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An Implicit High-Order Spectral Difference Method for the Compressible Navier-Stokes Equations Using Adaptive Polynomial Refinement

Barnes, Caleb J.
http://rave.ohiolink.edu/etdc/view?acc_num=wright1315591802

Abstract Details

2011, Master of Science in Engineering (MSEgr), Wright State University, Mechanical Engineering.
A high/variable-order numerical simulation procedure for gas dynamics problems was developed to model steep grading physical phenomena. Higher order resolution was achieved using an orthogonal polynomial Gauss-Lobatto grid, adaptive polynomial refinement and artificial diffusion activated by a pressure switch. The method is designed to be computationally stable, accurate, and capable of resolving discontinuities and steep gradients without the use of one-sided reconstructions or reducing to low-order. Solutions to several benchmark gas-dynamics problems were produced including a shock-tube and a shock-entropy wave interaction. The scheme's 1st-order solution was validated in comparison to a 1st-order Roe scheme solution. Higher-order solutions were shown to approach reference values for each problem. Uniform polynomial refinement was shown to be capable of producing increasingly accurate solutions on a very coarse mesh. Adaptive polynomial refinement was employed to selectively refine the solution near steep gradient structures and results were nearly identical to those produced by uniform polynomial refinement. Future work will focus on improvements to the diffusion term, complete extensions to the full compressible Navier-Stokes equations, and multi-dimension formulations.
George Huang, PhD (Advisor)
George Huang, PhD (Committee Member)
Joseph Shang, PhD (Committee Member)
Miguel Visbal, PhD (Committee Member)
114 p.
Fluid Dynamics; Mechanical Engineering
high-order; spectral difference; CFD; computational fluid dynamics; Euler equations; Euler; gas dynamics; polynomial refinement; adaptive polynomial refinement; artificial dissipation

Recommended Citations

Citations

  • Barnes, C. J. (2011). An Implicit High-Order Spectral Difference Method for the Compressible Navier-Stokes Equations Using Adaptive Polynomial Refinement [Master's thesis, Wright State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=wright1315591802

    APA Style (7th edition)

  • Barnes, Caleb. An Implicit High-Order Spectral Difference Method for the Compressible Navier-Stokes Equations Using Adaptive Polynomial Refinement. 2011. Wright State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=wright1315591802.

    MLA Style (8th edition)

  • Barnes, Caleb. "An Implicit High-Order Spectral Difference Method for the Compressible Navier-Stokes Equations Using Adaptive Polynomial Refinement." Master's thesis, Wright State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=wright1315591802

    Chicago Manual of Style (17th edition)

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© 2011, all rights reserved.
This open access ETD is published by Wright State University and OhioLINK.