  Recent observations of reflected propagating and standing slow-mode waves in
hot flaring coronal loops have spurred our investigation into their underlying
excitation and damping mechanisms. To understand these processes, we conduct
2.5D magnetohydrodynamic (MHD) simulations using an arcade active region model
that includes a hot and dense loop. Our simulations allow for in-depth
parametric investigations complementing and expanding our previous 3D MHD
modeling results. We excite these waves in two distinct models as motivated by
observations from the SDO/AIA. Model 1 incorporates classical compressive
viscosity coefficient, while Model 2 adopts a 10-times enhanced viscosity
coefficient. We find that: (1) Our 2.5D MHD simulations reinforce previous
conclusions derived from 1D and 3D MHD models that significantly enhanced
viscosity is crucial for the rapid excitation of standing slow waves with
damping times consistent with observations by Wang et al. (2015). (2) We
uncover that nonlinearity in Model 1 delays the conversion of a reflected
propagating wave into a standing wave. In contrast, Model 2 exhibits a much
weak influence of nonlinearity. (3) Our results reveal that the transverse
temperature structure holds more influence on wave behavior than the density
structure. In Model 1, increased loop temperature contrast significantly
enhances wave trapping within the structure, mitigating the impact of
temperature-dependent viscous damping. Conversely, in Model 2, the impact of
temperature structure on wave behavior weakens in comparison to the effect of
viscosity. (4) Model 1 displays evident nonlinear coupling to the fast and kink
magnetoacoustic waves and pronounced wave leakage into the corona. However,
analyzing three observed wave events by SDO/AIA aligns with Model 2
predictions, providing further support for the substantial viscosity increase.
