3. Mass and volume of particles | Introduction to the particle method

In this column, I would like to write about mass and volume of particles in the particle method. Figure 1(a) shows water in a tank. In the particle method, water is expressed by particles as shown in Fig.1 (b). For example, if water of 100 kg is expressed by 100 particles, each particle has mass of 1kg. If a larger number of particles are used, more complex phenomena can be expressed by the particles. However, it takes a longer computational time for simulation as a larger number of particles is used. ​

The particle size is determined considering the required spatial resolution and the computational time. In general, it is difficult to find the best particle size in advance. Therefore, we first solve a phenomena using relatively large particles. Then, we decrease the particles’ size if it is necessary.

(a)Actual water​
(b)Water expressed by particles​

Fig.1 Conceptual image of water in a tan

​It is assumed that every particle has its own constant mass. Therefore, if particles are not deleted or generated, the total and local mass is exactly conserved because the number of particles does not change. The characteristic of the perfect mass conservation is one of the advantages of the particle method.

Fluid total volume is approximately maintained in the particle method. Although the volume conservation is not exact, the volume change is small enough for most engineering problems. This is because particles’ position is corrected so that the fluid volume does not change. Pressure gradient is used for the position correction.​

1. 越塚誠一, 柴田和也, 室谷浩平, 粒子法入門, 丸善出版, 2014年6月25日, ISBN-13: 978-4621088340​

 About The Author

Kazuya Shibata, Ph.D.
Assistant Professor at Department of System Innovation, Graduate School of Engineering, The University of Tokyo.