This project addresses the needs of scientific communities studying the Earth, planets, stars, and their cosmic environments for a robust and extensible modeling framework specifically adapted to the surface of a sphere. The aim is to develop a very general scientific software framework called GeoMesh-HAMMER that is suitable for running on supercomputers. GeoMesh-HAMMER will be used to study the dynamics of different space plasma environments, including the magnetospheres around planets, stellar winds, and planetary nebulae. The novelty of this approach is in leveraging recent advances in modeling technologies for rarefied plasmas that are not in a state of equilibrium, but whose thermal properties are affected by magnetic fields and the presence of different gas species. In addition, the framework aims to implement state of the art techniques to concentrate the computational resources on the regions of greatest interest, such as a shock wave in front of a magnetosphere, or a burst of plasma from the sun known as a coronal mass ejection, with a much sparser allocation of computing resources for the surrounding space. This approach dramatically improves the efficiency of computer models, resulting in increased productivity and reduced power usage. GeoMesh-HAMMER will be built using an open source development strategy in collaboration with space science and astrophysics communities to maximize the impact on as many fields of study as possible. The adaptive multi-level framework