Parallel simulations for a 2D x/z two-phase flow fluid-solid particle model

•A parallel algorithm for a 2D x/z two-phase Eulerian approach is presented.•The numerical scheme is based on a projection technique and a finite volume method.•The parallelization is designed using block domain decomposition.•Convergence of the SOR method and the Bi-CGSTAB method are compared.•The...

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Vydáno v:	Computers & fluids Ročník 173; s. 103 - 110
Hlavní autoři:	Uh Zapata, M., Pham Van Bang, D., Nguyen, K.D.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier Ltd 15.09.2018 Elsevier BV
Témata:	Algorithms Beds Bi-CGSTAB Coloring Computer simulation Distributed memory Domain decomposition Domain decomposition methods Erosion Hydraulic jets Mathematical models Message passing MPI Numerical methods Parallel processing Particle interactions Sediment erosion Sediment transport Sediments Simulation SOR Two dimensional flow Two dimensional models Two phase flow Bi-CGSTAB Sediment erosion Two-phase flow Domain decomposition MPI SOR
ISSN:	0045-7930, 1879-0747
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Abstract	•A parallel algorithm for a 2D x/z two-phase Eulerian approach is presented.•The numerical scheme is based on a projection technique and a finite volume method.•The parallelization is designed using block domain decomposition.•Convergence of the SOR method and the Bi-CGSTAB method are compared.•The erosion of granular beds is adopted to verify the algorithm performance. The importance of the two-phase flow model relies upon the correct simulation of specific problems in which the passive tracer model fails; however, the mathematical and numerical models need to be improved in order to reproduce fluid-solid particle interactions of greater complexity. Such is the case with regard to simulating erosion patterns suffered upon horizontal granular beds by means of a vertical water jet as shown here. Moreover, sequential platforms have proven to be insufficient in providing the required computational power needed to obtain fast and detailed simulations. In this paper, a fully parallel algorithm for a two-dimensional x/z two-phase Eulerian approach is presented and applied for the numerical solution of the erosion of sediment beds. The parallelization is designed by a row and column block domain decomposition technique using a distributed memory platform with Message Passing Interface (MPI). Arising from the numerical method, a Poisson problem for the pressure is solved at each time step. The discretization results in a non-symmetric variable-coefficient linear system which is solved using several parallel Successive Over-Relaxation (SOR) algorithms, including partitioning and coloring methods. The specification of the optimal relaxation parameter to achieve efficiency is found numerically. Results show that SOR methods achieve faster convergence rates and the simulation time achieves an order similar to that required for the typical, widely-used Bi-Conjugate Gradient Stabilized (Bi-CGSTAB) method. The performances of the algorithms are evaluated in terms of speedup and efficiency. The results indicate that the parallel code significantly improves the results of the sequential calculation in general.
AbstractList	The importance of the two-phase flow model relies upon the correct simulation of specific problems in which the passive tracer model fails; however, the mathematical and numerical models need to be improved in order to reproduce fluid-solid particle interactions of greater complexity. Such is the case with regard to simulating erosion patterns suffered upon horizontal granular beds by means of a vertical water jet as shown here. Moreover, sequential platforms have proven to be insufficient in providing the required computational power needed to obtain fast and detailed simulations. In this paper, a fully parallel algorithm for a two-dimensional x/z two-phase Eulerian approach is presented and applied for the numerical solution of the erosion of sediment beds. The parallelization is designed by a row and column block domain decomposition technique using a distributed memory platform with Message Passing Interface (MPI). Arising from the numerical method, a Poisson problem for the pressure is solved at each time step. The discretization results in a non-symmetric variable-coefficient linear system which is solved using several parallel Successive Over-Relaxation (SOR) algorithms, including partitioning and coloring methods. The specification of the optimal relaxation parameter to achieve efficiency is found numerically. Results show that SOR methods achieve faster convergence rates and the simulation time achieves an order similar to that required for the typical, widely-used Bi-Conjugate Gradient Stabilized (Bi-CGSTAB) method. The performances of the algorithms are evaluated in terms of speedup and efficiency. The results indicate that the parallel code significantly improves the results of the sequential calculation in general. •A parallel algorithm for a 2D x/z two-phase Eulerian approach is presented.•The numerical scheme is based on a projection technique and a finite volume method.•The parallelization is designed using block domain decomposition.•Convergence of the SOR method and the Bi-CGSTAB method are compared.•The erosion of granular beds is adopted to verify the algorithm performance. The importance of the two-phase flow model relies upon the correct simulation of specific problems in which the passive tracer model fails; however, the mathematical and numerical models need to be improved in order to reproduce fluid-solid particle interactions of greater complexity. Such is the case with regard to simulating erosion patterns suffered upon horizontal granular beds by means of a vertical water jet as shown here. Moreover, sequential platforms have proven to be insufficient in providing the required computational power needed to obtain fast and detailed simulations. In this paper, a fully parallel algorithm for a two-dimensional x/z two-phase Eulerian approach is presented and applied for the numerical solution of the erosion of sediment beds. The parallelization is designed by a row and column block domain decomposition technique using a distributed memory platform with Message Passing Interface (MPI). Arising from the numerical method, a Poisson problem for the pressure is solved at each time step. The discretization results in a non-symmetric variable-coefficient linear system which is solved using several parallel Successive Over-Relaxation (SOR) algorithms, including partitioning and coloring methods. The specification of the optimal relaxation parameter to achieve efficiency is found numerically. Results show that SOR methods achieve faster convergence rates and the simulation time achieves an order similar to that required for the typical, widely-used Bi-Conjugate Gradient Stabilized (Bi-CGSTAB) method. The performances of the algorithms are evaluated in terms of speedup and efficiency. The results indicate that the parallel code significantly improves the results of the sequential calculation in general.
Author	Pham Van Bang, D. Uh Zapata, M. Nguyen, K.D.
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Cites_doi	10.1063/1.4863989 10.1016/j.proeng.2013.07.106 10.1017/S002211207200120X 10.1016/j.advwatres.2009.04.001 10.1007/BF00951252 10.1090/S0025-5718-1968-0242392-2 10.13031/2013.22686 10.1137/040604777 10.1016/j.powtec.2013.02.017 10.1137/0913035 10.1016/j.advwatres.2012.03.009 10.1017/S0022112007008567 10.1061/(ASCE)0893-1321(2009)22:1(24) 10.1016/0032-5910(89)80008-7 10.1016/j.jcp.2012.02.023 10.1007/s11431-010-4165-3
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Snippet	•A parallel algorithm for a 2D x/z two-phase Eulerian approach is presented.•The numerical scheme is based on a projection technique and a finite volume... The importance of the two-phase flow model relies upon the correct simulation of specific problems in which the passive tracer model fails; however, the...
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SubjectTerms	Algorithms Beds Bi-CGSTAB Coloring Computer simulation Distributed memory Domain decomposition Domain decomposition methods Erosion Hydraulic jets Mathematical models Message passing MPI Numerical methods Parallel processing Particle interactions Sediment erosion Sediment transport Sediments Simulation SOR Two dimensional flow Two dimensional models Two phase flow
Title	Parallel simulations for a 2D x/z two-phase flow fluid-solid particle model
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