## 6.1. An Approach to Error Identification, Estimation and Validation

An evaluation of CFD capabilities has to ensure that the different types of errors are identified and, as far as possible, treated separately. It is known from single-phase studies that the quantification and documentation of modeling errors (as in turbulence models, for example) can be achieved only if the other major sources of errors are reduced below an “acceptable” level. In an ideal world, this would mean, among other demands, that solutions are provided for grids and with timesteps that are fine enough so that numerical errors can be neglected. This is not a trivial task and the separation of errors cannot always be achieved. These difficulties will be greatly increased by the inclusion of multi-phase physics and unsteady effects. Nevertheless, the worst strategy would be to avoid the subject and to provide solutions on a single grid, with a single timestep, and with other uncertainties in initial conditions and boundary conditions not evaluated. This would result in solutions that would be of little use for the validation goals.

An essential quantity in the quality assurance procedure is the definition of target variables. They will mainly be scalar (integral) quantities (for instance, forces, heat transfer rates, and maximum temperature) or one-dimensional distributions, such as the wall heat transfer along a certain line. Convergence studies can be based on these variables without a reference to the grid used in the simulation. They can also be used for an asymptotic evaluation of convergence on unstructured meshes. Even more important, these quantities are of immediate meaning to engineers and enable them to understand the uncertainty from a physical standpoint. A danger of integral or local scalar quantities is that they might not be sensitive enough to detect local changes in the solutions under grid refinement. This should be kept in mind during the analysis.

In order to tackle the problem, it is necessary to first define the different type of errors that can impact a CFD simulation. It is then required that you list the most promising strategies in order to reduce or avoid these errors. Based on these strategies, procedures have to be defined that can be used for the test case simulations.

It might be not possible to rigorously perform the error estimation and reduction procedures described in the following sections for the complex demonstration cases. However, the best attempt should be made to follow the principal ideas and to avoid single grid solutions without sensitivity studies. For these cases, it is even more important to follow a stringent documentation procedure and to list the possible deficiencies and uncertainties in the simulations.

The strategies for the reduction and evaluation of numerical errors have been developed for single-phase flows. There is no principal difference between the single- and multi-phase flow formulations. They are both based on (ensemble) averaged equations, and are mathematically similar. From a physical standpoint, there are however significant additional challenges due to the presence of the different phases, besides the obviously higher demands on model formulation. One of the additional complication lies in the presence of sharp interfaces between the phases, which require a higher degree of grid resolution than usually necessary for single-phase flows. In addition, multi-phase flows have a higher affinity to physical instabilities that might be suppressed on coarse grids, but appear under grid refinement. (This effect is sometimes also observed in single-phase flows. An example is the blunt trailing edge of an airfoil, where extreme grid refinement will eventually capture the vortex shedding of the mixing layer). It is to be kept in mind that the brute application of procedures might not lead to the desired results. Also in these cases, the spirit behind the guidelines should be followed and carried as far as possible.

Validation studies have to be based on experimental data. These data can introduce significant errors into the comparison. It is therefore required to select the project test cases with attention to potential error sources and experimental uncertainties. Definitions on the different types of test cases as well as on the requirements for the project are given in Selection and Evaluation of Experimental Data.

Release 18.2 - © ANSYS, Inc. All rights reserved.