Accession Number : ADA180794

Title :   Reversed Stability Conditions in Transient Finite Element Analysis.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Malkus,David S. ; Plesha,Michael E. ; Liu,Meng-Ru

Report Date : FEB 1987

Pagination or Media Count : 24

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.

Descriptors :   *FLUID MECHANICS, *STABILITY, *FINITE ELEMENT ANALYSIS, ALGORITHMS, DAMPING, ELASTIC WAVES, INTEGRATION, MASS, NAVIER STOKES EQUATIONS, NONNEWTONIAN FLUIDS, NUMERICAL METHODS AND PROCEDURES, OPTIMIZATION, PENALTIES, REVERSIBLE, TRANSIENTS

Subject Categories : Fluid Mechanics
      Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE