Supercomputer Modelling of Spatially-heterogeneous Coagulation using MPI and CUDA

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

doi:10.1007/978-3-030-36592-9_33

Cited by 3 publications

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The detailed cross-validation of the accuracy and efficiency of the new method in comparison with coarse-graining and Monte Carlo approaches has been reported in our previous works [24,43,46]. Moreover, in the case of equation ( 2) and simple generalization of these equations, such fast algorithms can be utilized in parallel; a good parallel scaling may be achieved at modern computing clusters [47,48] supported by thousands of central processing unit (CPU)-cores and graphics processing unit (GPU) accelerators.…”

Section: Numerical Simulationsmentioning

confidence: 81%

Aggregation in non-uniform systems with advection and localized source

Zagidullin¹,

Смирнов²,

Matveev³

et al. 2022

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We explore analytically and numerically agglomeration driven by advection and localized source. The system is inhomogeneous in one dimension, viz. along the direction of advection. It is characterised by the kinetic coeﬃcients – the advection velocity, diﬀusion coeﬃcient and the reaction kernel, quantifying the aggregation rates. We analyze a simpliﬁed model with mass-independent advection velocity, diﬀusion coeﬃcient, and reaction rates. We also examine a model with mass-dependent coeﬃcients arising in the context of aggregation with sedimentation. For the quasi-stationary case and simpliﬁed model, we obtain an exact solution for the spatially dependent agglomerate densities. For the case of mass dependent coeﬃcients we report a new conservation law and develop a scaling theory for the densities. For the numerical eﬃciency we exploit the low-rank approximation technique; this dramatically increases the computational speed and allows simulations of very large systems. The numerical results are in excellent agreement with the predictions of our theory.

show abstract