Numerical Analysis of Filter Based Stabilization for Evolution Equations

Abstract

We consider filter based stabilization for evolution equations (in general) and for the Navier-Stokes equations (in particular). The first method we consider is to advance in time one time step by a given method and then to apply an (uncoupled and modular) filter to get the approximation at the new time level. This filter based stabilization, although algorithmically appealing, is viewed in the literature as introducing far too much numerical dissipation to achieve a quality approximate solution. We show that this is indeed the case. We then consider a modification: Evolve one time step, Filter, Deconvolve then Relax to get the approximation at the new time step. We give a precise analysis of the numerical diffusion and error in this process and show it has great promise, confirmed in several numerical experiments.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2010
Accession Number
ADA512969

Entities

People

  • Monika Neda
  • Vincent J. Ervin
  • William J. Layton

Organizations

  • Clemson University

Tags

Communities of Interest

  • Energy and Power Technologies
  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Boundary Layer
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Equations
  • Error Analysis
  • Finite Element Analysis
  • Fluid Dynamics
  • Fluid Flow
  • Functional Analysis
  • Hydrodynamics
  • Incompressible Flow
  • Large Eddy Simulation
  • Mathematical Analysis
  • Numerical Analysis
  • Viscous Flow

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Computational Modeling and Simulation
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)