We describe the Uintah Computational Framework (UCF), a set of software components and libraries that facilitate the simulation of partial differential equations on structured adaptive mesh refinement grids using hundreds to thousands of processors. The UCF uses a non-traditional approach to achieving parallelism, employing an abstract taskgraph representation to describe computation and communication. This representation has a number of advantages that affect the performance of the resulting simulation. We demonstrate performance of the system on a solid mechanics algorithm, two different computational fluid-dynamics (CFD) algorithms, as well as coupled CFD/mechanics algorithms. We show performance of the UCF using up to 2000 processors.