The fabrication of large silicon nitride ceramic components is intricate and demands expertise in gas pressure liquid phase sintering (GPS-LPS). The forefront technology of finite element (FEM) thermo-mechanical modeling plays a key role in sizing aerospace components that necessitate high precision and mechanical strength. A comprehensive sintering simulation should encompass not only densification and grain growth models but also consider the heating environment, accounting for gas convection, conduction, and surface-to-surface radiation. Moreover, silicon nitride sintering simulation addresses the intricate behavior, including the swelling phenomenon during the transitions from intermediate to final stage sintering. The challenge of significant slumping in hollow parts, resulting in costly rejection, is a primary concern for industrial companies when dealing with low-viscosity liquid phase sintering. Validation of the model is achieved through the computation of simple cylindrical cases, while a meticulous comparison between simulations and sintering experiments on complex hollow bodies and deflection bars facilitates precise adjustment of the shear viscosity theoretical parameter derived from the Skorohod-Olevsky continuum theory of sintering. The findings from these simple cases guide the simulation of a complex geometry representative of typical aerospace components, determining the ideal sintering configuration to mitigate slumping issues.