Parallel Solvers For Incompressible Navier-Stokes Equations And Scalable Tools For Fem Applications
Creators: name: K. Georgiev
Publisher: name: Zenodo
Year: 2012
Subjects: scalable algorithms, FEM, CFD

description: The White Paper content is focused on: a) construction and analysis of novel scalable algorithms to enhance scientific applications based on mesh methods (mainly on finite element method (FEM) technology); b) optimization of a new class of algorithms on many core systems.<br>
From one site, the commonly accepted benchmark problem in computational fluid dynamics (CFD) – time dependent system of incompressible Navier-Stokes equations, is considered. The activities were motivated by advanced large-scale simulations of turbulent flows in the atmosphere and in the ocean, simulation of multiphase flows in order to extract average statistics, solving subgrid problems as part of homogenization procedures etc. The computer model is based on implementation of a new class of parallel numerical methods and algorithms for time dependent problems. It only requires solution of tridiagonal linear systems and therefore it is computationally very efficient, with a computational complexity of the same order as that of an explicit scheme, and yet, unconditionally stable. The scheme is particularly convenient for parallel implementation. Among the most important novel ideas is to avoid the transposition which is usually used in alternating directions time stepping algorithms. The final goal is to provide portable tools for integration in commonly accepted codes like Elmer and OpenFOAM. The new development software is organized as a computer library for using of researchers dealing with solution of incompressible Navier-Stokes equations<br>
From other hand, we implement and develop new scalable algorithms and software for FEM simulations with typically O(109) degrees of freedom in space for an IBM Blue Gene/P computer. We have considered voxel and unstructured meshes; stationary and time dependent problems; linear and nonlinear models The performed work was focused on the development of scalable mesh methods, and tuning of the related software tools mainly to the IBM Blue Gene/P architecture but other massively parallel computers and MPI clusters were taken into account too. Efficient algorithms for time stepping, mesh refinement and parallel mappings were implemented. The aim here is again providing software tools for integration in Elmer and OpenFOAM. The computational models address discrete problems in the range of O(109) degrees of freedom in space. The related time stepping techniques and iterative solvers are targeted to meet the Tier-1 and (further) Tier-0 requirements.<br>
Scalability on 512 IBM Blue Gene/P nodes and several other high performance computing clusters is currently documented for the tested software modules and some of them are presented in this paper. Comparison results of running Elmer code on Intel cluster (16 cores, Intel Xeon X5560) and on IBM Blue Gene/P computer can be found. Variants of 1D, 2D and 3D domain partitioning for the 3D test problems were systematically analysed showing the advantages of the 3D partitioning for the Blue Gene/P communication system.