Direct Flux via Virtual Faces (DFVF-overset): An interpolation-free, fully conservative scheme for overset CFD with direct calculation of intergrid flux

In this thesis a new, conservative and interpolation-free, method for computation of solutions to partial differential equations on overset grids is presented. Conventional overset approaches rely on discretising and solving the governing equations on each grid separately. Communication between the grids is then realised through interpolation from one grid to another. This is a source of error in the solution, and compromises the conservative properties of the system. The new technique, termed Direct Flux via Virtual Faces, or DFVF-overset, eliminates the need for interpolation. Instead, flux between overlapping cells on overset grids is calculated directly. A term for intercell face area is derived for overlapping cells which do not share faces, using a generalised, meshless form of the finite volume method. The composite system of overlapping grids can thus be discretised as one monolithic system. The errors associated with interpolation are eliminated and strict conservation is maintained. The method is implemented for the open-source CFD library OpenFOAM, and its performance is benchmarked against solutions using existing, interpolation-based overset techniques, as well as single-grid solutions. The accuracy of the technique is verified against analytical or published experimental results. In the solution of the Poisson equation, the method shows second-order convergence. For incompressible lid-driven cavity flow, DFVF-overset produces results close to single-grid solutions and displays similar grid convergence properties. In static and dynamic multiphase cases solved with a volume-of-fluid method, conventional overset schemes display loss of liquid mass, whereas DFVF-overset demonstrates strict conservation of mass and close agreement with single-grid solutions. The new technique produces continuous and smooth velocity and pressure fields, whereas existing interpolation-based techniques show discontinuities at the overset boundary. DFVF-overset shows potential to provide enhanced accuracy in any application where overset grids have utility, and to enable the use of overset in cases where current interpolation-based techniques are unsuitable, by combining the accuracy and conservative properties of a single-grid solver with the practical benefits of overset.

Funder

Irish Research Council

Publisher

University of Galway

Rights

CC BY-NC-ND

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University of Galway Theses (PhD Theses)