Efficient p-multigrid spectral element model for water waves and marine offshore structures

In marine offshore engineering, cost-efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a fully nonlinear potential flow (FNPF) model discretized using a Galerkin spectral element method to serve as a basis for handling both wave propagation and wave-body interaction with high computational efficiency within a single modellingapproach. We design and propose an efficientO(n)-scalable computational procedure based on geometric p-multigrid for solving the Laplace problem in the numerical scheme. The fluid volume and the geometric features of complex bodies is represented accurately using high-order polynomial basis functions and unstructured meshes with curvilinear prism elements. The new p-multigrid spectralelement model can take advantage of the high-order polynomial basis and thereby avoid generating a hierarchy of geometric meshes with changing number of elements as required in geometric h-multigrid approaches. We provide numerical benchmarks for the algorithmic and numerical efficiency of the iterative geometric p-multigrid solver. Results of numerical experiments are presented for wave propagation and for wave-body interaction in an advanced case for focusing design waves interacting with a FPSO. Our study shows, that the use of iterative geometric p-multigrid methods for theLaplace problem can significantly improve run-time efficiency of FNPF simulators.Comment: Submitted to an international journal for peer revie

Semiannual report

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period 1 Oct. 1994 - 31 Mar. 1995

Parallel implementation of 3D global MHD simulations for Earth’s magnetosphere

AbstractThis paper presents a dynamic domain decomposition (D3) technique for implementing the parallelization of the piecewise parabolic method (PPM) for solving the ideal magnetohydrodynamics (MHD) equations. The key point of D3 is distributing the work dynamically among processes during the execution of the PPM algorithm. This parallel code utilizes D3 with a message passing interface (MPI) in order to permit efficient implementation on clusters of distributed memory machines and may also simultaneously exploit threading for multiprocessing shared address space architectures. 3D global MHD simulation results for the Earth’s magnetosphere on the massively parallel supercomputers Deepcomp 1800 and 6800 demonstrate the scalability and efficiency of our parallelization strategy

Grid generation for the solution of partial differential equations

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given

Seventh Copper Mountain Conference on Multigrid Methods

The Seventh Copper Mountain Conference on Multigrid Methods was held on 2-7 Apr. 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection shows its rapid trend to further diversity and depth

[Activity of Institute for Computer Applications in Science and Engineering]

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science

Parallel finite element modeling of the hydrodynamics in agitated tanks

Mixing in the transition flow regime -- Technology to mix in transition flow regime -- Methods to characterize mixing hydrodynamics -- Challenges to numerically model transition flow regime in agited tanks -- Transition flow regime in agitated tanks -- Parallel computing -- Numerical modeling of the agitators motion -- Overall methodological approach -- Computational resources -- Program development strategy -- Parallel finite element simulations of incompressible viscous fluid flow by domain decomposition with Lagrange multipliers -- Parallel numerical model -- Parallel implementation -- Three-dimensional benchmark cases -- A parallel finite element sliding mesh technique for the Navier-Stokes equation -- Numerical method -- Parallel implementation -- Numerical examples -- Parallel performance -- Finite element modeling of the laminar and transition flow of the Superblend dual shaft coaxial mixer on parallel computers -- Superblend coaxial mixer configuration -- Numerical model -- Hydrodynamics in Superblend coaxial mixer -- Mixing -- Mixing efficiency -- Parallel finite element solver -- Parallel sliding mesh technique -- Simulation of the hydrodynamics of a stirred tank in the transition regime -- Recommendations for future research -- Parallel algorithms -- Simulation of agited and the transition flow regime