Reversed Stability Conditions in Transient Finite Element Analysis.

Abstract

Numerical methods which introduce artificially unstable modes are discussed. In structural and elastodynamics these result from optimal mass lumping with higher-order elements. In fluid mechanics an additional source of these modes can be a penalty function with alternating signs. These modes yield unstable modal equations; however, they do not necessarily imply unstable transient integration in the presence of algorithmic damping. Stable integration can be achieved by satisfying a stability condition in which the roles of space-step and time-step are reversed. Elastodynamics, the Navier-Stokes equations, and non-Newtonian fluids provide numerical examples. Keywords: Lumping; Mass matrix; Trapezoidal method.

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1987
Accession Number
ADA180794

Entities

People

  • David S. Malkus
  • Meng-ru Liu
  • Michael E. Plesha

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Computational Fluid Dynamics
  • Computational Science
  • Equations
  • Finite Element Analysis
  • Fluid Dynamics
  • Fluid Mechanics
  • Mathematics
  • Mechanics
  • Navier Stokes Equations
  • Physics
  • Stability Conditions

Readers

  • Control Systems Engineering.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematics or Statistics

Technology Areas

  • Space
  • Space - Hall-Effect Thruster