The Leibniz Supercomputing Centre (LRZ) and the Bavarian Competence Network for Technical and Scienti?c High Performance Computing (KONWIHR) publish in the present book results of numerical simulations facilitated by the High P- formance Computer System in Bavaria (HLRB II) within the last two years. The papers were presented at the Fourth Joint HLRB and KONWIHR Review and - sult Workshop in Garching on 8th and 9th December 2009, and were selected from all progress reports of projects that use the HLRB II. Similar to the workshop two years ago, the majority of the contributed papers belong to the area of computational ?uid dynamics (CFD), condensed matter physics, astrophysics, chemistry, computer sciences and high-energy physics. We note a considerable increase of the user c- munity in some areas: Compared to 2007, the number of papers increased from 6 to 12 in condensed matter physics and from 2 to 5 in high-energy physics. Bio s- ences contributed only one paper in 2007, but four papers in 2009. This indicates that the area of application of supercomputers is continuously growing and entering new ?elds of research. The year 2007 saw two major events of particular importance for the LRZ. First, after a substantial upgrade with dual-core processors the SGI Altix 4700 superc- puter reached a peak performance of more than 62 Tera?op/s. And second, the n- pro?t organization Gauss Centre for Supercomputing e. V. (GCS) was founded on April 13th.