0
Technical Briefs

Understanding the Boundary Stencil Effects on the Adjacent Field Resolution in Compact Finite Differences

[+] Author and Article Information
Stephen A. Jordan

 Naval Undersea Warfare Center, Newport, RI 02842jordansa@npt.nuwc.navy.mil

J. Fluids Eng 130(7), 074502 (Jun 25, 2008) (7 pages) doi:10.1115/1.2948366 History: Received May 31, 2007; Revised April 05, 2008; Published June 25, 2008

When establishing the spatial resolution character of a composite compact finite differencing template for high-order field solutions, the stencils selected at nonperiodic boundaries are commonly treated independent of the interior scheme. This position quantifies a false influence of the boundary scheme on the resultant interior dispersive and dissipative consequences of the compound template. Of the three ingredients inherent in the composite template, only its numerical accuracy and global stability have been properly treated in a coupled fashion. Herein, we present a companion means for quantifying the resultant spatial resolution properties that lead to improved predictions of the salient problem physics. Compact boundary stencils with free parameters to minimize the field dispersion (or phase error) and dissipation are included in the procedure. Application of the coupled templates for resolving the viscous Burgers wave and two-dimensional acoustic scattering reveal significant differences in the predictive error.

FIGURES IN THIS ARTICLE
<>
Copyright © 2008 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Spatial resolution errors of the explicit (4e and 5e) and several compact finite difference schemes; 4–8 denotes formal order

Grahic Jump Location
Figure 2

Real (dispersion) and imaginary (dissipation) distributions of modified wave numbers for composite compact finite difference template (3‐4‐3)(1); (3) third-order-accurate on boundary, (4) fourth-order accurate in field

Grahic Jump Location
Figure 3

Real (dispersion) and imaginary (dissipation) distributions of modified wave numbers for composite compact finite difference template (5‐5‐6‐5‐5)(3); (5) fifth-order-accurate on boundary and first interior point, (6) sixth-order Pade-type in remaining field

Grahic Jump Location
Figure 4

Dispersive distributions of composite compact finite difference template (22‐4‐22)(1); (22) two-parameters (a=4, η=−1∕2) second-order-accurate on boundary, (4) fourth-order Pade-type in interior

Grahic Jump Location
Figure 5

Real (dispersion) and imaginary (dissipation) distributions of modified wavenumbers for composite compact finite difference template (43‐4‐43)(2); (43) explicit fourth-order three-parameter family defined on boundary

Grahic Jump Location
Figure 6

Energy loss in solutions of Burgers equation using composite template (3-4-3)

Grahic Jump Location
Figure 7

Solutions of Burgers equation using composite template (3-4-3)

Grahic Jump Location
Figure 8

Predictive errors (L2 norm) at the fictitious boundary of composite templates as applied to the viscous Burgers equation; ‖L2‖=[(1∕N)Σ∣ue′−ufd′∣2]1∕2; optimized composite templates are (22‐4‐22)(1), (43‐4‐43)(2), and (5‐5‐6‐5‐5)(3)

Grahic Jump Location
Figure 9

Radial pressure distribution of acoustic scatter problem (45deg, t=4); optimized composite templates are (22‐4‐22)(1) and (43‐4‐43)(2)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In