A Global Preconditioning Method for the Euler Equations
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| Titel: | A Global Preconditioning Method for the Euler Equations |
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| Autoren: | Yildirim, B. Gazi |
| Quelle: | Theses and Dissertations |
| Verlagsinformationen: | Scholars Junction |
| Publikationsjahr: | 2003 |
| Schlagwörter: | Newton formulation, Characteristic variable boundary conditions, flux difference splitting, euler equations, preconditioning |
| Beschreibung: | This study seeks to validate a recently introduced global preconditioning technique for the Euler equations. Energy and enthalpy equations are nondimensionalized by means of a reference enthalpy, resulting in increased numerical accuracy for low-speed flows. A cellbased, finite volume formulation is used, with Roe flux difference splitting and both explicit and implicit time integration schemes. A Newton-linearized iterative implicit algorithm is implemented, with Symmetric Gauss-Seidel (LU/SGS) nested sub-iterations. This choice allows one to retain time accuracy, and eliminates approximate factorization errors, which become dominant at low speed flows. The linearized flux Jacobians are evaluated by numerical differentiation. Higher-order discretization is constructed by means of the MUSCL approach. Locally one-dimensional characteristic variable boundary conditions are implemented at the farfield boundary. The preconditioned scheme is successfully applied to the following traditional test cases used as benchmarks for local preconditioning techniques: point disturbance, flow angle disturbance, and stagnation point arising from the impingement of two identical jets. The flow over a symmetric airfoil and a convergentdivergent nozzle are then simulated for arbitrary Mach numbers. The preconditioned scheme greatly enhances accuracy and convergence rate for low-speed flows (all the way down to M ≈ 10E − 4). Some preliminary tests of fully unsteady flows are also conducted. |
| Publikationsart: | text |
| Dateibeschreibung: | application/pdf |
| Sprache: | unknown |
| Relation: | https://scholarsjunction.msstate.edu/td/150; https://scholarsjunction.msstate.edu/context/td/article/1149/viewcontent/etd_07152003_164237.pdf |
| Verfügbarkeit: | https://scholarsjunction.msstate.edu/td/150 https://scholarsjunction.msstate.edu/context/td/article/1149/viewcontent/etd_07152003_164237.pdf |
| Dokumentencode: | edsbas.8F42C341 |
| Datenbank: | BASE |
Nájsť tento článok vo Web of Science | Abstract: | This study seeks to validate a recently introduced global preconditioning technique for the Euler equations. Energy and enthalpy equations are nondimensionalized by means of a reference enthalpy, resulting in increased numerical accuracy for low-speed flows. A cellbased, finite volume formulation is used, with Roe flux difference splitting and both explicit and implicit time integration schemes. A Newton-linearized iterative implicit algorithm is implemented, with Symmetric Gauss-Seidel (LU/SGS) nested sub-iterations. This choice allows one to retain time accuracy, and eliminates approximate factorization errors, which become dominant at low speed flows. The linearized flux Jacobians are evaluated by numerical differentiation. Higher-order discretization is constructed by means of the MUSCL approach. Locally one-dimensional characteristic variable boundary conditions are implemented at the farfield boundary. The preconditioned scheme is successfully applied to the following traditional test cases used as benchmarks for local preconditioning techniques: point disturbance, flow angle disturbance, and stagnation point arising from the impingement of two identical jets. The flow over a symmetric airfoil and a convergentdivergent nozzle are then simulated for arbitrary Mach numbers. The preconditioned scheme greatly enhances accuracy and convergence rate for low-speed flows (all the way down to M ≈ 10E − 4). Some preliminary tests of fully unsteady flows are also conducted. |
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