Solution Verification Linked to Model Validation, Reliability, and Confidence Page: 4 of 6
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6/15/2004 1:01 PM
Step "B" in the 4-step "ABCD" validation process is that of Solution Verification. Solution
Verification is the process of assuring that a model approximating a physical reality with a
discretized continuum (e.g. finite element) code converges in each discretized domain to a
converged answer on the quantity of subsequent validation interest. This is accomplished
in the spatial domain by subdividing the elements or cells on the entire grid or portions of
the grid, as shown in Figure 1.
I I 11111 I
Figure 1. "B" of "ABCD": Solution Verification quantifies the proximity to convergence,
and the model uncertainties we may be forced to accept.
Stated to the extreme, we do not care, in solution verification, if the converged answer is right
or wrong; the issue of obtaining the correct (i.e. 2+2=4) answer is the realm of code
verification. If we modeled finer and finer meshes and converged to 2+2=5, with an order of
convergence consistent with our numerical technique, we should be happy. The fact that we
obtained 2+2=5 would be dealt with as a code verification error, not a failure of solution
verification. So the process for solution verification would be to run our discretized continuum
model at finer and finer meshes, and obtain both a converged solution and a smooth order of
convergence. Such a "smooth" convergence plot is shown in Figure 2.
When the mesh convergence results such as the combustion example shown in Figure 2, we
can proceed to obtain estimates of uncertainty due to Solution Verification as detailed in the
full paper and in many prior references. The result is typically expressed as error estimate on a
log-log plot, with a straight line showing the order (power) of convergence as in Figure 3:
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Logan, R W & Nitta, C K. Solution Verification Linked to Model Validation, Reliability, and Confidence, report, June 16, 2004; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc895096/m1/4/: accessed November 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.