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WENO Tests

WENO Tests. Z.G. Xiong. Fundamental Principle WENO Tests Weighted Essentially Non-Oscillatory. Fundamental Principle. HD Equations(Euler Equations ):. Governing Equations (Conservation Equations):. Discrete Methods: finite difference. Shock Treatment : Shock Capture. WENO History:

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WENO Tests

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  1. WENO Tests Z.G. Xiong

  2. Fundamental Principle • WENO Tests Weighted Essentially Non-Oscillatory

  3. Fundamental Principle • HD Equations(Euler Equations):

  4. Governing Equations (Conservation Equations):

  5. Discrete Methods: • finite difference

  6. Shock Treatment : • Shock Capture

  7. WENO History: • TVD(TVB)—ENO—WENO

  8. WENO Technology: • space discretization:

  9. flux splitting:

  10. Time discretization: Runge-Kutta method

  11. Time step:

  12. WENO Tests • Shock Tube Tests • Problem: ρ1= 1.5 p1= 1.0 ρ2= 1.0 p2= 0.2

  13. Simulation: Grid: 64 polytropic index : 1.4 movie: comparison: (Feng et al, 2004)

  14. Sedov Tests • Problem: E0 ρ0

  15. analytic solution (Landau & Lifshitz): shock evolution:

  16. physical quantity profile: Density profile:

  17. Simulation: initial condition: boundary condition: equivalent extrapolation grid: 128 x128 x128

  18. Results: 1. shock evolution movie: a. xyz system b. rθφ system

  19. evolution law: a. xyz system b. rθφ system

  20. 2. density profile: simulation result:

  21. simulation result vs analytic result:

  22. New problem: • Smoothing technique

  23. Thank You!

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