The purpose of this statement is to establish
and clarify acceptable standards for the publication of numerical results.
It supplements the previously established JHT Policy on
Reporting Uncertainties in Experimental Measurements and Results (1).
In developing the current policy, the policy statement on control of numerical
accuracy adopted by the
ASME Journal of Fluids Engineering (2) was consulted, as well as similar
policy statements currently under consideration by the AIAA journals and
the International Journal for
Numerical Methods in Fluids. We appreciate the willingness of those involved
with the development of these latter policies to share their thinking
with us and to allow our adoption
of specific elements of their policy statements. Succinctly stated, the
editorial policy of the JOURNAL OF HEAT TRANSFER regarding the review
and publication of numerical studies
is as follows:
NOTE: The JOURNAL OF HEAT TRANSFER
will not accept for review or publication any manuscript reporting the
numerical solution of a heat transfer problem that fails to establish
adequately the accuracy of the computed results.
The implementation of this policy will be at
the discretion of the editor and associate editors in association with
the reviewers, and will be guided, in essence, by the considerations set
forth below and by the view attributed to Kline (3), in the context of
experimental uncertainty analysis, that " . . . any appropriate analysis
is far better than none as long as the procedure is explained."
To be specific, all manuscripts submitted
for review that include numerical simulations must contain the following
A problem statement that is of sufficient
clarity and completeness to allow the reproduction of the results by informed
readers. As a minimum, this should include a statement of the governing
equations solved, all relevant boundary and initial conditions, and values
of associated physical and numerical parameters. Values for any adjustable
or arbitrary parameters employed to obtain the solution must be explicitly
A description of the solution technique employed. If a standard method
is used, the description can be via reference to appropriate prior publications.
If a new method is introduced, the description must be sufficiently complete
to allow implementation of the numerical scheme and replication of relevant
results by informed readers.
The numerical solution must be supplemented with acceptable accuracy estimates
for both the method employed and the results presented. A single calculation
using a fixed discretization will not be acceptable, since no error estimate
can be inferred from such a calculation.
Authors may use any appropriate method for
the estimation of errors. One, or more, of the following approaches may
be useful in this regard:
Comparison of numerical results with those
from a sufficiently similar model problem available in the literature,
possessing a known exact or highly accurate approximate analytical solution;
or with an established, high-accuracy, fine-grid, numerical benchmark
solution of the same, or closely similar, problem. A precisely defined
and documented grid refinement or grid coarsening study. Marginal refinement
showing a qualitative convergence trend is not acceptable. Other numerical
and arbitrary parameters such as time step, convergence criterion, and
boundaries of the computational domain should also be varied to ensure
that the results are independent of these quantities. Comparison with
reliable experimental results that possess an associated established uncertainty.
Noting "reasonable agreement" with experimental data is not, in general,
sufficient justification for acceptance of numerical results, especially
when adjustable parameters are involved. Numerical and experimental results
may be plotted or tabulated to indicate the level of agreement.
In the approaches described above, references
to grid refinement are intended to be interpreted in a general sense to
include numerical methods that are not explicitly dependent on a
computational grid in the manner typically associated with, say, finite
difference methods. For example, grid-free methods would require modification
of the number, or size, of discrete
elements in the computation to establish error estimates. An additional
comment is in order regarding comparisons of numerical results with experimental
data. It is recognized that, when
the results of a numerical simulation are compared with experimental data,
it may not be possible to separate errors in modeling from those associated
with the numerical method. In these
situations, a separate estimate of the numerical error should be established.
In rare situations where none of the above approaches can be satisfactorily
employed to establish the
accuracy of the results, other methods of error estimation acceptable
to the editor, associate editors, and reviewers may be appropriate. For
an illustration of many of the elements
involved in establishing the accuracy of a numerical solution, the study
of natural convection reported by deVahl Davis (4), or the method discussed
by Roache(5) for the uniform
reporting of grid refinement studies may be consulted.
By implementation of this policy, it is the
intent of the editorial board to establish guideline requirements for
the publication of numerical results and to enhance the quality of
publications involving numerical simulations. It is not our intent to
effect a significant increase in the length of papers published in the
JOURNAL OF HEAT TRANSFER, or to impose
excessive requirements on prospective authors. Rather, we hope to elicit
a "good faith" effort from authors to establish the accuracy of their
- The Editorial Board
- ASME JOURNAL OF HEAT TRANSFER, Vol. 115, February 1993, pp. 5-6.
- ASME JOURNAL OF FLUIDS ENGINEERING, Vol. 115, September 1993, pp. 339-340.
- Kline, S.J., 1985, "The Purposes of Uncertainty Analysis," ASME JOURNAL
OF FLUIDS ENGINEERING, Vol. 107, pp. 153-164.
- deVahl Davis, G., 1983, "Natural Convection of Air in a Square Cavity: A
Bench Mark Numerical Solution," INTERNATIONAL JOURNAL OF NUMERICAL METHODS
IN FLUIDS, Vol. 3, pp. 249-264.
- Roache, P.J., 1993, "A Method for Uniform Reporting of Grid Refinement Studies,"
Quantification of Uncertainty in Computational Fluid Dynamics, ASME FED-Vol.
158, pp. 109-120.