Direct numerical simulations computational demand

Direct numerical simulation (DNS) is a powerful tool to investigate the velocity distribution and density fluctuation of multiphase flow systems, thus facilitates revealing the mechanisms of nonequilibrium behavior. Due to its high demand in computing resources, current DNS is largely hmited to simulations over static arrays of particles or smaU-sized, periodic flow domains, which are expected to be close to local equilibrium states. Thus, the nonequilibrium characteristics of multiphase flow are hard to be fuUy revealed. Recent release of hybrid computing hardware boosts the rapid development of DNS with respect to the scales of time and space... 

Because the electronic energy Ee(q) in Eq. [8] and its derivatives must be calculated at each integration step of a classical trajectory, a direct dynamics simulation is usually very computationally intense. A standard numerical integration time step is /St = 10 " s. Thus, if a trajectory is integrated for 10 s, 10" evaluations of Eq. (8) are required for each trajectory. An ensemble for a trajectory simulation may be as small as 100 events, but even with such a small ensemble 10 " electronic structure calculations are required. Because of such computational demands, it is of interest to determine the lowest level of electronic structure theory and smallest basis set that gives an adequate representation for the system under study. In the following parts of this section, semiempirical and ab initio electronic structure theories and mixed electronic structure theory (quantum mechanical) and molecular mechanical (i.e. QM/MM) approaches for performing direct dynamics are surveyed. 

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