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

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