A fourth-order finite volume method for direct numerical simulation of turbulence at higher Reynolds numbers

At ECCOMAS 94 we have presented results of a direct numerical simulation (DNS) of turbulent flow in a lid-driven cubical cavity at a Reynolds number Re = 10,000. The 3D, unsteady, incompressible Navier-Stokes equations were solved using a second-order finite volume method on a 100(8) (stretched) grid. The outcomes agreed well with the experimental data of Prasad and Koseff. Here, we will discuss a fourth-order finite volume method which yields a solution on a 50(3) grid that agrees better with the experimental data, for less than one twentieth of the CPU-time. This savings of costs allows for simulations at higher Reynolds numbers. With the improved simulation method, a DNS of a turbulent driven cavity flow at Re = 50,000 is performed using a 192(3) grid. Time-mean quantities and power spectra are computed. Mean velocities at Re = 50,000 will be compared with mean velocities at Re = 10,000.