Abstract A low-diffusion self-adaptive flux-vector splitting method is presented for the Euler equations. The flux-vector is here split into convective and acoustic parts following the formulation recently proposed by the authors. This procedure is based on the Zha-Bilgen (or previously Baraille et al. for the Euler barotropic system) approach enriched by a dynamic flow-dependent splitting parameter based on the local Mach number. As a consequence, in the present self-adaptive splitting, the convective and acoustic parts decouple in the low-Mach number regime whereas the complete Euler equations are considered for the sonic and highly subsonic regimes. The low diffusive property of the present scheme is obtained by adding anti-diffusion terms to the momentum and the energy components of the pressure flux in the acoustic part of the present splitting. This treatment results from a formal invariance principle preserving the discrete incompressible phase space through the pressure operator. Numerical results for several carefully chosen one- and two-dimensional test problems are finally investigated to demonstrate the accuracy and robustness of the proposed scheme for a wide variety of configurations from subsonic to highly subsonic flows.

中文翻译：

---

可压缩流的低扩散自适应通量矢量分裂方法

摘要 针对欧拉方程，提出了一种低扩散自适应磁通矢量分裂方法。根据作者最近提出的公式，通量矢量在这里被分为对流和声学部分。此过程基于 Zha-Bilgen（或之前用于欧拉正压系统的 Baraille 等人）方法，该方法通过基于本地马赫数的动态依赖于流动的分裂参数丰富。因此，在目前的自适应分裂中，对流和声学部分在低马赫数状态下解耦，而完整的欧拉方程被考虑用于音速和高亚音速状态。本方案的低扩散特性是通过将反扩散项添加到本次分裂的声学部分中的压力通量的动量和能量分量来获得的。这种处理源于通过压力算子保留离散不可压缩相空间的形式不变性原理。最后对几个精心选择的一维和二维测试问题的数值结果进行了研究，以证明所提出的方案对于从亚音速到高度亚音速流动的各种配置的准确性和鲁棒性。