This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1002/fld.4380 This article is protected by copyright. All rights reserved. A novel method to calculate the pressure interaction between dust and fluid using SPH Jihoe Kwon* and Heechan Cho Department of Energy Resources Engineering, Seoul National University, Seoul 151-744, Korea *Corresponding author: Tel: +82 2880 1895, fax: +82 2 871 8938. Email address: iori96@snu.ac.kr (J. Kwon). Abstract Unstable behavior of smoothed particle hydrodynamics (SPH) dust particles, such as clumping or fingering under certain conditions, has been reported by several researchers who have conducted studies on dusty fluid SPH. The simulation results in this study show that this instability is numerical, and the instability is mainly attributable to the ill-interpolated pressure gradient in the interaction term between two phases. In this paper, we introduce a new method to calculate the pressure force interaction term between dust and fluid particles. The key idea is to first interpolate the pressure gradient at SPH fluid particles, and then use the values to calculate the pressure gradient at SPH dust particles, in a consecutive manner. To compare the new method with the existing method, we first conducted an interpolation of pressure gradient at hydrostatic equilibrium under gravity to estimate any error. The results show that the new method is more accurate. We then conducted additional numerical tests, namely, dust-liquid counter-flow, sedimentation in a confined tank, and sedimentation in the presence of turbulence. The unphysical unstable behavior of SPH dust particles such as clumping or fingering were significantly reduced in the new method. The results also show that the instability becomes more significant when using the existing method especially for the case when simulating a flow with relatively high concentration of dust or for the case in which inertia dominates the dynamics of dust particles. Especially, in those cases, the existing method should be avoided, and the newly proposed method is highly recommended. Keywords: smoothed particle hydrodynamics, dust-liquid flow, pressure interaction, consecutive interpolation, particle method, multi-phase flows