Many three-dimensional fluid dynamics problems are characterized by a very large degree of contraction, expansion, and/or rotation of the fluid.
Examples include stellar core collapse, supernova explosions, star and galaxy formation, and inertial confinement fusion applications. Compression or expansion of matter in these problems may reach many orders of magnitude. Local features of the flow in these problems may be significantly compressed, expanded, and advected over large distances. This puts extreme demands on numerical resolution and on the quality of numerical advection algorithms. For a rotating fluid, large compression or expansion may also lead to large numerical errors in conservation of angular momentum. I will discuss one approach to modeling such flows based on the computations in a non-inertial expanding (or contracting) and rotating reference frame used in combination with adaptive mesh refinement (both cell-based and grid-based). I will present the analytical description of the method and its numerical properties. Finally, I will
discuss the results of tests and some model problems, such as the implosion of a perturbed shell driven by a converging Guderley-type shock wave.
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