Abstract: We present a physically-based fluid simulation with dynamic grid refinement on parallel SIMD graphics hardware. The irregular and dynamic structure of an adaptive grid requires sophisticated memory access patterns as well as a decomposition of the problem for parallel processing and the distribution of tasks to multiple threads. In this paper, we focus on the representation and management of the dynamic grid on the graphics device for an efficient parallelization of the advection step and the iterative solving of the Poisson equation. In order to achieve high performance, we utilize the hardware's capabilities like fast cache access and trilinear filtering. Furthermore, expensive data transfer between host and device is minimized to avoid a major bottleneck. We report results on the inherent overhead of the dynamic grid compared to an equivalent Cartesian grid. In addition, a visual simulation of smoke is presented with radiosity-based illumination and volume ray casting at interactive frame rates.