Ralf Deiterding

Construction and Application of an AMR Algorithm for Distributed Memory Computers

The blockstructured adaptive mesh refinement (AMR) technique of Berger and Collela is tailored especially for the efficient simulation of instationary supersonic flow phenomena on high-performance computers. While the parallelization of the method on shared memory architectures is relatively straight-forward, appropriate distribution strategies for the emerging generation of distributed memory machines are a topic of on-going research. In this talk, we propose a locality-preserving domain decomposition that partitions the entire AMR hierarchy from the base level on. We demonstrate that our approach reduces the communication costs and simplifies the implementation. A precise topological notation is employed to introduce the sequential AMR method and to explain the necessary extensions in parallel. Emphasis is put on the effective parallelization of the flux correction procedure, which is indispensable for conservative finite volume schemes. Briefly, we sketch the design of our public-domain framework AMROC (Adaptive Mesh Refinement in Object-oriented C++) that implements the proposed algorithms generically. Beside an easily reproducible standard benchmark, we show AMROC simulations of transient hydrogen-oxygen detonations with detailed non-equilibrium chemistry for nine gaseous species that impressively demonstrate the advantages in employing a massively parallel AMR algorithm. In particular, the first successful three-dimensional regular cellular structure simulation with detailed chemistry and a two-dimensional detonation diffraction, which is in perfect agreement with experimental results, are presented. These simulations were run effectively on a Linux-Beowulf-cluster of 48 CPUs and spent 1500-2000h CPU time in the numerical update routines.