The aim of Validation is to determine the accuracy of a given mathematical model, i.e. to determine the difference between the physical reality and the solution of the mathematical model (δmodel). Validation refers to the mathematical model and not to the computer code and is performed for selected flow quantities of a given problem. Therefore, it is an ongoing activity that requires the definition of quantities of interest (Φ) a measurement of the physical reality (experiment) and a (numerical) solution of the mathematical model.

There are several methods proposed in the open literature to quantify δmodel. In this page we give a brief description of the procedure proposed by the V&V 20 ASME Standards Committee


The modeling error of a quantity of interest δmodel(Φ) is expected to be contained in the interval E-Uval(Φ) ≤ δmodel(Φ) E+Uval(Φ)  95 out 100 times, where E is the comparison error and Uval(Φ)  is the validation uncertainty. The comparison error is the difference between the experimental measurement Φdata  and the numerical solution Φnum, E=Φdata-Φnum, whereas the validation uncertainty includes contributions from the experimental Udata(Φ) , numerical  Unum(Φ) and input parameter uncertainties Uinput(Φ). The determination of Uinput(Φ) is typically obtained with Uncertainty Quantification (UQ) methods that are discussed in [1]. For independent values of the three uncertainties, the validation uncertainty is obtained from Uval(Φ)=√[(Udata(Φ))2+(Unum(Φ))2+(Uinput(Φ))2].

It must be stated that this procedure does not lead to a pass/fail decision. The outcome of the Validation exercise is an interval that contains the modeling error. The analyst has to decide if the limits of the interval are acceptable or not depending on the intended use of the model. Furthermore, Uval(Φ) does not say anything about the model. However, it reflects the quality of the Validation exercise. As discussed in [1],  Uval(Φ)<<E means that and so the modeling error δmodel≈E is accurately estimated. On the other hand, if Uval(Φ)>>E  we have a modeling error range that is significantly larger than the comparison error and so the Validation exercise may be inconclusive. In such conditions, the procedure provides information to determine which sources of uncertainty should be reduced.

[1] Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer, The American Society of Mechanical Engineers (ASME), ASME V&V 20, 2009