The Heavy Ion Fusion Science Virtual National Laboratory(a collaboration of LBNL, LLNL, and PPPL) is using intense ion beams to heat thin foils to the "warm dense matter" regime at <~;; 1 eV, and is developing capabilities for studying target physics relevant to ion-driven inertial fusion energy. The need for rapid target heating led to the development of plasma-neutralized pulse compression, with current amplification factors exceeding 50 now routine on the Neutralized Drift Compression Experiment (NDCX). Construction of an improved platform, NDCX-II, has begun at LBNL with planned completion in 2012. Using refurbished induction cells from the Advanced Test Accelerator at LLNL, NDCX-II will compress a ~;;500 ns pulse of Li+ ions to ~;;1 ns while accelerating it to 3-4 MeV over ~;;15 m. Strong space charge forces are incorporated into the machine design at a fundamental level. We are using analysis, an interactive 1D PIC code (ASP) with optimizing capabilities and centroid tracking, and multi-dimensional Warpcode PIC simulations, to develop the NDCX-II accelerator. This paper describes the computational models employed, and the resulting physics design for the accelerator.