Numerical Computation of a Viscous Flow around a Circular Cylinder on a Cartesian Grid

We introduce a novel cut-cell Cartesian grid method that preserves the spectral properties of convection and diffusion. That is, convection is discretised by a skewsymmetric operator and diffusion is approximated by a symmetric positive-definite coefficient matrix. Such a symmetry-preserving discretisation of the Navier-Stokes equations is stable on any grid, and conserves the mass, momentum and kinetic energy if the dissipation is turned off. The discrete convective operator can be integrated explicitly in time for Courant numbers up to 1. In other words, the convective discretisation is such that small boundary cells do not lead to a sharpening of the convective stability restriction. Severe diffusive stability restrictions to the time step are bypassed by treating the diffusive flux through no-slip walls implicitly in time. The method is tested for an incompressible, unsteady flow around a circular cylinder at Re = 100. Numerical results are compared to experimental data.