A hybrid scheme is developed that enables advanced simulations, such as multiphase flows, in complex flow setups with compressible flow solvers using a staggered arrangement of flow variables. For this purpose, a weighted essentially non-oscillatory (WENO) scheme is adapted for staggered grids and combined with a finite difference central scheme. Hybrid weights that maintain continuity in time are computed based on a limiter constructed from the deviation of the local weights from the optimal weights. A total variation diminishing (TVD) interpolation is introduced to avoid numerical oscillations from the flow field. Additionally, the finite difference operators are reformulated in a flux-based finite volume form for convective terms in order to avoid spurious oscillations for turbulent configurations. For demonstrating the accuracy of the newly developed scheme and its improvements compared to the existing schemes, a modified wavenumber analysis is shown. Furthermore, the new scheme is applied to single and multiphase test cases. Finally, it is used for simulating the needle-opening process of a gasoline direct injector (GDI) and predicting the amount of gas inside the nozzle.

开发了一种混合方案，可以在复杂的流动设置中使用可压缩流动求解器使用流动变量的交错排列来实现高级模拟，例如多相流。为此，加权本质上非振荡 (WENO) 方案适用于交错网格，并与有限差分中心方案相结合。保持时间连续性的混合权重是基于根据局部权重与最佳权重的偏差构造的限制器计算的。引入总变差递减 (TVD) 插值以避免流场的数值振荡。此外，有限差分算子在基于通量的有限体积形式中重新表述为对流项，以避免湍流配置的虚假振荡。为了证明新开发方案的准确性及其与现有方案相比的改进，显示了修改后的波数分析。此外，新方案适用于单相和多相测试用例。最后，用于模拟汽油直喷器（GDI）的开针过程，预测喷嘴内的气体量。