Title: Frozen-field Modeling of Coronal Condensations with MPI-AMRVAC I: Demonstration in two-dimensional models

Abstract: Large-scale coronal plasma evolutions can be adequately described by magnetohydrodynamics (MHD) equations. However, full multi-dimensional MHD simulations require substantial computational resources. Given the low plasma $\beta$ in the solar corona, in many coronal studies, it suffices to approximate the magnetic field to remain topologically fixed and effectively conduct one-dimensional (1D) hydrodynamic (HD) simulations instead. This approach is often employed in studies of coronal loops and their liability to form condensations related to thermal instability. While 1D HD simulations along given and fixed field line shapes are convenient and fast, they are difficult to directly compare with multi-dimensional phenomena. Therefore, it is more convenient to solve volume-filling, multi-dimensional versions of the MHD equations where we freeze the magnetic field, transforming it into frozen-field HD (ffHD) equations for simulation. We have incorporated this ffHD module into our open-source MPI-AMRVAC code and tested it using a two-dimensional (2D) evaporation--condensation model to study prominence formation due to radiative losses. The 2D ffHD results are compared with those from actual 2D MHD and pseudo-2D HD simulations, analyzing the differences and their causes. Pseudo-2D studies account for the known {flux tube} expansion effects. Overall, the performance of 2D ffHD is close to that of 2D MHD and pseudo-2D HD. The 2D tests conducted in this paper will be extended in follow-up studies to 3D simulations based on analytical or observational approaches.