Frozen-field Modeling of Coronal Condensations with MPI-AMRVAC II: Optimization and application in three-dimensional models

The frozen-field hydrodynamic (ffHD) model is a simplification of the full magnetohydrodynamical (MHD) equations under the assumption of a rigid magnetic field, which significantly reduces computational complexity and enhances efficiency. In this work, we combine the ffHD prescription with hyperbolic thermal conduction (TC) and the Transition Region Adaptive Conduction (TRAC) method to achieve further optimization. A series of two-dimensional tests are done to evaluate the performance of the hyperbolic TC and the TRAC method. The results indicate that hyperbolic TC, while showing limiter-affected numerical dissipation, delivers outcomes comparable to classic parabolic TC. The TRAC method effectively compensates for the underestimation of enthalpy flux in low-resolution simulations, as evaluated on tests that demonstrate prominence formation. We present an application of the ffHD model that forms a three-dimensional prominence embedded in a magnetic flux rope, which develops into a stable slab-like filament. The simulation reveals a prominence with an elongated spine and a width consistent with observations, highlighting the potential of the ffHD model in capturing the dynamics of solar prominences. Forward modeling of the simulation data produces synthetic images at various wavelengths, providing insights into the appearance of prominences and filaments in different observational contexts. The ffHD model, with its computational efficiency and the demonstrated capability to simulate complex solar phenomena, offers a valuable tool for solar physicists, and is implemented in the open-source MPI-AMRVAC framework.