Moving Finite Elements in 2-D.

Abstract

In this second year of effort, truly large-scale computing aspects of PDE's (partial differential equations) have been addressed. MFE (moving finite element) node movement properties of highly sheared fluid flows and shocks were studied. The following results were obtained: (1) extremely large nodal savings were obtained by the MFE method in highly sheared shock examples; (2) such ODE solvers as the Gear method require significant restructuring of their internal code logic in order to achieve improved time step and error-controlling policies in PDE applications; (3) iterative linear solvers are required in order to accommodate large MFE grid meshes; (4) a new iterative solver of linear systems was developed in order to attain large convergence rates in advection-diffusion equations with highly inhomogeneous mesh spacings, which cannot be solved satisfactorily with other existing linear solvers; (5) first-generation regularization schemes resolved highly sheared flows; and, although large grid aspect ratios were resolved successfully, new regularization functions which homogenize MFE grid cells should be developed in future work; and (6) singularities which are frequently troublesome in cylindrical and spherical co-ordinates are eliminated naturally in MFE inner product formulations. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 03, 1983
Accession Number
ADA131279

Entities

People

  • Robert J. Gelinas

Tags

Communities of Interest

  • Materials and Manufacturing Processes
  • Weapons Technologies

DTIC Thesaurus Topics

  • Aspect Ratio
  • Computations
  • Continuum Mechanics
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Flow
  • Fluid Dynamics
  • Fluid Flow
  • Linear Systems
  • Mathematics
  • Mechanics
  • Navier Stokes Equations
  • Partial Differential Equations
  • Physics Laboratories
  • Turbulent Mixing
  • Two Dimensional

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Mechanics and Fluid Dynamics.

Technology Areas

  • Space