We present a new higher-order accurate finite difference explicit jump Immersed Interface Method ( EJIIM ) 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 high 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.  In the process, we show the superiority of the proposed strategy over the EJIIM and other existing IIM methods . We also simulate the steady-state flow past a circular cylinder governed by the Navier-Stokes equations . In all the cases our computed results extremely close to the available numerical and experimental results.
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.
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EJIIM
HEJIIM
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high order
higher-order
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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.
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. We also simulate the steady-state flow past a circular cylinder governed by the Navier-Stokes equations
by establishing the rate of convergence and grid independence of the computed solutions