We present a co-scaling grid formalism and its implementation in the magnetohydrodynamics code Athena++. The formalism relies on flow symmetries in astrophysical problems involving expansion, contraction, and center-of-mass motion. The grid is evolved at the same time order as the fluid variables. The user specifies grid evolution laws, which can be independent of the fluid motion. Applying our implementation to standard hydrodynamic test cases leads to improved results and higher efficiency, compared to the fixed-grid solutions.
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