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Journal of Scientific Computing

, Volume 81, Issue 1, pp 217–251 | Cite as

A Second-Order Boundary Condition Capturing Method for Solving the Elliptic Interface Problems on Irregular Domains

  • Hyuntae Cho
  • Heejae Han
  • Byungjoon Lee
  • Youngsoo Ha
  • Myungjoo KangEmail author
Article
  • 189 Downloads

Abstract

A second-order boundary condition capturing method is presented for the elliptic interface problem with jump conditions in the solution and its normal derivative. The proposed method is an extension of the work in Liu et al. (J Comput Phys 160(1):151–178, 2000) to a higher order. The motivation of proposed method is that the approximated value at the interface can be reconstructed by proper interpolation based on the level set representation from Gibou et al. (J Comput Phys 176(1):205–227, 2002). A second-order accurate method is constructed, both in the solution and its gradient, using second-order finite difference approximation. Several numerical results demonstrate that the proposed method is indeed second-order accurate in the solution and its gradient in the \(L^{2}\) and \(L^{\infty }\) norms.

Keywords

Elliptic interface problems Irregular domains Ghost fluid method Level-set method Finite difference method 

Notes

Acknowledgements

The research of Byungjoon Lee was supported by NRF Grant 2017R1C1B1008626 and POSCO Science Fellowship of POSCO TJ Park Foundation. The research of Myungjoo Kang was supported by the National Research Foundation of Korea (NRF)(2015R1A15A1009350, 2017R1A2A1A17069644).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Hyuntae Cho
    • 1
  • Heejae Han
    • 1
  • Byungjoon Lee
    • 2
  • Youngsoo Ha
    • 1
  • Myungjoo Kang
    • 1
    Email author
  1. 1.Department of Mathematical SciencesSeoul National UniversitySeoulKorea
  2. 2.Department of MathematicsThe Catholic University of KoreaBucheonKorea

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