ISSN:
0271-2091
Keywords:
Numerical Analysis
;
Finite Difference Schemes
;
Hyperbolic Equations
;
Wave Propagation
;
Group Velocity
;
Pure Advection
;
Spurious Solutions
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
There are spurious phenomena in the numerical approximation of the hyperbolic equations of fluid dynamics that may be investigated by invoking concepts which originate from wave propagation theory. Many of the significant results which have been obtained by pursuing this kind of analysis are reviewed in this paper by using as an illustration a family of implicit approximations of the simple linear advection equation. Included in this family of algorithms are the common six-point implicit finite difference scheme, the linear finite element/Galerkin scheme and the ‘box’ method.The phase and group velocities of sinusoidal solutions are brought into the analysis of the accuracy and of the spurious reflection or scattering phenomena which are created at computational boundaries and in non-uniform grids. General properties become apparent in this Fourier/wave propagation approach to the analysis. One of these is in the form of an analogy with quantum mechanics. Another shows that certain energy norms of the errors are independent of time discretization, i.e. depend on space discretization alone.
Additional Material:
23 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/fld.1650070502
