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The finite volume hydro code Sprout uses a simple expanding Cartesian grid to track outflows for several orders of magnitudes in expansion. It captures shocks whether they are aligned or misaligned with the grid, and provides second-order convergence for smooth flows. The code's expanding mesh capability reduces numerical diffusion drastically for outflows, especially when the analytic nature of the bulk flow is known beforehand. Sprout can be used to study fluid instabilities in expanding flows, such as in SN explosions and jets; it resolves fine fluid structures at small length scales and expand the mesh gradually as the structures grow.