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Parallel performance has been a challenging topic in streamline visualization for large unstructured flow datasets on parallel distributed-memory computers. It depends strongly on domain partitions. Unsuitable partitions often lead to severe load imbalance and high frequent communications among the domain partitions. To address the problem, we present an approach to flow data partitioning taking account of flow directions and features. Multilevel spectral graph bisection method is employed to reduce communication and synchronization overhead among distributed domains. Edge weights in the corresponding adjacent matrix is defined based on an anisotropic local diffusion operator which assigns strong coupling along flow direction and weak coupling orthogonal to flow. Meanwhile, the distributions of seed points and flow features such as vortex structure are also considered in partitioning so as to obtain good load balance. The experimental results are given to show the feasibility and effectiveness of our method.