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Quadrature based moment methods
Quadrature-based moment methods (QBMM) are a class of computational fluid dynamics (CFD) methods for solving Kinetic theory and is optimal for simulating phases such as rarefied gases or dispersed phases of a multiphase flow. The smallest "particle" entities which are tracked may be molecules of a single phase or granular "particles" such as aerosols, droplets, bubbles, precipitates, powders, dust, soot, etc. Moments of the Boltzmann equation are solved to predict the phase behavior as a continuous (Eulerian) medium, and is applicable for arbitrary Knudsen number and arbitrary Stokes number . Source terms for collision models such as Bhatnagar-Gross-Krook (BGK) and models for evaporation, coalescence, breakage, and aggregation are also available. By retaining a quadrature approximation of a probability density function (PDF), a set of abscissas and weights retain the physical solution and allow for the construction of moments that generate a set of partial differential equations (PDE's). QBMM has shown promising preliminary results for modeling granular gases or dispersed phases within carrier fluids and offers an alternative to Lagrangian methods such as Discrete Particle Simulation (DPS). The Lattice Boltzmann Method (LBM) shares some strong similarities in concept, but it relies on fixed abscissas whereas quadrature-based methods are more adaptive. Additionally, the Navier–Stokes equations(N-S) can be derived from the moment method approach.
==Method==
QBMM is a relatively new simulation technique for granular systems and has attracted interest from researchers in computational physics, chemistry, and engineering. QBMM is similar to traditional CFD methods, which solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, but QBMM accomplishes this by modeling the fluid as consisting of fictive particles, or nodes, that constitute a discretized PDF. A node consists of an abscissa/weight pair and the weight defines the probability of finding a particle that has the value of its abscissa. This quadrature approximation may also be adaptive, meaning that the number of nodes can increase/decrease to accommodate appropriately complex/simple PDF's. Due to its statistical nature, QBMM has several advantages over other conventional Lagrangian methods, especially in dealing with complex boundaries, incorporating microscopic interactions (such as collisions), parallelization of the algorithm, and computational costs being largely independent of particle population. The numerical methods for solving the system of partial differential equations can be interpreted as the propagation (with a flux term) and interactions (source terms) of fictitious particle probabilities in an Eulerian framework.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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