Title: Numerically stable formulations of convective terms for turbulent compressible flows Show Chinese title

Title: 对湍流可压缩流动对流项的数值稳定形式

Abstract: A systematic analysis of the discrete conservation properties of non-dissipative, central-difference approximations of the compressible Navier-Stokes equations is reported. A general triple 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. Show Chinese abstract

Abstract: 对不可耗散的可压缩Navier-Stokes方程的中心差分近似的离散守恒性质进行系统分析。考虑了非线性对流项的一般三重分裂，并通过推导一个两参数的分裂形式族，全面表征了能量保持的格式。文献中之前提出的格式被证明是这个族中的特定成员；同时引入并讨论了新的分裂方式。此外，对能量方程不同选择（即总能量和内能、熵）所产生的守恒性质进行了深入分析。结果显示，通过在派生族中适当自适应选择分裂形式可以获得额外的守恒量。论文还讨论了主要不变量的局部守恒，这是构建高保真激波捕捉方法的基本性质。针对零粘度下的Taylor-Green涡进行的数值测试完全验证了理论结果，并表明仔细选择分裂方式和能量形式可以提供显著鲁棒和准确的结果。