  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.
