A Cartesian cut cell method for incompressible viscous flow

An implementation of the Cartesian cut cell method for modelling incompressible laminar flow is investigated. Solid bodies or boundaries in the flow domain are cut out of a background Cartesian grid. As a result, some cut cells at solid boundary surfaces are generated. With the boundary cut cells, special treatment is needed while integrating the governing equations. A novel hybrid technique involving surface cell trimming and interpolation is applied. To test the accuracy of this approach, it is applied to three benchmark cases: (i) flow in a plane channel skewed to the computational grid lines, (ii) wall-driven flow in an inclined box and (iii) flow past a cylinder. Agreement is found with analytical, numerical benchmark and experimental data. Results suggest that in many practical applications, false diffusion errors will be more significant than the cut boundary cell treatment. When using non-flow aligned Cartesian grids higher order convective term treatments are recommended.