2010 Volume 4 Issue 1 Pages 64-75
A consistent scheme for computation of the Reynolds stress and turbulent kinetic energy budgets is proposed for incompressible turbulent flow simulation using the finite difference method on a nonuniform staggered grid system. The present scheme is derived from the Navier-Stokes equation discretized by using the second-order energy-conservative finite differential method. The Reynolds stress and turbulent kinetic energy budgets in a fully developed channel flow computed by using the proposed schemes are compared with those by using the consistent scheme proposed for a uniform grid [Suzuki and Kawamura, Trans. JSME/B, Vol. 60, No. 578 (1994), pp. 3280-3286] and an intuitive scheme. The residuals in the Reynolds normal stress and turbulent kinetic energy budgets computed by using the present scheme and Suzuki-Kawamura scheme are found to be both sufficiently small. We also apply the same idea to the discretization of Reynolds shear stress budget, although the consistency is imperfect, be derived the numerical test shows that the residual is slightly smaller than that computed by the other schemes.
