weno tests

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!