A Second Order Ghost Fluid Method for an Interface Problem of the Poisson Equation (Communications in Computational Physics, 2017)
A second order Ghost Fluid method is proposed for the treatment of interfaceproblems of elliptic equations with discontinuous coefficients. By appropriate useof auxiliary virtual points, physical jump conditions are enforced at the interface. Thesigned distance function is used for the implicit description of irregular domain. Withthe additional unknowns, high order approximation considering the discontinuity canbe built. To avoid the ill-conditioned matrix, the interpolation stencils are selectedadaptively to balance the accuracy and the numerical stability. Additional equationscontaining the jump restrictions are assembled with the original discretized algebraicequations to form a new sparse linear system. Several Krylov iterative solvers aretested for the newly derived linear system. The results of a series of 1-D, 2-D testsshow that the proposed method possesses second order accuracy in L∞ norm. Besides,the method can be extended to the 3-D problems straightforwardly. Numerical resultsreveal the present method is highly efficient and robust in dealing with the interfaceproblems of elliptic equations.