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This article can be considered as an extension of the paper of Fukagata et al. ͓Phys. Fluids 14, L73 ͑2002͔͒ which derived an analytical expression for the constituent contributions to skin friction in a turbulent channel, pipe, and plane boundary layer flows. In this paper, we extend the theoretical analysis of Fukagata et al. ͑formerly limited to canonical cases with two-dimensional mean flow͒ to a fully three-dimensional situation allowing complex wall shapes. We start our analysis by considering arbitrarily shaped surfaces and then formulate a restriction on a surface shape for which the current analysis is valid. A theoretical formula for skin friction coefficient is thus given for streamwise and spanwise homogeneous surfaces of any shape, as well as some more complex configurations, including spanwise-periodic wavy patterns. The theoretical analysis is validated using the results of large eddy simulations of a turbulent flow over straight and wavy riblets with triangular and knife-blade cross-sections. Decomposition of skin friction into different constituent contributions allows us to analyze the influence of different dynamical effects on a skin friction modification by riblet-covered surfaces.

An overlapping mesh methodology that is spectrally accurate in space and up to third-order accurate in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The ability to decompose a global domain into separate, but overlapping, subdomains eases mesh generation procedures and increases flexibility of modeling flows with complex geometries. The methodology employs implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrallyaccurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. The overlapping mesh methodology is thoroughly validated using two-dimensional and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal convergence is documented and is in agreement with the nominal order of accuracy of the solver. The influence of long integration times, as well as inflow-outflow global boundary conditions on the performance of the overlapping grid solver is assessed. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics with the overlapping grids is validated against published available experimental and other computation data. Scaling tests are presented that show near linear strong scaling, even for moderately large processor counts.

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