Direct Flux via Virtual Faces (DFVF-overset): Interpolation-free, conservative, overset CFD using a generalised finite volume method

Abstract

We present DFVF-overset (Direct Flux via Virtual Faces), a conservative overset scheme based on a general form of the finite volume method, originally derived for a meshless method, which intrinsically supports overlapping cells. Fluxes pass between overlapping cells through virtual faces which have rigorously defined area. Exact conservation is retained, and the method does not require interpolation between constituent grids. The new technique has been implemented as a preprocessor for the open-source CFD library OpenFOAM, and validated for a number of 1D and 2D cases. In a 1D diffusion case, the method converges to an analytical solution in the second order. For the lid-driven cavity, DFVF-overset results are close to single-grid solutions and display similar convergence towards a benchmark solution. The new method produces smooth velocity fields, and on a relatively coarse grid, it resolves a tertiary vortex which is absent in interpolation-based overset solutions. 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 shows promise for applications where conventional overset is unsuitable due to interpolation errors or lack of conservation.