A new symmetry-preserving Cartesian-grid method for computing flow past arbitrarily shaped objects

This paper deals with a numerical method for solving the unsteady, incompressible Navier–Stokes equations in domains of arbitrarily shaped boundaries, where the boundary is represented using the Cartesian‐grid approach. We introduce a novel cut‐cell discretization, which preserves the symmetry of convection and diffusion. That is, convection is discretized by a skew‐symmetric operator and diffusion is approximated by a symmetric, positive‐definite coefficient matrix. The resulting semi‐discrete (continuous in time) system conserves the kinetic energy if the dissipation is turned off; the energy decreases if dissipation is turned on. The method is successfully tested for an incompressible, unsteady flow around a circular cylinder at Re=100. Copyright © 2005 John Wiley & Sons, Ltd.