This project extends the high-order spectral difference (SD) method for three-dimensional compressible viscous flows to systems with moving boundaries and deformable grids, and also to combine it with the time-spectral (TS) method to treat periodic unsteady flows. Compared to conventional time accurate methods, the SD-TS method has the potential to significantly reduce the computational cost of simulating time periodic flows. The extension to moving boundaries is needed to enable application of the high order SD methodology to perform accurate simulations of numerous devices in energy and transportation systems, such as wind turbines, rotorcraft and autonomous flapping wing micro air vehicles. Recent development of the SD method by the principal investigator and his colleagues has confirmed it accuracy, robustness and efficiency in dealing with high Reynolds number turbulent flows. The SD method offers a great flexibility in choosing optimal spatial discretization by varying the polynomial order. A baseline SD code has been developed based on quadrilateral/hexahedral grid elements. An element splitting algorithm has also been developed to partition each triangular/tetrahedral element into three or four quadrilateral/hexahedral elements. This enables the use of general grids with mixed elements. For time-dependent high-Reynolds number problems, implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) time stepping approach has been developed in conjunction with a p-multigrid method to speed up convergence of the SD solver. In order to achieve the above goal of treating devices as complex as a rotating wind turbine, the proposed research must address several major challenges. The main tasks being undertaken in the ongoing research by the investigator and his colleagues are 1) Extension of the SD method to moving and deformable grids by transforming the Navier-Stokes equations on a moving physical domain to a fixed reference domain by a blended mapping technique; 2) Parallelization of the three-dimensional solver using MeTis for domain decomposition and MPI for message passing; 3) Development of non-conforming hexahedral elements with hanging nodes to allow geometric flexibility and variable order; 4) Implementation of the Time Spectral method to reduce the computational cost of simulating periodic time dependent flows.
The numerical simulation techniques being developed in this project are crucial to advancing technology in a wide range of energy and transportation systems, with significant potential for reducing environmental impact. Many such systems require simulations of flows with moving boundaries. An immediate target of the research is to improve the state of the art in wind turbine design. The importance of sustainable energy both to reduce U.S. dependence on imported oil supplies and to reduce environmental damage due to fossil fuels is by now widely recognized. Wind power is a resource with tremendous untapped potential. Existing commercial flow simulation codes use low order methods which are too numerically dissipative to allow accurate tracking of the vortex wake which are crucial to wind turbine performance. The high order methods which will result from this project will provide a basis for the systematic future development of superior wind turbine designs. Potential applications to transportation systems which could have significant economic and environmental benefits include drag reduction of road vehicles, both passenger cars and trucks, and improvements in the efficiency and reduction of the acoustic signature of gas turbines and rotorcraft, both of which incorporate moving blades.
