We propose an anisotropic diffusion-advection partial differential equation (PDE) model for visualizing time-dependent vector fields on domains with arbitrary geometry and on surfaces without need for parameterization. We employ the shifted-linear interpolation method of Blu et al. for resampling during advection, which helps to reduce smoothing artifacts. Our PDE-based method for visualizing time-dependent vector fields allows us to reduce flickering artifacts in animated visualization in two ways. First, we use temporally coherent initial noise images as initial solution for the advection-diffusion equation. Second, we apply advection and diffusion over a finite time span of the unsteady flow, which trades animation smoothness for blurriness of final images. We discretize the diffusion term using the finite differencing method and the advection term using the method of characteristics. We implemented our discretized model and study parameters to find a balance between temporal coherency and image blurriness.
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