Volume 22, Issue 4
A Second Order Ghost Fluid Method for an Interface Problem of the Poisson Equation

Cheng Liu & Changhong Hu

Commun. Comput. Phys., 22 (2017), pp. 965-996.

Published online: 2017-10

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  • Abstract

A second order Ghost Fluid method is proposed for the treatment of interface problems of elliptic equations with discontinuous coefficients. By appropriate use of auxiliary virtual points, physical jump conditions are enforced at the interface. The signed distance function is used for the implicit description of irregular domain. With the additional unknowns, high order approximation considering the discontinuity can be built. To avoid the ill-conditioned matrix, the interpolation stencils are selected adaptively to balance the accuracy and the numerical stability. Additional equations containing the jump restrictions are assembled with the original discretized algebraic equations to form a new sparse linear system. Several Krylov iterative solvers are tested for the newly derived linear system. The results of a series of 1-D, 2-D tests show that the proposed method possesses second order accuracy in L norm. Besides, the method can be extended to the 3-D problems straightforwardly. Numerical results reveal the present method is highly efficient and robust in dealing with the interface problems of elliptic equations.

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@Article{CiCP-22-965, author = {}, title = {A Second Order Ghost Fluid Method for an Interface Problem of the Poisson Equation}, journal = {Communications in Computational Physics}, year = {2017}, volume = {22}, number = {4}, pages = {965--996}, abstract = {

A second order Ghost Fluid method is proposed for the treatment of interface problems of elliptic equations with discontinuous coefficients. By appropriate use of auxiliary virtual points, physical jump conditions are enforced at the interface. The signed distance function is used for the implicit description of irregular domain. With the additional unknowns, high order approximation considering the discontinuity can be built. To avoid the ill-conditioned matrix, the interpolation stencils are selected adaptively to balance the accuracy and the numerical stability. Additional equations containing the jump restrictions are assembled with the original discretized algebraic equations to form a new sparse linear system. Several Krylov iterative solvers are tested for the newly derived linear system. The results of a series of 1-D, 2-D tests show that the proposed method possesses second order accuracy in L norm. Besides, the method can be extended to the 3-D problems straightforwardly. Numerical results reveal the present method is highly efficient and robust in dealing with the interface problems of elliptic equations.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0155}, url = {http://global-sci.org/intro/article_detail/cicp/9989.html} }
TY - JOUR T1 - A Second Order Ghost Fluid Method for an Interface Problem of the Poisson Equation JO - Communications in Computational Physics VL - 4 SP - 965 EP - 996 PY - 2017 DA - 2017/10 SN - 22 DO - http://doi.org/10.4208/cicp.OA-2016-0155 UR - https://global-sci.org/intro/article_detail/cicp/9989.html KW - AB -

A second order Ghost Fluid method is proposed for the treatment of interface problems of elliptic equations with discontinuous coefficients. By appropriate use of auxiliary virtual points, physical jump conditions are enforced at the interface. The signed distance function is used for the implicit description of irregular domain. With the additional unknowns, high order approximation considering the discontinuity can be built. To avoid the ill-conditioned matrix, the interpolation stencils are selected adaptively to balance the accuracy and the numerical stability. Additional equations containing the jump restrictions are assembled with the original discretized algebraic equations to form a new sparse linear system. Several Krylov iterative solvers are tested for the newly derived linear system. The results of a series of 1-D, 2-D tests show that the proposed method possesses second order accuracy in L norm. Besides, the method can be extended to the 3-D problems straightforwardly. Numerical results reveal the present method is highly efficient and robust in dealing with the interface problems of elliptic equations.

Cheng Liu & Changhong Hu. (2020). A Second Order Ghost Fluid Method for an Interface Problem of the Poisson Equation. Communications in Computational Physics. 22 (4). 965-996. doi:10.4208/cicp.OA-2016-0155
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