The DoE's ASCI (Accelerated Strategic Computing Initiative) program and the NSF's PACI (Partnerships in Advanced Computational Infrastructure) program are putting in place very large computing systems that share a common architecture, that of the DSM (or SMP) cluster. These systems, with thousands of the fastest microprocessors available, are the most capable computing platforms in the country today. A hierarchical shared memory approach to structuring programs for efficient computation on these systems will be discussed. An example of an explicit gas dynamics code, PPM, will be given which illustrates general techniques for efficient code design at several levels of the memory hierarchy. A demonstration of this code executing on two 128-processor Origin-2000 machines at NCSA will be discussed. The two machines shared a fast disk system which permitted fault tolerant computation with dynamic load balancing between the two machines on time scales of 10 seconds or less. Prospects for extending this approach to restructure codes with dynamically changing, adaptively refined meshes will be discussed. Ideas for adapting the approach to handle implicit algorthms, in which global information is needed in order to update each grid cell on each time step will also be discussed. Finally, some recent results of large-scale gas dynamics simulations carried out with PPM on these new DSM and SMP cluster systems using grids ranging from 138 million to 8 billion cells will be shown in the form of animations of volume rendered images.