A Complex-boundary Treatment Method for Finite Volume Schemes with Cut-Cartesian Cell Mesh

In this paper, a second-order accurate method was developed for calculating fluid flows in complex geometries. This method uses cut-Cartesian cell mesh in finite volume framework. Calculus is employed to relate fluxes and gradients along curved surfaces to cell-averaged values. The resultant finite difference equations are sparse diagonal systems of equations. This method does not need repeated polynomial interpolation or reconstruction. Two-dimensional incompressible lid-driven semi-circular cavity flow at two Reynolds numbers was simulated with the current method and second-order accuracy was reached. The current method might be extended to third-order accuracy.