A novel Cartesian CFD cut cell approach

A new approach to evaluating the fluxes on the faces of Cartesian cut cells is presented. In contrast to most established techniques where the value of a flow variable is only defined at specific points within a cell, in the new approach, the variable values are defined throughout the cell using spline functions. This ensures the first derivatives of the flow variables are continuous throughout the computational domain which is not achieved with existing finite volume methods. For cut cells the values of the variables along the cut faces are therefore defined and hence the mass and momentum fluxes are readily evaluated to second order accuracy. The method is validated against three test cases where analytical solutions or extensive experimental and computational data exists. The test cases are flow in an annulus, flow around an isolated cylinder and laminar boundary layer development on a flat plate inclined at a range of angles to the gridlines. For these test cases, the flow is accurately resolved in the cut cells. The method therefore realises the potential of Cartesian CFD as a more efficient computational tool than more commonly used body fitted methods.