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The ability to extract and follow time-varying flow features in volume data generated from large-scale numerical simulations enables scientists to effectively see and validate modeled phenomena and processes. Extracted features often take much less storage space and computing resources to visualize. Most feature extraction and tracking methods first identify features of interest in each time step independently, then correspond these features in consecutive time steps of the data. Since these methods handle each time step separately, they do not use the coherency of the feature along the time dimension in the extraction process. In this paper, we present a prediction-correction method that uses a prediction step to make the best guess of the feature region in the subsequent time step, followed by growing and shrinking the border of the predicted region to coherently extract the actual feature of interest. This method makes use of the temporal-space coherency of the data to accelerate the extraction process while implicitly solving the tedious correspondence problem that previous methods focus on. Our method is low cost with very little storage overhead, and thus facilitates interactive or runtime extraction and visualization, unlike previous methods which were largely suited for batch-mode processing due to high computational cost.