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Stabilization and scalable block preconditioning for the Navier-Stokes equations

Journal of Computational Physics

Cyr, Eric C.; Shadid, John N.; Tuminaro, Raymond S.

This study compares several block-oriented preconditioners for the stabilized finite element discretization of the incompressible Navier-Stokes equations. This includes standard additive Schwarz domain decomposition methods, aggressive coarsening multigrid, and three preconditioners based on an approximate block LU factorization, specifically SIMPLEC, LSC, and PCD. Robustness is considered with a particular focus on the impact that different stabilization methods have on preconditioner performance. Additionally, parallel scaling studies are undertaken. The numerical results indicate that aggressive coarsening multigrid, LSC and PCD all have good algorithmic scalability. Coupling this with the fact that block methods can be applied to systems arising from stable mixed discretizations implies that these techniques are a promising direction for developing scalable methods for Navier-Stokes. © 2011.

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TYPE Journal Article YEAR 2012
ScopusOSTI

Scalable stabilized fe formulations for simulating turbulent reacting flows in light water reactors

11AIChE - 2011 AIChE Annual Meeting, Conference Proceedings

Pawlowski, Roger P.; Shadid, John N.; Smith, Tom M.; Cyr, Eric C.

This presentation will discuss progress towards developing a large-scale parallel CFD capability using stabilized finite element formulations to simulate turbulent reacting flow and heat transfer in light water nuclear reactors (LWRs). Numerical simultation plays a critical role in the design, certification, and operation of LWRs. The Consortium for Advanced Simulation of Light Water Reactors is a U. S. Department of Energy Innovation Hub that is developing a virtual reactor toolkit that will incorporate science-based models, state-of-the-art numerical methods, modern computational science and engineering practices, and uncertainty quantification (UQ) and validation against operating pressurized water reactors. It will couple state-of-the-art fuel performance, neutronics, thermal-hydraulics (T-H), and structural models with existing tools for systems and safety analysis and will be designed for implementation on both today's leadership-class computers and next-generation advanced architecture platforms. We will first describe the finite element discretization utilizing PSPG, SUPG, and discontinuity capturing stabilization. We will then discuss our initial turbulence modeling formulations (LES and URANS) and the scalable fully implicit, fully coupled solution methods that are used to solve the challenging systems. These include globalized Newton-Krylov methods for solving the nonlinear systems of equaitons and preconditioned Krylov techniques. The preconditioners are based on fully-coupled algebraic multigrid and approximate block factorization preconditioners. We will discuss how these methods provide a powerful integration path for multiscale coupling to the neutronics and structures applications. Initial results on scalabiltiy will be presented. Finally we will comment on our use of embedded technology and how this capbaility impacts the application of implicit methods, sensitivity analysis and UQ.

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TYPE Conference YEAR 2011
ScopusOSTI
Results 176–200 of 268
Results 176–200 of 268