In the present work, we propose a novel hybrid explicit jump immersed interface approach in conjunction with a higher order compact (HOC) scheme for simulating transient complex flows governed by the streamfunction-vorticity ($\psi$-$\zeta$) formulation of the Navier-Stokes (N-S) equations for incompressible viscous flows. A new strategy has been adopted for the jump conditions at the irregular points across the interface using Lagrangian interpolation on a Cartesian grid. This approach, which starts with the discretization of parabolic equations with discontinuities in the solutions, source terms and the coefficients across the interface, can easily be accommodated into simulating flow past bluff bodies immersed in the flow. The superiority of the approach is reflected by the reduced magnitude and faster decay of the errors in comparison to other existing methods. It is seen to handle several fluid flow problems having practical implications in the real world very efficiently, which involves flows involving multiple and moving bodies. This includes the flow past a stationary circular and a twenty-four edge cactus cylinder, flows past two tandem cylinders, where in one situation both are fixed and in another, one of them is oscillating transversely with variable amplitude in time. To the best of our knowledge, the last two examples have been tackled for the first time by such an approach employing the $\psi$-$\zeta$ formulation in finite difference set-up. The extreme closeness of our computed solutions with the existing numerical and experimental results exemplifies the accuracy and the robustness of the proposed approach.
翻译:在目前的工作中,我们提出一种新的混合式明显跳跃潜伏界面方法,结合一个更高顺序的契约(HOC)方案,以模拟由流函数-曲流($psi$-$\zeta$)调控的瞬态复杂流动,模拟纳维尔-斯托克斯(N-S)等式的形成,以抑制性粘结性流动;为在界面各不规则点的跳跃条件采用一种新的战略,使用拉格兰杰在产油网上的内插法。这一方法首先从溶液、源值条件和界面间系数不连续性的抛物方方程式分离开始,可以很容易地适应于流动的流动中,即纳维利-斯托克斯-斯托克斯(N-S)等方程式的形成,其优越性反映于错误与其他现有方法相比的减少幅度和更快的衰减;据认为,它解决了在现实世界中具有实际影响的若干流动问题,这涉及多个和移动体的体。这包括一个固定圆流式的方程式,以及一个边缘方方方程式的方程式,其精确度可容纳的直径直径直径的体,在两个直径的体内,最后两个直径直径轴的体内,其内,其直径直径直径直线的体的体的体,其内,其内,其内,一个直径直径直径直径直为一个直线数数数数为一个直线数,其内。