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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: - PowerPoint PPT Presentation
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WENO Tests
Z.G. Xiong
• Fundamental Principle
• WENO Tests Weighted Essentially Non-Oscillatory
Fundamental Principle
• HD Equations(Euler Equations):
0)()2
(
0
0
2
vPv
edt
d
Pdt
vd
vdt
d
• Governing Equations (Conservation Equations):
• Discrete Methods:
• finite difference
• Shock Treatment :
• Shock Capture
• WENO History:
• TVD(TVB)—ENO—WENO
• WENO Technology:• space discretization:
• flux splitting:
• Time discretization:
Runge-Kutta method
• Time step:
WENO Tests
• Shock Tube Tests • Problem:
ρ1= 1.5p1= 1.0
ρ2= 1.0p2= 0.2
• Simulation:
Grid: 64
polytropic index : 1.4
movie:
comparison:
(Feng et al, 2004)
• Sedov Tests• Problem: E0
ρ0
• analytic solution (Landau & Lifshitz):
shock evolution:
15.1,3/5
)/( 510
20
tERs
• physical quantity profile:
Density profile:
• Simulation:
initial condition:
boundary condition:
equivalent extrapolation
grid: 128 x128 x128
0
0
100.2
10
0
0
3240
510
p
v
cmg
ergE
• Results: 1. shock evolution
movie:
a. xyz system
b. rθφ system
evolution law:
a. xyz system
b. rθφ system
2. density profile:
simulation result:
simulation result vs analytic result:
• New problem:
• Smoothing technique
• Thank You!