Multigrid pressure solver for proppant transport modelling in hydraulic fracturing simulators

A. A. Osiptsov, S. A. Boronin, E. A. Muravleva

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    1 Citation (Scopus)

    Abstract

    The multigrid method in the form of MGCS V-cycles with matrix-dependent prolongations is implemented for solving linear equations resulting from a standard discretization of a 2D elliptic equation (5-point "cross" stencil). Simplicity of input data allows incorporation of the solver into any relevant commercial or research code. The performance of MGCS is compared against other iterative (in-house BiCGStab preconditioned by ILU(2) factorization, PyAMG) and direct (DSS from Intel MKL library) solvers. The following performance tests are considered: 1) synthetically-generated matrices with large contrast in elements; 2) matrices formed during simulations of multiphase flows in hydraulic fractures/slots with large viscosity contrast (up to 106). Dependence of the performance of MGCS on the number of smoothing iterations at each mesh level and aspect ratio of mesh cells is studied. It is found that the best performance is gained by MGCS V-cycles with a single smoothing iteration per mesh level on meshes with square cells. Increasing the aspect ratio of the mesh cells and increasing the number of smoothing iterations per mesh level typically slows down the convergence rate. The MGCS code shows the best performance as compared to other solvers tested. The speed-up increases significantly with an increase in the mesh resolution.

    Original languageEnglish
    Title of host publication3rd EAGE Workshop on High Performance Computing for Upstream 2017
    PublisherEuropean Association of Geoscientists and Engineers, EAGE
    Pages74-78
    Number of pages5
    ISBN (Electronic)9781510850828
    DOIs
    Publication statusPublished - 2017
    Event3rd EAGE Workshop on High Performance Computing for Upstream 2017 - Athens, Greece
    Duration: 1 Oct 20174 Oct 2017

    Publication series

    Name3rd EAGE Workshop on High Performance Computing for Upstream 2017

    Conference

    Conference3rd EAGE Workshop on High Performance Computing for Upstream 2017
    Country/TerritoryGreece
    CityAthens
    Period1/10/174/10/17

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