TY - JOUR

T1 - Fast method to simulate dynamics of two-phase medium with intense interaction between phases by smoothed particle hydrodynamics: Gas-dust mixture with polydisperse particles, linear drag, one-dimensional tests

AU - Stoyanovskaya, Olga

AU - Davydov, Maxim

AU - Arendarenko, Maxim

AU - Isaenko, Elizaveta

AU - Markelova, Tamara

AU - Snytnikov, Valeriy

N1 - Funding Information:
This study was funded by the Russian Science Foundation grant number 19-71-10026 . We thank anonymous reviewers for their constructive suggestions and helpful comments, we are grateful to Olga Drozhzhina for her assistance with language editing.
Publisher Copyright:
© 2020 Elsevier Inc.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/4/1

Y1 - 2021/4/1

N2 - To simulate the dynamics of fluid with polydisperse particles on macroscale level, one has to solve hydrodynamic equations with several relaxation terms, representing momentum transfer from fluid to particles and vice versa. For small particles, velocity relaxation time (stopping time) can be much shorter than dynamical time of fluid that makes this problem stiff and thus computationally expensive. We present a new fast method for computing several stiff drag terms in two-phase polydisperse medium with Smoothed Particle Hydrodynamics (SPH). In our implementation, fluid and every fraction of dispersed phase are simulated with different sets of particles. The method is based on (1) linear interpolation of velocity values in drag terms, (2) implicit approximation of drag terms that conserves momentum with machine precision, and (3) solution of system of N linear algebraic equations with O(N2) arithmetic operation instead of O(N3). We studied the properties of the proposed method on one-dimensional problems with known solutions. We found that we can obtain acceptable accuracy of the results with numerical resolution independent of short stopping time values. All simulation results discussed in the paper are obtained with open source software.

AB - To simulate the dynamics of fluid with polydisperse particles on macroscale level, one has to solve hydrodynamic equations with several relaxation terms, representing momentum transfer from fluid to particles and vice versa. For small particles, velocity relaxation time (stopping time) can be much shorter than dynamical time of fluid that makes this problem stiff and thus computationally expensive. We present a new fast method for computing several stiff drag terms in two-phase polydisperse medium with Smoothed Particle Hydrodynamics (SPH). In our implementation, fluid and every fraction of dispersed phase are simulated with different sets of particles. The method is based on (1) linear interpolation of velocity values in drag terms, (2) implicit approximation of drag terms that conserves momentum with machine precision, and (3) solution of system of N linear algebraic equations with O(N2) arithmetic operation instead of O(N3). We studied the properties of the proposed method on one-dimensional problems with known solutions. We found that we can obtain acceptable accuracy of the results with numerical resolution independent of short stopping time values. All simulation results discussed in the paper are obtained with open source software.

KW - Aerodynamical drag

KW - Intense interphase interaction

KW - Multi-fluid SPH

KW - Polydisperse dusty gas

KW - Smoothed particle hydrodynamics (SPH)

UR - http://www.scopus.com/inward/record.url?scp=85097105212&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2020.110035

DO - 10.1016/j.jcp.2020.110035

M3 - Article

AN - SCOPUS:85097105212

VL - 430

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

M1 - 110035

ER -