Author
Harland M. Glaz
Other affiliations: White Oak Conservation, Silver Spring Networks
Bio: Harland M. Glaz is an academic researcher from University of Maryland, College Park. The author has contributed to research in topics: Godunov's scheme & Inviscid flow. The author has an hindex of 15, co-authored 36 publications receiving 2574 citations. Previous affiliations of Harland M. Glaz include White Oak Conservation & Silver Spring Networks.
Papers
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TL;DR: In this paper, a second-order projection method for the Navier-Stokes equations is proposed, which uses a specialized higher-order Godunov method for differencing the nonlinear convective terms.
1,287 citations
TL;DR: A procedure for constructing solutions to the Riemann problem for gas dynamics with a general convex equation of state is given in this paper, where approximate procedures involving a local parametrization of the EO of state are introduced in order to calculate numerical fluxes in conservative finite difference schemes.
569 citations
TL;DR: The Riemann problem for two-dimensional gas dynamics with isentropic or polytropic gas is considered and the required relations for the initial data and the symmetry properties of the solutions are given.
Abstract: The Riemann problem for two-dimensional gas dynamics with isentropic or polytropic gas is considered. The initial data is constant in each quadrant and chosen so that only a rarefaction wave, shock wave, or slip line connects two neighboring constant initial states. With this restriction sixteen (respectively, fifteen) genuinely different wave combinations for isentropic (respectively, polytropic) gas exist. For each configuration the numerical solution is analyzed and illustrated by contour plots. Additionally, the required relations for the initial data and the symmetry properties of the solutions are given. The chosen calculations correspond closely to the cases studied by T. Zhang and Y. Zheng [SIAM J. Math. Anal., 21 (1990), pp. 593–630], so that the analytical theory can be directly compared to our numerical study.
355 citations
TL;DR: In this paper, a direct comparison is made for several occurrences of oblique shock-wave reflections between interferometric results obtained at the University of Toronto Institute for Aerospace Studies (UTIAS) 10 cm x 18 cm hypervelocity shock tube and numerical results obtained by using a current computational method for solving the Euler equations.
Abstract: A direct comparison is made for several occurrences of oblique shock-wave reflections between interferometric results obtained at the University of Toronto Institute for Aerospace Studies (UTIAS) 10 cm x 18 cm hypervelocity shock tube and numerical results obtained by using a current computational method for solving the Euler equations. Very good qualitative agreement is obtained for equilibrium and frozen flow fields except in small regions where the experiments were dominated by viscous flow. The quantitative agreement is very close in some cases but can be out by 10-15% in cases with non-equilibrium flow or viscous structures or both. Additional parametrized sequences of calculations are presented to assess the utility of the present numerical method in constructing the various reflection- transition lines for perfect inviscid flows in the shock-wave Mach number, wedge-angle ($M\_s, \theta\_w$)-plane, and the validity of the `boundary- layer defect' theory.
102 citations
TL;DR: In this article, the complicated local interactions of nonlinear waves are resolved through asymptotic analysis and this is then used to construct a random choice method to calculate general unsteady flowfields.
71 citations
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Book•
01 Jan 2002TL;DR: The CLAWPACK software as discussed by the authors is a popular tool for solving high-resolution hyperbolic problems with conservation laws and conservation laws of nonlinear scalar scalar conservation laws.
Abstract: Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.
5,791 citations
TL;DR: This work recognizes the need for additional dissipation in any higher-order Godunov method of this type, and introduces it in such a way so as not to degrade the quality of the results.
3,892 citations
3,822 citations
TL;DR: An automatic, adaptive mesh refinement strategy for solving hyperbolic conservation laws in two dimensions and how to organize the algorithm to minimize memory and CPU overhead is developed.
2,650 citations
TL;DR: The first version of a new-generation simulation code, FLASH, solves the fully compressible, reactive hydrodynamic equations and allows for the use of adaptive mesh refinement and contains state-of-the-art modules for the equations of state and thermonuclear reaction networks.
Abstract: We report on the completion of the first version of a new-generation simulation code, FLASH. The FLASH code solves the fully compressible, reactive hydrodynamic equations and allows for the use of adaptive mesh refinement. It also contains state-of-the-art modules for the equations of state and thermonuclear reaction networks. The FLASH code was developed to study the problems of nuclear flashes on the surfaces of neutron stars and white dwarfs, as well as in the interior of white dwarfs. We expect, however, that the FLASH code will be useful for solving a wide variety of other problems. This first version of the code has been subjected to a large variety of test cases and is currently being used for production simulations of X-ray bursts, Rayleigh-Taylor and Richtmyer-Meshkov instabilities, and thermonuclear flame fronts. The FLASH code is portable and already runs on a wide variety of massively parallel machines, including some of the largest machines now extant.
2,319 citations