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A Multigrid-Accelerated Three-Dimensional Transient-Flow Code and its Application to a New Test Problem

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Abstract

A multigrid-assisted solver for the three-dimensional time-dependent incompressible Navier-Stokes equations on graded Cartesian meshes is developed. The spatial accuracy is third-order for the convective terms and fourth-order for the viscous terms, and a fractional-step strategy ensures second-order time accuracy. To achieve good time-wise efficiency a multigrid technique is used to solve the highly time-consuming pressure-Poisson equation that requires to be solved at every time step. The speed-up achieved by multigrid is shown in tabular form. The performance and accuracy of the code are first ascertained by computing the flow in a single-sided lid-driven cubic cavity with good grid-economy and comparing the results available in the literature. The code, thus validated, is then applied to a new test problem we propose and various transient and asymptotically obtained steady-state results are presented. Given the care taken to establish the credibility of the code and the good spatio-temporal accuracy of the discretization, these results are accurate and may be used for ascertaining the performance of any computational algorithm applied to this test problem.

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Authors and Affiliations

  1. School of Mechanical and Building Science, Vellore Institute of Technology, Vellore, 632014, India

    D. Santhosh Kumar

  2. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, 781039, India

    Anoop K. Dass

  3. Department of Applied Mechanics, Indian Institute of Technology Delhi Hauz Khas, New Delhi, 110016, India

    Anupam Dewan

Authors
  1. D. Santhosh Kumar
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  2. Anoop K. Dass
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  3. Anupam Dewan
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Correspondence to Anupam Dewan.

Additional information

Biography: KUMAR D. Santhosh (1979-), Male, Ph. D., Associate Professor

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Kumar, D., Dass, A.K. & Dewan, A. A Multigrid-Accelerated Three-Dimensional Transient-Flow Code and its Application to a New Test Problem. J Hydrodyn 22, 838–846 (2010). https://doi.org/10.1016/S1001-6058(09)60124-4

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  • DOI: https://doi.org/10.1016/S1001-6058(09)60124-4

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