We present a new higher-order accurate finite difference explicit jump Immersed Interface Method (HEJIIM) for solving two-dimensional elliptic problems with singular source and discontinuous coefficients in the irregular region on a compact Cartesian mesh. We propose a new strategy for discretizing the solution at irregular points on a nine point compact stencil such that the higher-order compactness is maintained throughout the whole computational domain. The scheme is employed to solve four problems embedded with circular and star shaped interfaces in a rectangular region having analytical solutions and varied discontinuities across the interface in source and the coefficient terms. We also simulate a plethora of fluid flow problems past bluff bodies in complex flow situations, which are governed by the Navier-Stokes equations; they include problems involving multiple bodies immersed in the flow as well. In the process, we show the superiority of the proposed strategy over the EJIIM and other existing IIM methods by establishing the rate of convergence and grid independence of the computed solutions. In all the cases our computed results extremely close to the available numerical and experimental results.
翻译:我们提出了一个新战略,在9点紧凑的紧凑点上将非正常点的解决方案分解,以便在整个计算领域保持较高顺序的紧凑性。该计划用于解决一个矩形区域圆形和恒星形状界面所嵌入的四个问题,在源和系数条件的界面之间有分析解决方案和不同不连续性。我们还模拟了在复杂流动情况下过去虚张体的过多流动问题,这些问题由纳维尔-斯托克斯方程式管理;这些问题包括处于流动中的多个机构的问题。在此过程中,我们通过确定计算解决方案的趋同率和网格独立率,展示拟议战略优于EJIIM和其他现有IIM方法的优势。在所有这些情况下,我们计算的结果都非常接近现有的数字和实验结果。