A novel higher order compact-immersed interface approach for elliptic problems

We present a new higher-order accurate finite difference explicit jump Immersed Interface Method for solving two-dimensional elliptic problems with singular source and discontinuous coefficients in the irregular region on compact Cartesian mesh. propose strategy discretizing solution at points nine-point stencil such that compactness is maintained throughout whole computational domain. The scheme employed to solve four embedded circular- star-shaped interfaces rectangular having analytical solutions varied discontinuities across interface coefficient terms. also simulate plethora of fluid flow past bluff bodies complex situations which are governed by Navier–Stokes equations; they include involving multiple immersed as well. In process, we show superiority proposed over method other existing methods establishing rate convergence grid independence computed solutions. all cases, our results extremely close available numerical experimental results.