Keywords: immersed boundary method, parallel calculation, particle moving, multiphase flow, numerical simulation, particle sediment.

Gas-solid multiphase flow exists widely in nature and in industry. In the numerical study of multiphase flow, some new numerical techniques for the simulation of multiphase flow are proposed which contain the volume effect of the particles. The immersed boundary method based on the uniform Cartesian grids has been applied for the simulation of multiphase system [1,2]. Due to the great computational cost, parallel schemes are necessary, and some schemes are proposed recently [3,4]. The parallel efficiency is high when the particles are distributed in the flow field uniformly because the particles (or Lagrangian points) are calculated on each processor are almost the same. And for the case with non-uniform distribution of the particle phase such as the fluidized bed, the workload for some processors are very heavy while it is quite light for some other processors. The cost for each time step is determined by the processor with the heaviest workload. To increase the computational speed, the workload on each processor should be redistributed. The processors with light workloads help the processors with heavy workloads to finish the particle-related calculation. Based on this spirit, a parallel scheme is proposed in present paper to balance the workload of the particle-related operations on each processor when the immersed boundary method is applied for the simulation of the multiphase system.

In order to validate the parallel scheme proposed in present paper for workload balance, three cases are conducted. The first case is the simulation of a solid particle settling in a rectangular channel. The good agreement of the particle settling velocity between the present result and the experimental results of Mordant and Pinton [5] validates the accuracy of the present algorithm. The second case is that one processor is full of 66 particles and the other processors do not contain any particle. Very high parallel efficiency is obtained when two and three processors are applied which are 0.966 and 0.91, respectively. A greater number of the processors used for parallel calculation leads to a lower parallel efficiency. The third case is the simulation of the sedimentation of 660 particles in a closed box. This case shows the ability of present parallel scheme in the calculation of a large number particles. In this case, the entire parallel efficiency is higher than 0.9.

1

M. Uhlmann, "An immersed boundary method with direct forcing for the simulation of particulate flows", Journal of Computational Physics, 209, 448-476, 2006. doi:10.1016/j.jcp.2005.03.017

2

Z. Wang, J. Fan, K. Luo, "Combined multi-direct forcing and immersed boundary method for simulating flows with moving particles", International Journal of Multiphase Flow, 34, 283-302, 2008. doi:10.1016/j.ijmultiphaseflow.2007.10.004

3

M. Uhlmann, "Simulation of particulate flows on multi-processor maschines with distributed memory", CIEMAT, Technical Report, No. 1039, Madrid, Spain, ISSN-1135-9420, 2003.

4

Z. Wang, J. Fan, K. Luo, "Parallel computing strategy for the simulation of particulate flows with immersed boundary method", Science in China Series E: Technological Sciences, 51, 1169-1176, 2008. doi:10.1007/s11431-008-0144-3

5

N. Mordant, J.F. Pinton, "Velocity measurement of a settling sphere", The European Physical Journal B, 18, 343-352, 2000. doi:10.1007/PL00011074

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