Scientists in many disciplines use spatial mesh models to study physical phenomena. Simulating natural phenomena by changing meshes over time helps to understand and predict future behavior of the phenomena. The higher the precision of the mesh models, the more insight do the scientists gain and they thus continuously increase the detail of the meshes and build them as detailed as their instruments and the simulation hardware allow. In the process, the data volume also increases, slowing down the execution of spatial range queries needed to monitor the simulation considerably. Indexing speeds up range query execution, but the overhead to maintain the indexes is considerable because almost the entire mesh changes unpredictably at every simulation step. Using a simple linear scan, on the other hand, requires accessing the entire mesh and the performance deteriorates as the size of the dataset grows. In this paper we propose OCTOPUS, a strategy for executing range queries on mesh datasets that change unpredictably during simulations. In OCTOPUS we use the key insight that the mesh surface along with the mesh connectivity is sufficient to retrieve accurate query results efficiently. With this novel query execution strategy, OCTOPUS minimizes index maintenance cost and reduces query execution time considerably. Our experiments show that OCTOPUS achieves a speedup between 7.2x and 9.2x compared to the state of the art and that it scales better with increasing mesh dataset size and detail.