0
TECHNICAL BRIEFS

Weighting Factors for Single-Step Trapezoidal Method

[+] Author and Article Information
Fuzhang Zhao

Department of Mechanical Engineering and Mechanics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104Fuzhang.Zhao@drexel.edu

J. Heat Transfer 128(4), 409-412 (Nov 07, 2005) (4 pages) doi:10.1115/1.2175155 History: Received June 15, 2005; Revised November 07, 2005

The uses of a weighting factor along with a time step in a single-step trapezoidal method to solve a first-order parabolic system have been systematically studied. The weighting factors are used in two main types: constants and variables. The most commonly used constant weighting factors can be defined by the ratio of the Fibonacci sequence. Among them, the optimal weighting factor is 0.618, resulting in a balance between the overall accuracy and efficiency. With the finite element formulation, the space and time dimensions can be discretized separately. For the time discretization only, there exists a zero-error dimensionless time step if a weighting factor is within the range of 0.5–1.0. By taking advantage of the zero-error condition, the weighting factor can be correlated with a time step. The influence of spatial dimensions is lumped into a nonzero eigenvalue of the system. Through validity tests of two benchmark linear problems, the variable weighting factor for a single-step trapezoidal method is shown to be accurate, efficient, and stable. The relevant features have been captured.

FIGURES IN THIS ARTICLE
<>
Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

DAE as a function of DTS with different θ

Grahic Jump Location
Figure 2

Temperature comparison for example 1

Grahic Jump Location
Figure 3

Error as a function of position for example 2

Grahic Jump Location
Figure 4

Error comparison as a function of time step and methods

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.

Related Journal Articles
Related eBook Content
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