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- Recent experiments in precision spectroscopy of hydrogen isotopologs provide new avenues to test fundamental physics, including quantum electrodynamics (QED) and speculative theories like extra dimensions or a fifth fundamental force. Discrepancies between experimental results and QED predictions for HD rovibrational transitions question the validity of QED applied to molecules. Moreover an unexpected asymmetry in the absorption lineshape obtained experimentally has no explanation yet. This master thesis developed a numerical simulation of HD saturated cavity absorption spectroscopy. The simulation reproduced symmetric Lamb-dip lineshapes in steady-state and transient regimes, validating its approach. However, issues such as the need for a correction factor and approximations regarding the transit time remain. This work is therefore a preliminary work for addressing asymmetries in absorption profiles and ultimately improving experimental accuracy in HD spectroscopy.