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SOLVING IMMERSED INTERFACE PROBLEMS USING A NEW INTERFACIAL POINTS-BASED FINITE DIFFERENCE APPROACH
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DOI：10.1137/16M1106006.png)
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Abstract
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A new finite difference scheme based on the higher-order compact technique is presented for solving problems with complex immersed interfaces in arbitrary dimensions. The scheme is designed for general interface problems in which the coefficients, the source term, the solution, and its normal flux may be discontinuous across the interface. The originality of the scheme lies in the use of additional values at interfacial points (points at which grid lines intersect the interface) as nodes in the stencil, which allows straightforward use of the standard finite difference approximations. Appropriate interpolation techniques are used on both sides of the interface to determine the interfacial values. Numerical tests are carried out to validate the scheme for solving elliptic equations in both two and three dimensions, which show that the proposed scheme has overall second-order accuracy. The scheme thus developed is also applied to solve incompressible, two-dimensional Stokes flows. In this process, we compare our computed results with the results obtained from existing schemes, and in most of the cases, our scheme is found to produce relatively better results.
Keywords:
immersed interface
HOC scheme
elliptic equations
discontinuous coefficients
Stokes flows
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