Hybrid scheme for complex flows on staggered grids and application to multiphase flows

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.(c) 2019 Published by Elsevier Inc.