Development of Godunov CMoC-CT Code

Code Test12: MHD KELVIN-HELMHOLTZ INSTABILITY (c.f., Frank et al.1996)
See the J,Stone's web page as a reference of MHD Kelvin-Helmholtz Test

t = 1.0 t = 2.5 t = 5.0




Code Test11 : MHD RAYLEIGH-TAYLOR INSTABILITY (c.f., Jun et al.1995)
See the J,Stone's web page as a reference of MHD Rayleigh-Taylor Test

t = 4.5 t = 9.0 t = 12.5




    Following analyses refer to Jin et al. 1995

    Growth rates in Linear, HD and MHD cases Growth rates in the case Bx = 0.06 Growth rates in the case Bx = 0.065 Growth rates in the case Bx = 0.07





Code Test10 : PROPAGATION OF TWO DIMENSIONAL SHEAR ALFVEN WAVE (c.f., Clarke et al.1996)
    Domain : 0 < x < 200, 0 < y < 200 (200 × 200 grid)
    Density: Uniform (&rho = 1.0)
    Pressure: Uniform (P = 3.0/5.0)
    Magnetic Field : Bx = By = 2 1/2 , Bz = 0.0
    Initial Speeds : Vx = 0.0, Vy = 0.0, Vz = 0.001 for x2 + y2 < 100.0,Vz = 0.0 for x2 + y2 > 100.0,
    Specific Heat: &gamma = 5/3

    Vz @t = 0.5 vz @t = 2.5 Vz @t = 7.5 vz @t = 12.5





Code Test9 : PROPAGATION OF SHEAR ALFVEN WAVE (c.f., Clarke et al.1996)
    Domain : 0.0 < x < 3.0 (150 grid)
    Density: Uniform (&rho = 1.0)
    Pressure: Uniform (P = 1.0)
    Magnetic Field : Bx = 1.0, By = 0.0, Bz = 0.0
    Initial Speeds : Vx = 0.0, Vy = 0.001, Vz = 0.0
    Specific Heat: &gamma = 2.0

    Vy @t = 0.75 By @t = 0.75



Code Test8 : MHD SHOCK TUBE PROBLEM (c.f., Brio&Wu1988)


    Density Pressure X-Velocity Y-Velocity By-Magnetic Field




Code Test7 : KELVIN-HELMHOLTZ INSTABILITY (c.f., Frank et al.1996)
See the J,Stone's web page as a reference of Kelvin-Helmholtz Instability's Test
    Domain : |x| < 0.5, |y| < 0.5
    BC : Periodic everywhere
    Initial Velocity & Density : Vx = 0.5, &rho = 1 for |y| > 0.25, Vx = - 0.5, &rho = 2 for |y| < 0.25
    Initial Pressure & Specific Heat: P = 2.5, &gamma =1.4 everywhere
    Perturbation : &deltaVx,&deltaVy = 0.01&alpha; where "&alpha" is the random number between 0 and 1.

    Random number "&alpha" is given by the following simple way;
    Function &alpha(dumy)
    Integer &psi,X,M
    Save X
    Data X/759375/
    Data &psi/15/
    Data M/1000001/
    X = mod(&psi*X,M)
    &alpha = X/float(M)
    return
    end

t = 1.0 t = 2.5 t = 5.0 Stone's result (t = 1.0)




Code Test6 : RAYLEIGH-TAYLOR INSTABILITY
(c.f., Jun et al.1995 & S. Chandrasekhar, "Hydrodynamic and Hydromagnetic Stability")
See the J,Stone's web page as a reference of Rayleigh-Taylor Instability's Test
    Multi Mode Perturbation
    Domain : |x| < 0.25, |y| < 0.35
    BC : Periodic @ |x| = 0.25, Mirror @ |y| = 0.35
    Density: &rho = 2 for y > 0; &rho = 1 for y < 0
    Gravity : g = - 0.1
    Pressure & Specific Heat: Hydrostatic Equilibrium [P = 2.5 - 0.1y&rho], &gamma = 1.4
    Perturbation: Vy = 0.01&alpha [1 + cos(8&piy/3)]/2 where " &alpha " is the random number between 0 and 1.

    Random number "&alpha" is given by the following simple way;
    Function &alpha(dumy)
    Integer &psi,X,M
    Save X
    Data X/759375/
    Data &psi/15/
    Data M/1000001/
    X = mod(&psi*X,M)
    &alpha = X/float(M)
    return
    end

t = 4.5 t = 9.0 t = 12.5 Stone's result




    Single Mode Perturbation
    Domain : |x| < 0.25,|y| < 0.75
    BC : Periodic@ |x| = 0.25, Mirror@ |x| = 0.75
    Density : &rho = 2 for y > 0; &rho = 1 for y < 0
    Gravity : g = g0 = - 0.1
    Pressure & Specific Heat: Hydrostatic Equilibrium [P = 2.5 - 0.1y&rho, &gamma = 1.4 ]
    Perturbation : Vy = 0.01[1 + cos(4&pix)][1 + cos(3&piy)]/4

    Following analyses refer to Jin et al. 1995
    Growth rates of a single mode perturbation (Dashed-lines represent linear growth rate, solid and dotted lines are nonlinear one) Low Resolution Result (x,y)=(100,300) @ t = 12.75 High Resolution Result (x,y)=(200,600) @ t = 12.75




TEST FOR "KINEMATIC VISCOSITY" AND "BODY FORCE"

Code Test5 : HYDROSTATIC EQUIRIBLIUM Code Test4 : VISCOUS DIFFUSION (Compressible Navier-Stokes Equation)
FUNDAMENTAL HYDRODYNAMIC CODE TEST

Code Test3 : TWO INTERACTING BLAST WAVES (Ref., Woodward&Colella1984)
Code Test2 : 2-D SHOCK TUBE PROBLEM - DIAGONAL SHOCK -
Code Test1 : 1-D SHOCK TUBE PROBLEM - SOD's PROBLEM -
  • Reference
    Updated 22, March 2007