Abstract
Direct numerical simulations of fully developed turbulence in an open channel flowwere performed to clarify the effects of coherent structure on flow dynamics under a free surface. A numerical analysis method was constructed in a generalized curvilinear coordinate system to apply arbitrary complicated boundary conditions. First, a fifthorder accurate upwind difference scheme for the convective tam was considered in a one-dimensional linear convection problem to develop the appropriate discretization of the spatial derivatives. The results showed that the fifth-order upwind scheme yielded a superior performance in comparison with UTOPIA, conservative six-point scheme, TVD Lax Wendrofi CIP and sixth-order central difference method. Furthermore, the direct numerical simulations were in good agreement with velocity fluctuation statistics of a conventionally obtained DNS data base and clarified the interaction of a coherent vortex with both a free surface and fixed wall.
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