A-posteriori and a-priori tests

15.7 A-posteriori and a-priori tests

Two tests are used to verify LES models. The comon way is the a-posteriori test. The LES simulation is performed and then the flow parameters obtained from the simulation are compared with these from measurement. Depending on comparison results the conclusion about quality of LES models is drawn. The disadvantage of such approach is that the LES results are affected by modelling errors, errors of approximation of differential operators and round- ing errors. In a-posteriori test they can not be separated.

Direct test of quality of subgrid stresses is the a-priori test. First, the subgrid stress is calculated at each time instant from the definition

S GSdef ij

e (15.29)

Then the subgrid stress is computed again at each time instant from any model, say Smagorinsky one

3 S GSdef

kk

averaged in time are compared each with other. If

S GSdef

the SGS model is accurate.

A big difficulty of a-priori tests is the determination of velocities Qu i . For that it is necessary first to obtain the unfiltered velocities u i with spatial and temporal resolutions compared with the Kolmogorov scales. At present this is a big challenge to measure three components of velocity in a volume with high spatial and temporal resolutions. The Particle Image Velocimetry (PIV) measurements are mostly planar measurements within a two dimensional window. Direct Numerical Simulation data are often used as the source for a-priori tests. Three components of velocity in a volume, obtained from DNS, are filtered and utilized for the test. However, it should be noted that DNS simulation is restricted by relatively low Reynolds numbers, whereas main laws of LES are valid for high Re numbers.

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