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Title: A comparison of parallel block multi-level preconditions for the incompressible Navier-Stokes equations.

Abstract

No abstract prepared.

Authors:
Publication Date:
Research Org.:
Sandia National Laboratories
Sponsoring Org.:
USDOE
OSTI Identifier:
891699
Report Number(s):
SAND2006-0265C
TRN: US200622%%203
DOE Contract Number:
AC04-94AL85000
Resource Type:
Conference
Resource Relation:
Conference: Proposed for presentation at the 10th Copper Mountain Conference on Iterative Methods held April 2-7, 2006 in Copper Mountain, CO.
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ITERATIVE METHODS; NAVIER-STOKES EQUATIONS; COMPARATIVE EVALUATIONS

Citation Formats

Shuttleworth, Robert R. A comparison of parallel block multi-level preconditions for the incompressible Navier-Stokes equations.. United States: N. p., 2006. Web.
Shuttleworth, Robert R. A comparison of parallel block multi-level preconditions for the incompressible Navier-Stokes equations.. United States.
Shuttleworth, Robert R. Sun . "A comparison of parallel block multi-level preconditions for the incompressible Navier-Stokes equations.". United States. doi:.
@article{osti_891699,
title = {A comparison of parallel block multi-level preconditions for the incompressible Navier-Stokes equations.},
author = {Shuttleworth, Robert R.},
abstractNote = {No abstract prepared.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 2006},
month = {Sun Jan 01 00:00:00 EST 2006}
}

Conference:
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  • In recent years, considerable effort has been placed on developing efficient and robust solution algorithms for the incompressible Navier-Stokes equations based on preconditioned Krylov methods. These include physics-based methods, such as SIMPLE, and purely algebraic preconditioners based on the approximation of the Schur complement. All these techniques can be represented as approximate block factorization (ABF) type preconditioners. The goal is to decompose the application of the preconditioner into simplified sub-systems in which scalable multi-level type solvers can be applied. In this paper we develop a taxonomy of these ideas based on an adaptation of a generalized approximate factorization of themore » Navier-Stokes system first presented in [25]. This taxonomy illuminates the similarities and differences among these preconditioners and the central role played by efficient approximation of certain Schur complement operators. We then present a parallel computational study that examines the performance of these methods and compares them to an additive Schwarz domain decomposition (DD) algorithm. Results are presented for two and three-dimensional steady state problems for enclosed domains and inflow/outflow systems on both structured and unstructured meshes. The numerical experiments are performed using MPSalsa, a stabilized finite element code.« less
  • Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed in the presence of highly refined grids or high-aspect ratio elements.
  • The combination of (1) very efficient solution methods (Multigrid), (2) adaptivity, and (3) parallelism (distributed memory) clearly is absolutely necessary for future oriented numerics but still regarded as extremely difficult or even unsolved. We show that very nice results can be obtained for real life problems. Our approach is straightforward (based on {open_quotes}MLAT{close_quotes}). But, of course, reasonable refinement and load-balancing strategies have to be used. Our examples are 2D, but 3D is on the way.
  • The modeling goal is to develop accurate and efficient, yet reasonably versatile numerical models for simulating the evolution of the velocity, temperature, and pollutant concentration fields associated with air flow over complex terrain in the planetary boundary layer. Since both the physics (e.g., stratified shear flows) and the geometry are complex, fairly fine spatial resolution (say, approx. 10/sup 4/ nodes) will often be required. The longer-term goal is to be able to do faster than real time simulations in response to emergency situations. It is with these points in mind that a finite element code was developed which entails manymore » short-cuts and simplifications compared to the conventional Galerkin finite element method (GFEM); in fact, the resulting scheme is probably better described as a hybrid method (FEM/FDM). Many aspects of these short-cuts have been described and/or are discussed in more detail elsewhere. Here, attention is focused on the effects of using 1-poing quadrature to approximate the resulting Galerkin integrals.« less
  • Why the advective form for the primitive variable formulation of the inviscid Boussinesq (or Navier-Stokes) equations is nonconservative and how several potentially useful conservative formulations can be generated is demonstrated. Several forms are considered which conserve the following quantities individually or in combinations: total energy, temperature (enthalpy), temperature squared, or none of the above (advective form). Finally the numerical performance and stability of these various formulations are compared via numerical solutions of the time-dependent, inviscid equations of motion employing the finite element method.