This paper presents an extension to a general-purpose hydrodynamic simulation model for laser-based processes, enabling the simulation of ultrashort pulse laser ablation of dielectric materials. The model incorporates free electron generation through multi-photon and tunneling ionization, avalanche ionization, charge carrier recombination, as well as their diffusion and advection. These processes are fully coupled with compressible multi-phase hydrodynamic equations, allowing for the investigation of phenomena typically unobservable experimentally. A comprehensive validation against experimental data assesses the model's accuracy across various laser parameters. The study also includes a detailed parameter analysis, providing insights into optimal processing conditions. Additionally, the effects of novel beam shapes on ablation dynamics and material removal efficiency are explored, such as the employment of Laguerre-Gaussian beams with orbital angular momentum, so called vortex beams. This extended model offers a powerful tool for understanding and optimizing ultrashort pulse laser ablation of dielectric materials.