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BY-NC-ND 4.0 license Open Access Published by De Gruyter January 1, 2007

On Parallel Numerical Algorithms for Simulating Industrial Filtration Problems

  • R. Čiegis EMAIL logo , O. Iliev and Z. Lakdawala


The performance of oil filters used in the automotive industry can be significantly improved, especially when computer simulation is an essential component of the design process. In this paper, we consider parallel numerical algorithms for solving mathematical models describing the process of filtration, filtering solid particles out of liquid oil. The Navier — Stokes — Brinkmann system of equations is used to describe the laminar flow of incompressible isothermal oil. The space discretization in the complicated filter geometry is based on the finite-volume method. Special care is taken for an accurate approximation of the velocity and pressure on the interface between the fluid and the porous media. The time discretization used here is a proper modification of the fractional time step discretization (cf. Chorin scheme) of the Navier- Stokes equations, where the Brinkmann term is considered in both the prediction and the correction substeps. A data decomposition method is used to develop a parallel algorithm, where the domain is distributed among the processors by using a structured reference grid. The MPI library is used to implement the data communication part of the algorithm. A theoretical model is proposed for the estimation of the complexity of the given parallel algorithm and a scalability analysis is done on the basis of this model. The results of the computational experiments are presented, and the accuracy and efficiency of the parallel algorithm is tested on real industrial geometries.

Received: 2007-04-25
Revised: 2007-05-26
Accepted: 2007-06-21
Published Online: 2007
Published in Print: 2007

© Institute of Mathematics, NAS of Belarus

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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