Multiscale modeling of gas-particle systems: consistency, closures, and the correct governing equations

In the literature, there is a large variety of different equations that are claimed to be the ‘governing equations’ of gas–solid flows. One reason for the large variety of governing equations is that there exist many different ways to define a ‘resolved’ flow quantity that all come with different properties and implications. In the present paper, the existing approaches are structured, and it is clearly distinguished which parts of the governing equations are exact and which are modeled and therefore only valid under certain circumstances. We discuss what the different definitions of ‘resolved’ flow quantities mean physically and how they differ from the instantaneous flow quantities. We further discuss common misconceptions in closure modeling and how to preserve consistency throughout the simulation process, from the governing equations, over the discretization, to the interpretation of the results.