Spatial filter averaging approach of probabilistic method to linear second-order partial differential equations of the parabolic type

Loire, Sophie; Mezić, Igor

doi:10.1016/j.jcp.2012.08.035

Cited by 2 publications

(1 citation statement)

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“…We employ a backward particle tracking for calculation of particle trajectory. It is often used in a Lagrangian stochastic method 8,11 for its valuable advantages: a solution is given in any desired domain and the lack of coverage issue is avoided. Particle trajectory that departs from a target point x A p (t 0 ) is tracked backward in time to detect the initial position x A p (t i ), where x ¡ 22 or x ¢ 2.…”

Section: Analytical Methods and Techniquesmentioning

confidence: 99%

An approach for accurate simulation of liquid mixing in a T-shaped micromixer

2013

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In this paper, we propose a new computational method for efficient evaluation of the fluid mixing behaviour in a T-shaped micromixer with a rectangular cross section at high Schmidt number under steady state conditions. Our approach enables a low-cost high-quality simulation based on tracking of fluid particles for convective fluid mixing and posterior solving of a model of the species equation for molecular diffusion. The examined parameter range is Re = 1.33 × 10(-2) to 240 at Sc = 3600. The proposed method is shown to simulate well the mixing quality even in the engulfment regime, where the ordinary grid-based simulation is not able to obtain accurate solutions with affordable mesh sizes due to the numerical diffusion at high Sc. The obtained results agree well with a backward random-walk Monte Carlo simulation, by which the accuracy of the proposed method is verified. For further investigation of the characteristics of the proposed method, the Sc dependency is examined in a wide range of Sc from 10 to 3600 at Re = 200. The study reveals that the model discrepancy error emerges more significantly in the concentration distribution at lower Sc, while the resulting mixing quality is accurate over the entire range.

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Section: Analytical Methods and Techniquesmentioning

confidence: 99%