This article is cited in 1 paper

Methods and algorithms of computational mathematics and their applications

Lagrangian method for stiff problems of two-phase dynamics with relaxation: particle-mesh vs particle-particle

O. P. Stoyanovskaya

Lavrentiev Institute of Hydrodynamics SB RAS

Abstract: To simulate the dynamics of gas-dust mixtures at the macroscale level, it is necessary to solve numerically a gas-dynamic equations with relaxation terms describing the transfer of momentum and energy from gas to particles and vice versa. For ultrafine particles, the time of relaxation is much shorter than the time at which the dynamics of the medium is considered. We study the Lagrangian method for gas-dust mixture simulation named Two-Fluid Smoothed Particle Hydrodynamics (TFSPH). TFSPH implies that each phase (gas and particles) is modeled by its own set of particles. Within the framework of TFSPH, two approaches to calculating the relaxation interaction (drag) are known: particle-particle and particle-mesh. Previously it was found in numerical experiments that for small relaxation times, the particle-particle approach suffers from waves overdissipation, while the particle-mesh approach is free from this drawback. We provide the first explanation of this phenomenon using computational mathematics.

Keywords: uniform numerical methods, Two-Fluid Smoothed Particle Hydrodynamics, SPH-IDIC, gas-dust mixture, stiff relaxation terms, stiff drag.

UDC: 519.63

Received: 11.04.2025
Accepted: 15.05.2025

DOI: 10.26089/NumMet.v26r215