A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow

Guo Chen, Zhilin Li, Ping Lin

    Research output: Contribution to journalArticlepeer-review

    40 Citations (Scopus)
    1 Downloads (Pure)

    Abstract

    Biharmonic equations have many applications, especially in fluid and solid mechanics, but is difficult to solve due to the fourth order derivatives in the differential equation. In this paper a fast second order accurate algorithm based on a finite difference discretization and a Cartesian grid is developed for two dimensional biharmonic equations on irregular domains with essential boundary conditions. The irregular domain is embedded into a rectangular region and the biharmonic equation is decoupled to two Poisson equations. An auxiliary unknown quantity ?u along the boundary is introduced so that fast Poisson solvers on irregular domains can be used. Non-trivial numerical examples show the efficiency of the proposed method. The number of iterations of the method is independent of the mesh size. Another key to the method is a new interpolation scheme to evaluate the residual of the Schur complement system. The new biharmonic solver has been applied to solve the incompressible Stokes flow on an irregular domain.
    Original languageEnglish
    Pages (from-to)113-133
    Number of pages21
    JournalAdvances in Computational Mathematics
    Volume29
    Issue number2
    DOIs
    Publication statusPublished - 2008

    Keywords

    • Biharmonic equations

    Fingerprint Dive into the research topics of 'A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow'. Together they form a unique fingerprint.

    Cite this