A Compact Finite Volume Method for Direct Numerical Simulation of Incompressible Turbulent Flows

Direct Numerical Simulation (DNS) of turbulent flow and heat transfer requires that most of the energy-containing length and time scales must be accurately captured. The spatial resolution can be augmented in two complementary ways, i.e. either the grid spacing has to be reduced, by refining the computational mesh, or a more accurate spatial approximation should be used. In this work we present our approach for the development of a fourth-order, compact finite volume scheme for the DNS of incompressible turbulent flow and heat transfer. The numerical method is fourth order accurate, but it is shown that a further increase of accuracy does not represent a difficult task, and can be accomplished in a modular way. A staggered grid arrangement is employed, which presents well-known advantages concerning properties conservation and absence of unphysical pressure oscillations, of paramount importance in DNS. In this paper, after a concise description of the method, we present several test cases, which illustrate the main characteristics and capabilities of the proposed methodology