Abstract: This paper describes a simple modification to an Eulerian fluid simulation that permits the underlying mesh to deform independent of the simulated fluid's motion. The modification consists of a straightforward adaptation of the commonly used semi-Lagrangian advection method to account for the mesh's motion. Because the method does not require more interpolation steps than standard semi-Lagrangian integration, it does not suffer from additional smoothing and requires only the added cost of updating the mesh. By specifying appropriate boundary conditions, mesh boundaries can behave like moving obstacles that act on the fluid resulting in a number of interesting effects. The paper includes several examples that have been computed on moving tetrahedral meshes.