Direct raycasting of unstructured cell-centered data by discontinuity Roe-average computation

Abstract

In the field of computational fluid dynamics (CFD), the upwind finite volume method (FVM) is widely applied to solve 3D flows with discontinuity phenomena (e.g., shock waves). It produces unstructured data at the center of each cell (cell-centered data) with the flow discontinuity constraint on the inner-face between face-neighboring cells. For visualization, existing approaches with interpolation usually pre-extrapolate cell-centered data into cell-vertexed data (data values given at cell vertices) and only handle cell-vertexed data during actual rendering, which unconsciously depress the rendering accuracy and violate the discontinuity constraint. In this paper, we propose a novel method to visualize cell-centered data directly avoiding extrapolation and keep the discontinuity in the rendering data on the framework of multi-pass raycasting. During resampling, the field is reconstructed using the original cell-centered data value and the cell-gradient estimated by Green–Gauss theorem. To keep the discontinuity, we reconstruct the field at an inner-face resampled point using both the face-adjacencies and get two discontinuous field values. Then the field is obtained by computing Roe-average of the two. The analysis and experiments demonstrate that our approach gains a high-accuracy reconstruction and leads to a high-quality image.