This paper presents a research and implementation of a methodology to convert highly detailed Building Information Models (BIM) into geospatial 3D city models (Geo) at multiple Levels of Detail (LoDs). The work was developed within the Horizon Europe CHEK project, which aims to integrate BIM with 3D city models for automated building permit checking. Since BIM models, usually stored in the IFC standard, contain highly detailed and complex geometries that differ significantly from city model standards like CityGML and CityJSON, abstraction and conversion methods are required to generate usable outputs. Our study addresses this by developing a methodology that generates nine different LoDs from a single IFC input. These LoDs include both volumetric and surface-based abstractions for exterior and interior representations. The methodology involves voxelisation, filtering and simplification of surfaces, footprint derivation, storey abstraction, and interior geometry extraction. Together, these approaches allow flexible conversion tailored to specific applications, balancing accuracy, complexity, and computational efficiency. The methodology is implemented in a prototype tool named IfcEnvelopeExtractor. It automates IFC-to-CityGML/CityJSON conversion with minimal user input. The methodology was tested on a variety of models from the CHEK project and benchmark datasets, ranging from small houses to multi-storey buildings. The evaluation covered geometric accuracy, semantic accuracy, and model complexity. Results show that non-volumetric abstractions and interior abstractions performed very well, producing robust and accurate results. However, the accuracy decreased for volumetric and complex abstractions, particularly at higher LoDs. Problems included missing or incorrectly trimmed surfaces, and modelling gaps and tolerance issues in the input IFCs. These limitations reveal that the quality of the input BIM models significantly affects the reliability of conversions. Overall, the methodology demonstrates that automated, flexible, and open-source solutions can effectively bridge the gap between BIM and geospatial domains, contributing to scalable GeoBIM integration in practice.