Handling complex boundaries on a Cartesian grid using surface singularities

Research output: Contribution to journalArticle


this paper considers flow around arbitrarily shaped objects. The boundary conditions on the solidboundaries have been applied by replacing the boundary with a surface force distribution on the surface,such that the required boundary conditions are satisfied. The velocity on the boundary is determined byinterpolation or by local (Gaussian space) average. The source terms are determined iteratively as part ofthe solution. They are then averaged and are smoothed out to nearby computational grid points. Themethod has been applied both to test problems as well as to more complex engineering problems, wherethere are not many real competitive alternatives to the proposed method. Simulations of creeping flowaround a sphere were studied in order to evaluate the performance of different, competitive approaches of imposing boundary conditions. Using local averaging first-order accuracy is obtained; this can beimproved by using a Lagrangian polynomial instead, although the convergence is then considerablyslower. Simulations of flows around spheres in the Reynolds number range 1 – 1000 have been carriedout. Finally, the approach was used to describe the impellers in a turbine agitated mixer. For these cases,the results show overall good agreement with other computational and experimental results


Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Fluid Mechanics and Acoustics


  • Cartesian grid, stirred reactor, virtual boundary method
Original languageEnglish
Pages (from-to)125-150
Number of pages25
JournalInternational Journal for Numerical Methods in Fluids
Publication statusPublished - 2001
Publication categoryResearch