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Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations

Computers and Fluids

By:
and

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Abstract

The origin and nature of spurious oscillation modes that appear in mixed finite element methods are examined. In particular, the shallow water equations are considered and a modal analysis for the one-dimensional problem is developed. From the resulting dispersion relations we find that the spurious modes in elevation are associated with zero frequency and large wave number (wavelengths of the order of the nodal spacing) and consequently are zero-velocity modes. The spurious modal behavior is the result of the finite spatial discretization. By means of an artificial compressibility and limiting argument we are able to resolve the similar problem for the Navier-Stokes equations. The relationship of this simpler analysis to alternative consistency arguments is explained. This modal approach provides an explanation of the phenomenon in question and permits us to deduce the cause of the very complex behavior of spurious modes observed in numerical experiments with the shallow water equations and Navier-Stokes equations. Furthermore, this analysis is not limited to finite element formulations, but is also applicable to finite difference formulations. ?? 1983.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations
Series title:
Computers and Fluids
Volume
11
Issue:
1
Year Published:
1983
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Computers and Fluids
First page:
51
Last page:
68
Number of Pages:
18