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Full-Text Articles in Physical Sciences and Mathematics
Upwind And Symmetric Shock- Capturing Schemes, H.C. Yee
Upwind And Symmetric Shock- Capturing Schemes, H.C. Yee
United States National Aeronautics and Space Administration: Publications
The development of numerical methods for hyperbolic conservation laws has been a rapidly growing area for the last ten years. Many of the fundamental concepts and state-of-the-art developments can only be found in meeting proceedings or internal reports. This review paper attempts to give an overview and a unified formulation of a class of shock-capturing methods. Special emphasis will be on the construction of the basic nonlinear scalar second-order schemes and the methods of extending these nonlinear scalar schemes to nonlinear systems via the exact Riemann solver, approximate Riemann solvers, and flux-vector splitting approaches. Generalization of these methods to efficiently …
Implicit Tvd Schemes For Hyperbolic Conservation Laws In Curvilinear Coordinates, Helen Yee, A. Harten
Implicit Tvd Schemes For Hyperbolic Conservation Laws In Curvilinear Coordinates, Helen Yee, A. Harten
United States National Aeronautics and Space Administration: Publications
A one-parameter family of explicit and implicit upwind second-order-accurate, total variation diminishing (TVD) schemes has been developed by Harten. These TVD schemes have the property of not generating spurious oscillations when applied to one-dimensional nonlinear scalar hyperbolic conservation laws and constant coefficient hyperbolic systems. The goal of this work is to extend these methods to the multidimensional hyperbolic conservation laws in curvilinear coordinates. Various ways of linearizing the implicit operator and solution strategies to improve the computation efficiency of the implicit algorithm are discussed. Numerical experiments with some AGARD test cases for steady-state airfoil calculations show that the proposed linearized …