We apply the projection operator formalism to the problem of determining the asymptotic behavior of the lattice BGK equation in the hydrodynamic limit. As an alternative to the more usual Chapman-Enskog expansion, this approach offers many benefits. Most remarkably, it produces absolutely exact, though non-Markovian, hydrodynamic difference equations as an intermediate step. These are accurate ...

In this work we discuss a non-trivial effect of the interfacial curvature on the stability of uniformly and suddenly accelerated interfaces, such as liquid rims. The new stability analysis is based on operator and boundary perturbation theories and allows us to treat the Rayleigh–Taylor and Richtmyer–Meshkov instabilities as a single phenomenon and thus to understand the interrelation between t...

The development of a distributed parameter model of microalgae growth is presented. Two modelling frameworks for photo-bioreactor modelling, Eulerian and Lagrangian, are discussed and the complications residing in the multi-scale nature of transport and reaction phenomena are clarified. It is shown why is the mechanistic two time-scale model of photosynthetic factory the adequate model for biot...