A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations

Gao, X.; Owen, L. D.; Guzik, S. M.  J.

doi:10.1002/fld.4235

Title: A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations

Abstract

A fourth-order finite-volume method for solving the Navier–Stokes equations on a mapped grid with adaptive mesh refinement is proposed, implemented, and demonstrated for the prediction of unsteady compressible viscous flows. The method employs fourth-order quadrature rules for evaluating face-averaged fluxes. Our approach is freestream preserving, guaranteed by the way of computing the averages of the metric terms on the faces of cells. The standard Runge–Kutta marching method is used for time discretization. Solutions of a smooth flow are obtained in order to verify that the method is formally fourth-order accurate when applying the nonlinear viscous operators on mapped grids. Solutions of a shock tube problem are obtained to demonstrate the effectiveness of adaptive mesh refinement in resolving discontinuities. A Mach reflection problem is solved to demonstrate the mapped algorithm on a non-rectangular physical domain. The simulation is compared against experimental results. Future work will consider mapped multiblock grids for practical engineering geometries.

Authors:

Gao, X. ^[1]; Owen, L. D. ^[1]; Guzik, S. M. J. ^[1]

Colorado State Univ., Fort Collins, CO (United States)

Publication Date:: Mon Mar 28 00:00:00 EDT 2016

Research Org.:: Colorado State Univ., Fort Collins, CO (United States)

Sponsoring Org.:: USDOE Office of Energy Efficiency and Renewable Energy (EERE)

OSTI Identifier:: 1533176

Grant/Contract Number:: EE0006086

Resource Type:: Accepted Manuscript

Journal Name:: International Journal for Numerical Methods in Fluids

Additional Journal Information:: Journal Volume: 82; Journal Issue: 10; Journal ID: ISSN 0271-2091

Publisher:: Wiley

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Computer Science; Mathematics; Mechanics; Physics

Citation Formats


                    Gao, X., Owen, L. D., and Guzik, S. M.  J. A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations.  United States: N. p., 2016. 
Web.  doi:10.1002/fld.4235.

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                    Gao, X., Owen, L. D., & Guzik, S. M.  J. A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations.  United States.  https://doi.org/10.1002/fld.4235

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                    Gao, X., Owen, L. D., and Guzik, S. M.  J. Mon .  
"A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations".  United States.  https://doi.org/10.1002/fld.4235.  https://www.osti.gov/servlets/purl/1533176.

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@article{osti_1533176,

  title        = {A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations},

  author       = {Gao, X. and Owen, L. D. and Guzik, S. M.  J.},

  abstractNote = {A fourth-order finite-volume method for solving the Navier–Stokes equations on a mapped grid with adaptive mesh refinement is proposed, implemented, and demonstrated for the prediction of unsteady compressible viscous flows. The method employs fourth-order quadrature rules for evaluating face-averaged fluxes. Our approach is freestream preserving, guaranteed by the way of computing the averages of the metric terms on the faces of cells. The standard Runge–Kutta marching method is used for time discretization. Solutions of a smooth flow are obtained in order to verify that the method is formally fourth-order accurate when applying the nonlinear viscous operators on mapped grids. Solutions of a shock tube problem are obtained to demonstrate the effectiveness of adaptive mesh refinement in resolving discontinuities. A Mach reflection problem is solved to demonstrate the mapped algorithm on a non-rectangular physical domain. The simulation is compared against experimental results. Future work will consider mapped multiblock grids for practical engineering geometries.},

  doi          = {10.1002/fld.4235},

  journal      = {International Journal for Numerical Methods in Fluids},

  number       = 10,

  volume       = 82,

  place        = {United States},

  year         = {Mon Mar 28 00:00:00 EDT 2016},

  month        = {Mon Mar 28 00:00:00 EDT 2016}

}

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Works referencing / citing this record:

Correction: A Fourth-Order Finite-Volume Method with Adaptive Mesh Refinement for the Multifluid Plasma Model
conference, January 2018

Polak, Scott; Gao, Xinfeng
2018 AIAA Aerospace Sciences Meeting, 2018 AIAA Aerospace Sciences Meeting
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Title: A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations

Abstract

Citation Formats

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A cartesian grid embedded boundary method for the compressible Navier–Stokes equations
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Explicit and Implicit Multidimensional Compact High-Resolution Shock-Capturing Methods:Formulation
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