Three-dimensional simulations of the airborne COVID-19 pathogens using the advection-diffusion model and alternating-directions implicit solver

Marcin Łoś, Maciej Woźniak, Ignacio Muga, Maciej Paszynski

Research output: Contribution to journalArticlepeer-review

Abstract

In times of the COVID-19, reliable tools to simulate the airborne pathogens causing the infection are extremely important to enable the testing of various preventive methods. Advection-diffusion simulations can model the propagation of pathogens in the air. We can represent the concentration of pathogens in the air by “contamination” propagating from the source, by the mechanisms of advection (representing air movement) and diffusion (representing the spontaneous propagation of pathogen particles in the air). The three-dimensional time-dependent advection-diffusion equation is difficult to simulate due to the high computational cost and instabilities of the numerical methods. In this paper, we present alternating directions implicit isogeometric analysis simulations of the three-dimensional advection-diffusion equations. We introduce three intermediate time steps, where in the differential operator, we separate the derivatives concerning particular spatial directions. We provide a mathematical analysis of the numerical stability of the method. We show well-posedness of each time step formulation, under the assumption of a particular time step size. We utilize the tensor products of one-dimensional B-spline basis functions over the three-dimensional cube shape domain for the spatial discretization. The alternating direction solver is implemented in C++ and parallelized using the GALOIS framework for multi-core processors. We run the simulations within 120 minutes on a laptop equipped with i7 6700 Q processor 2.6 GHz (8 cores with HT) and 16 GB of RAM.

Original languageEnglish
Article numbere137125
JournalBulletin of the Polish Academy of Sciences: Technical Sciences
Volume69
Issue number4
DOIs
StatePublished - Aug 2021
Externally publishedYes

Keywords

  • Advection-diffusion
  • COVID-19
  • Implicit dynamics
  • Isogeometric analysis
  • Parallel alternating directions solver
  • Pathogen spread

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