Fully Conservative Discretizations for Local Grid Refinement DirkJan

Fully Conservative Discretizations for Local Grid Refinement Dirk-Jan Kort, Marc Dröge, Roel Verstappen, Fred Wubs, Arthur Veldman Problem Test: Poiseuille flow Direct Numerical Simulation of turbulent flow in a complex geometry is a main issue in Computational Fluid Dynamics. Often, a higher resolution is needed in only a small area to obtain an accurate solution. Shown are simulation results for a Poiseuille flow initiated with a uniform inflow velocity (u=0. 25), a time step of 0. 1 and a Reynolds number of 6. When solving the Navier-Stokes equations on a Cartesian grid in such a situation, computation time can be gained by using local grid refinement instead of stretching, as unnecessary calculations are avoided. global solution in locally refined area Illustrated is an example of the amount of cells saved by local grid refinement. Grid with stretching (1653 cells) Grid with local refinement (947 cells) Computer Model Future Work Local grid refinement has been implemented in a code which uses a fully staggered, symmetry-preserving discretization of the Navier-Stokes equations. This means To stress the importance of decreasing the computation time, consider the accurate simulation of flow past a golf ball. • the convective operator is represented by a skewsymmetric coefficient matrix; • the diffusive operator is represented by a symmetric, positive-definite matrix; • the divergence matrix Mh and gradient matrix Gh are related as Gh= – Mh*. Such a symmetry-preserving discretization of the Navier. Stokes equations is stable on any grid and conserves mass, momentum and, in absence of diffusion, kinetic energy. Computational Mechanics & Numerical Mathematics University of Groningen P. O. Box 800, 9700 AV Groningen www. math. rug. nl/~veldman/DNS/dns-home It is estimated, that ten cells per diameter of a dimple will give an accurate solution. Then the number of cells, and consequently the simulation time, will still be huge. In the future, even more computation time can be gained by implementing local time stepping. 635. 000. 008 R u. G