An efficient numerical method for a mathematical model of a transport of coagulating particles

Zagidullin, Rishat R.; Смирнов, А. П.; Matveev, S. A.; Тыртышников, Е. Е.

doi:10.3103/s0278641917040082

Cited by 11 publications

(8 citation statements)

References 15 publications

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“…In this work we propose a parallel implementation of the numerical method solving advection-coagulation equation from work [28]. The numerical scheme is parallelized along spatial axis x which promotes a good speedup of calculations.…”

Section: Discussionmentioning

confidence: 99%

“…In this section we revisit description of the fast numerical algorithm for advectioncoagulation equation from work [28]. First of all, we use an explicit Euler time-integration scheme with time step ∆t for solution of the Cauchy problem:…”

Section: Numerical Method Revisitedmentioning

confidence: 99%

“…Even though the list of phenomena for application of spatially homogeneous aggregation and fragmentation equations is really huge [25,26], there is an even broader class of spatially inhomogeneous models [19,22]. In this work we concentrate on analysis of advection-coagulation equation [28]:…”

Section: Introductionmentioning

confidence: 99%

“…f (t, x = 0, v) for definition of the Cauchy problem for advection-coagulation equation and its further numerical investigation. Recently, we proposed an efficient numerical method solving the Cauchy problem for this equation [28] and demonstrated its efficiency for the concrete examples of modelling problems. We revisit description of this algorithm in Section 1.…”

Section: Introductionmentioning

confidence: 99%

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Parallel Numerical Algorithm for Solving Advection Equation for Coagulating Particles

Matveev

Zagidullin

Смирнов

et al. 2018

JSFI

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In this work we present a parallel implementation of numerical algorithm solving the Cauchy problem for equation of advection of coagulating particles. This equation describes time-evolution of the concentration f (x, v, t) of particles of size v at the point x at the time-moment t. Our numerical algorithm is based on use of total variation diminishing (TVD) scheme and perfectly matching layers (PML) for approximation of advection operator along spatial coordinate x and utilization of the fast numerical method for evaluation of coagulation integrals exploiting low-rank decomposition of coagulation kernel coefficients and fast FFT-based implementation of convolution operation along particle size coordinate v. In our work we exploit one-dimensional domain decomposition approach along spatial coordinate x because it allows to avoid use of parallel FFT implementations which are very expensive in terms of data exchanges and have poor parallel scalability. Moreover, locality of finite-difference operator from TVD-scheme along x coordinate allows to obtain good scalability even for computing clusters with slow network interconnect due to modest volumes of data necessary for synchronization exchanges between times integration steps.

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Section: Discussionmentioning

confidence: 99%

Section: Numerical Method Revisitedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Parallel Numerical Algorithm for Solving Advection Equation for Coagulating Particles

Matveev

Zagidullin

Смирнов

et al. 2018

JSFI

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“…Nanoparticles are considered in various industrial applications due to their unique properties [1][2][3][4]. The formation of such particles by aggregation in cluster-cluster collisions appears in different environments in physics and chemistry [5,6].The transport of nanoparticles in gas and liquid environment is affected mostly by their size [7,8]. The ability to generate nanoparticles with known size in a controlled way is important because of the superior properties of nanoparticles [9,10].…”

Section: Introductionmentioning

confidence: 99%

Oscillating stationary distributions of nanoclusters in an open system

Matveev

Sorokin

Смирнов³

et al. 2020

Mathematical and Computer Modelling of Dynamical Systems

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Steady-state oscillations of nanoparticle populations in the system of colliding monomers and seed-clusters are observed for the range of the seed-cluster source with diffusion and ballistic collision kernels. The dynamics of nanoparticles in this system is driven by monomer-cluster and cluster-cluster irreversible aggregation and described in terms of the number of primary monomers per nanoparticle based on solving the population balance equations as described by the classical system of Smoluchowski equations. The oscillations of particles' concentrations arise with growing power of the source of seed-clusters and can remain visible for several orders of magnitute of particle sizes k. For the case of constant kinetic coefficients the novel semi-analytial solution of the utilized aggregation model is found and results of numerical simulations with use of up to 2 20 non-linear kinetic equations agree excellently with proposed theory.

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Supercomputer Modelling of Spatially-heterogeneous Coagulation using MPI and CUDA

Zagidullin

Смирнов

Matveev

et al. 2019

Communications in Computer and Information Science

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An efficient numerical method for a mathematical model of a transport of coagulating particles

Cited by 11 publications

References 15 publications

Parallel Numerical Algorithm for Solving Advection Equation for Coagulating Particles

Parallel Numerical Algorithm for Solving Advection Equation for Coagulating Particles

Oscillating stationary distributions of nanoclusters in an open system

Supercomputer Modelling of Spatially-heterogeneous Coagulation using MPI and CUDA

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