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A Discontinuous Galerkin Chimera Overset Solver

Galbraith, Marshall C
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1384427339

Abstract Details

2013, PhD, University of Cincinnati, Engineering and Applied Science: Aerospace Engineering.
This work summarizes the development of an accurate, efficient, and flexible Computational Fluid Dynamics computer code that is an improvement relative to the state of the art. The improved accuracy and efficiency is obtained by using a high-order discontinuous Galerkin (DG) discretization scheme. In order to maximize the computational efficiency, quadrature-free integration and numerical integration optimized as matrix-vector multiplications is employed and implemented through a pre-processor (PyDG). Using the PyDG pre-processor, a C++ polynomial library has been developed that uses overloaded operators to design an efficient Domain Specific Language (DSL) that allows expressions involving polynomials to be written as if they are scalars. The DSL, which makes the syntax of computer code legible and intuitive, promotes maintainability of the software and simplifies the development of additional capabilities. The flexibility of the code is achieved by combining the DG scheme with the Chimera overset method. The Chimera overset method produces solutions on a set of overlapping grids that communicate through an exchange of data on grid boundaries (known as artificial boundaries). Finite volume and finite difference discretizations use fringe points, which are layers of points on the artificial boundaries, to maintain the interior stencil on artificial boundaries. The fringe points receive solution values interpolated from overset grids. Proper interpolation requires fringe points to be contained in overset grids. Insufficient overlap must be corrected by modifying the grid system. The Chimera scheme can also exclude regions of grids that lie outside the computational domain; a process commonly known as hole cutting. The Chimera overset method has traditionally enabled the use of high-order finite difference and finite volume approaches such as WENO and compact differencing schemes, which require structured meshes, for modeling fluid flow associated with complex geometries. The large stencil associated with these high-order schemes can significantly complicate the inter-grid communication and hole cutting processes. Unlike these high-order schemes, the DG method always retains a small stencil regardless of the order of approximation. The small stencil of the DG method simplifies the inter-grid communication scheme as well as hole cutting procedures. The DG-Chimera scheme does not require a separate interpolation method because the DG scheme represents the solution as cell local polynomials. Hence, the DG-Chimera method does not require fringe points to maintain the interior stencil across inter-grid boundaries. Thus, inter-grid communication can be established as long as the receiving boundary is enclosed by or abuts the donor mesh. This makes the inter-grid communication procedure applicable to both Chimera and zonal meshes. The small stencil implies hole cutting can be performed without regard to maintaining a minimum stencil and thereby greatly simplifies hole cutting. Hence, the DG-Chimera scheme has the potential to greatly simplify the overset grid generation process. Furthermore, the DG-Chimera scheme is capable of using curved cells to represent geometric features. The curved cells resolve issues associated with linear Chimera viscous meshes used for finite volume and finite difference schemes. Finally, the convergence rate of the Chimera schemes is dramatically increased by linearization of the inter-grid communication.
Paul Orkwis, Ph.D. (Committee Chair)
John A. Benek, Ph.D. (Committee Member)
Shaaban Abdallah, Ph.D. (Committee Member)
Mark Turner, Sc.D. (Committee Member)
355 p.
Aerospace Materials
Computational Fluid Dynamics; Discontinuous Galerkin; Chimera Method; High Order Methods

Recommended Citations

Citations

  • Galbraith, M. C. (2013). A Discontinuous Galerkin Chimera Overset Solver [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1384427339

    APA Style (7th edition)

  • Galbraith, Marshall. A Discontinuous Galerkin Chimera Overset Solver. 2013. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1384427339.

    MLA Style (8th edition)

  • Galbraith, Marshall. "A Discontinuous Galerkin Chimera Overset Solver." Doctoral dissertation, University of Cincinnati, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1384427339

    Chicago Manual of Style (17th edition)

ucin1384427339
649
© 2013, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.