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WENO Tests Z.G. Xiong

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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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Page 1: WENO Tests

WENO Tests

Z.G. Xiong

Page 2: WENO Tests

• Fundamental Principle

• WENO Tests Weighted Essentially Non-Oscillatory

Page 3: WENO Tests

Fundamental Principle

• HD Equations(Euler Equations):

0)()2

(

0

0

2

vPv

edt

d

Pdt

vd

vdt

d

Page 4: WENO Tests

• Governing Equations (Conservation Equations):

Page 5: WENO Tests

• Discrete Methods:

• finite difference

Page 6: WENO Tests

• Shock Treatment :

• Shock Capture

Page 7: WENO Tests

• WENO History:

• TVD(TVB)—ENO—WENO

Page 8: WENO Tests

• WENO Technology:• space discretization:

Page 9: WENO Tests

• flux splitting:

Page 10: WENO Tests

• Time discretization:

Runge-Kutta method

Page 11: WENO Tests

• Time step:

Page 12: WENO Tests

WENO Tests

• Shock Tube Tests • Problem:

ρ1= 1.5p1= 1.0

ρ2= 1.0p2= 0.2

Page 13: WENO Tests

• Simulation:

Grid: 64

polytropic index : 1.4

movie:

comparison:

(Feng et al, 2004)

Page 14: WENO Tests

• Sedov Tests• Problem: E0

ρ0

Page 15: WENO Tests

• analytic solution (Landau & Lifshitz):

shock evolution:

15.1,3/5

)/( 510

20

tERs

Page 16: WENO Tests

• physical quantity profile:

Density profile:

Page 17: WENO Tests

• Simulation:

initial condition:

boundary condition:

equivalent extrapolation

grid: 128 x128 x128

0

0

100.2

10

0

0

3240

510

p

v

cmg

ergE

Page 18: WENO Tests

• Results: 1. shock evolution

movie:

a. xyz system

b. rθφ system

Page 19: WENO Tests

evolution law:

a. xyz system

b. rθφ system

Page 20: WENO Tests

2. density profile:

simulation result:

Page 21: WENO Tests

simulation result vs analytic result:

Page 22: WENO Tests

• New problem:

• Smoothing technique

Page 23: WENO Tests

• Thank You!