Indicators for the Quality Assessment of the Grid Resolution

The choice of the grid resolution in thermo-fluid dynamics simulations is to be made as a balance between the quality of the results and the computational effort. When quick results are needed, coarse resolutions are often used, but in some cases this could be detrimental for the reliability of the numerical results. However, it is well known that reducing the size of the mesh affects dramatically the overall simulation time. Several approaches can be used to ensure that the mesh size is appropriate to reproduce the fire and smoke dynamics for a given scenario with suitable computational effort and make reliable predictions. The first and most used approach consists of limiting the ratio between the characteristic fire diameter D∗ and the grid size dx inside a range based on a series of experimental tests reported in literature. This approach is generally used as a first step in order to define a tentative grid resolution for the given model. Other approaches consist of checking if some indicators are included in a literature-based range once the simulation has run. For example, the dimensionless parameter y+ is a measure of how well the near-wall field is solved and can be effectively useful when the roughness of the walls affects the overall flow field. The measure of turbulence resolution (MTR), instead, is a quantity related to the resolved i.e. calculated turbulent kinetic energy and gives an idea of how detailed the turbulence effects are accounted in the model. These indicators are certainly a significant source of information regarding the quality of the model as well as the need of local refinement. However, they are not a guarantee for the achievement of convergent results of the quantity of interest (e.g. temperature, visibility, FED) which from the engineering point view are as valuable as the quality assessment of the model. In the paper, the traditional indicators are reviewed from a theoretical point of view and the Pearson's coefficient is introduced as an attempt to add other statistical correlation principles. The purpose is to couple mesh quality metrics with a global convergence check of the quantity of interest of the fire safety analysis, driven also by aspects of conservativeness and computational cost. An application to a case study is also provided and shows pros and cons of the indicators.