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

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

Journal Article · Mon Mar 28 00:00:00 EDT 2016 · International Journal for Numerical Methods in Fluids

DOI:https://doi.org/10.1002/fld.4235· OSTI ID:1533176

Gao, X. ^[1]; Owen, L. D. ^[2]; Guzik, S. M. J. ^[2]

Colorado State Univ., Fort Collins, CO (United States); DOE/OSTI
Colorado State Univ., Fort Collins, CO (United States)

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.

View Accepted Manuscript (DOE)

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

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

Grant/Contract Number:: EE0006086

OSTI ID:: 1533176

Journal Information:: International Journal for Numerical Methods in Fluids, Journal Name: International Journal for Numerical Methods in Fluids Journal Issue: 10 Vol. 82; ISSN 0271-2091

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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Correction: A Fourth-Order Finite-Volume Method with Adaptive Mesh Refinement for the Multifluid Plasma Model Polak, Scott; Gao, Xinfeng 2018 AIAA Aerospace Sciences Meeting, 2018 AIAA Aerospace Sciences Meeting https://doi.org/10.2514/6.2018-2195.c1	conference	January 2018

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

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