In the field of computational fluid dynamics, the upwind finite volume method (FVM) is widely applied to solve the complicated flows with unstructured grids as the volumetric representation. It produces unstructured-grid cell-centered data at the center of each cell（control volume）with the flow discontinuity constraint on the inner-face between face-adjacencies. For visualization, existing reconstruction approaches violate the discontinuity constraint. As a result, the image has low quality due to the lost information of the discontinuity. This research presented a method to reconstruct the discontinuous states at a sample based on the dual control volumes on the framework of multi-pass raycasting. It guarantees that the field on the inner-face is discontinuous between face-adjacencies, which is in accord with the solution of the numerical computation. We also designed a synthesizer for the discontinuous segments based on the reconstruction above, so that the discontinuity information can be transferred to rendering data. The experiments demonstrate that our approach can obviously improve the image quality and clearly visualize the features in the flows.