A Cost-Effective Search of Collision Pairs in Lagrangian Particle Tracking Method

In the simulation of particle-laden flows, in which the inter-particle collisions have to be considered, using the Eulerian-Lagrangian approach, it is agreed that the search of collision pairs based on the deterministic particle tracking method together with the binary-collision, hard-sphere model is a time consuming job in the computational procedure particularly for the flow laden with a remarkably high number density of particles. A cost-effective algorithm for the particle tracking processes which include solving the equations of motion, searching the collision pairs, and updating the list of neighboring particles’ indices is developed. It is demonstrated in the turbulent, fully developed, particle-laden channel flows that the computational expenditure required for completing the particle tracking processes in a given Lagrangian time step can be optimally made with an approximately linear proportionally to the total number of particles (NPT) by setting the number of Lagrangian cells (Ncell) for computation in accordance with the criterion of NPT / Ncell = O(10°).

A Compact Unconditionally Stable Method for Time-Domain Maxwell's Equations

Higher order unconditionally stable methods are effective ways for simulating field behaviors of electromagnetic problems since they are free of Courant-Friedrich-Levy conditions. The development of accurate schemes with less computational expenditure is desirable. A compact fourth-order split-step unconditionally-stable finite-difference time-domain method (C4OSS-FDTD) is proposed in this paper. This method is based on a four-step splitting form in time which is constructed by symmetric operator and uniform splitting. The introduction of spatial compact operator can further improve its performance. Analyses of stability and numerical dispersion are carried out. Compared with noncompact counterpart, the proposed method has reduced computational expenditure while keeping the same level of accuracy. Comparisons with other compact unconditionally-stable methods are provided. Numerical dispersion and anisotropy errors are shown to be lower than those of previous compact unconditionally-stable methods.