Simulation of shallow transverse shear flow by generalized second moment method

Abstract

A numerical scheme known as [he second moment method is generalized to simulate advection and diffusion processes in a Lagrangian frame without projecting the data onto the Eulerian grid. Solutions of the Kε turbulence model equations, and the advection/diffusion equation of the dye. are obtained by this fully Lagrangian method in the simulations of a shallow transverse shear llow where the advection process in certain region of the flow is dominant over ihe turbulent diffusion. The results are compared with the data available from a recent series of experimental investigations on the shallow shear flows. The Lagrangian method is positive definite, mass conserving and unconditionally stable. The successful simulations in both the advection and diffusion dominant regions of the flow ascertain the robustness of the method.