide remarkably robust and accurate results.