Modern scientific applications consume massive volumes of data produced by computer simulations. Such applications require new data management capabilities in order to scale to terabyte-scale data volumes [32, 10]. The most common way to discretize the application domain is to decompose it into pyramids, forming an unstructured tetrahedral mesh. Modern simulations generate meshes of high resolution and precision, to be queried by a visualization or analysis tool. Tetrahedral meshes are extremely flexible and therefore vital to accurately model complex geometries, but also are difficult to index. To reduce query execution time, applications either use only subsets of the data or rely on different (less flexible) structures, thereby trading accuracy for speed. This paper presents efficient indexing techniques for generic spatial queries on tetrahedral meshes. Because the prevailing multidimensional indexing techniques attempt to approximate the tetrahedra using simpler shapes (rectangles) query performance deteriorates significantly as a function of the mesh’s geometric complexity. We develop Directed Local Search (DLS), an efficient indexing algorithm based on mesh topology information that is practically insensitive to the geometric properties of meshes. We show how DLS can be easily and efficiently implemented within modern database systems without requiring new exotic index structures and complex preprocessing. Finally, we present a new data layout approach for tetrahedral mesh datasets that provides better performance compared to the traditional space filling curves. In our PostgreSQL implementation DLS reduces the number of disk page accesses and the query execution time each by 25% up to a factor of 4.