Low Mach Number Problem

Hydro Tests

K
EGR vs alpha
Summary Plot

K
EGR 1e19
Convective Cells

K
EGR 1e16
Convective Cells

K
EGR 1e17
Convective Cells

K
EGR 1e18
Convective Cells

K
200x386
5 cm/z w Correlation

K
200x386
MLT Flux Studies

K
200x386
5 cm/z w Correlation

N0-K
250x152
10 cm/z

N0-K
250x197
10 cm/z

2D stgd
125x102
20 cm/z

2D stgd
250x197
10 cm/z

2D stgd
302x302, 3xWide
CFL 0.5

2D stgd
200x386, 4xWide
CFL 0.5

2D stgd
540x194, Deep/Wide
CFL 0.5

2D stgd
200x194, DOUBLE WIDE
CFL 0.5

2D stgd
200x98, 5.0 cm/z
CFL 0.5

2D stgd
200x52, 5.0 cm/z
Upwind C.T.

2D stgd
200x52, 5.0 cm/z
Momentum Avrg

2D stgd
400x102, 2.5 cm/z
Momentum Avrg

2D stgd
100x26, 10.0 cm/z
-Div(RhoVel)

2D stgd
200x102, 5.0 cm/z
-Div(RhoVel)

2D stgd
400x102, 2.5 cm/z
-Div(RhoVel)

2D stgd
200x52
-Div(RhoVel)

2D stgd
200x52
-Div(RhoVel)

2D stgd
500x52
-Div(RhoVel)

2D stgd
500x52
conservative rhoX

2D stgd
500x52
RHS Mean Subtract

1D BURST
2D Mode

1D stgd
540x52
Thermal-diffusional

K, 2D stgd
520x52
Temp EQ
Non-Conservative X

K, 2D stgd
120x52
Temp EQ
Non-Conservative X

K vs No-K, 2D stgd
520x52
Continutiy EQ
Conservative rhoX

K vs No-K, 2D stgd
520x52
Analytic drhodt EQ
Conservative rhoX

K, 2D stgd
520x52
Continutiy EQ
Conservative rhoX

K, 2D stgd
520x52
Conservative rhoX

K, 2D stgd
520x52
Temp flux up b.c.
w zero
He4/C12 separate

K, 2D stgd
500x52
All fixed up b.c.

K, 2D stgd
540x52
Flux Temp Grad b.c.

K, 2D stgd
540,580 x 52,100
All Fixed b.c.

K, 2D stgd
540,580 x 52,100
Fixed Temp b.c.

K, 2D stgd
540x52
Global Pert

K, 2D stgd
580x52
Global Pert

K, 2D stgd
540x52
Local Pert

New delta corrected
520x8
New agrees with old

1D Staggered
K, 1D
540x8
No flux extrap

1D Staggered
K, 1D
540x1

2D Staggered
K, 2D
540x102
Local Pert

2D Staggered
K, 1D
520x10

2D Staggered
K, 2D
580x102
Local Pertbn

2D Staggered
K, 2D
120x102
Local Pertbn

2D Staggered
K, 2D
580x102
New Delta

2D Staggered
K, 2D
120x102
New Delta

2D Staggered
K, 2D
580x52,102
New Delta

2D Staggered
K, 2D
580x27
Temp Advect Switch

2D Staggered
K, 2D
580x82
Temp Advect Switch

2D Staggered
K, 2D
580x102 higher domain

2D Staggered
K, 2D
520x102 wide domain

2D Staggered
K, 2D 26 wide domain
Vertical Slices

Negative temperature perturbation

Positive temperature perturbation

2D Staggered
K, 2D 26 wide domain
Perturbation placement study

1D Staggered
1D domain
Higher Initial Model
Thermo-Diffusional

2D Staggered
K, 2D domain widths
COLD Deep Initial Model
Analyt d(rho)/dt

3D Staggered
K, 3D
Analyt vs Numer d(rho)/dt
COLD Deep Initial Model

2D Staggered
K, 2D aspect ratio
COLD Deep Initial Model
Analyt d(rho)/dt

2D Staggered
K vs NO-K, 520x100
COLD Deep Initial Model
Analyt d(rho)/dt

2D Staggered
K, 520x50
COLD Deep Initial Model
Analyt d(rho)/dt

2D Staggered
K, 520x25
COLD Deep Initial Model
Analyt/Numer d(rho)/dt

2D Staggered
K vs No-K
COLD Deep Initial Model
d^2(rho vel)/d^2

2D Staggered
K vs No-K
COLD Deep Initial Model
Div[d(rho vel)/dt]

2D Staggered
K vs No-K
HOT Deep Initial Model

3D Staggered
CFL
HOT Deep Initial Model

3D Staggered
Dirichlet-Neumann-Periodic
HOT Deep Initial Model

3D Staggered
Dirichlet-Dirichlet-Periodic
Deeper Initial Model

2D Staggered
K, Hydra FISHPAK
Deeper Initial Model

1D BURST
thesis
no-K Tridiag

1D BURST
thesis
K Tridiag

1D
Diffusional-Thermal
Deep Initial Model

thesis

thesis

2D Staggered
K vs. No-K
Cool Initial Model

2D Staggered
No-K
FISHPAK

2D Staggered
Very Hot Model, 5 cm
FISHPAK vs. PETSc

3D Staggered
Very Hot Model, 5 cm
Artificial Adiabaticity

2D Staggered
"2D Psuedo-burst"
5 cm, Dirichlet-Neumann

3D Staggered
Conservative Composition
5 cm, Dirichlet-Neumann

3D Staggered
Momentum EQ b.c.
5 cm, Dirichlet-Neumann

3D Staggered
Perturbation
5 cm, Dirichlet-Neumann

3D Staggered
10.0 cm, 3D MPI(8)
Dirichlet-Neumann

3D Staggered
5.0 cm, 3D MPI(8)
Dirichlet-Neumann

3D Staggered
3D MPI(4)
Convective terms

3D Staggered
3D Serial vs. MPI
Convective terms

2D Staggered
Total He4 Test

2D Staggered
CFL = 0.01
1.25 cm/z

2D Staggered
CFL = 0.05
5 cm/z

2D Staggered
Frozen c_p (efficiency)
2.5 cm/z

2D Staggered
Small domains (Hydra)
2.5 cm/z

2D Staggered
MPI (NCSA)
2.5 cm/z

2D Staggered
2nd Order Upwinding
Constant He4 upper b.c.

2D Staggered
Constant He4 upper b.c.
2.5 cm/z

2D Staggered
Constant He4 upper b.c.
FISHPAK, Hydra

2D Staggered
Zero Velocity Lower b.c.
FISHPAK, Hydra

2D Staggered
WENO, FISHPAK, Hydra
Accretion Upper b.c.

2D Staggered
FISHPAK on Hydra
Accretion Upper b.c.

2D Staggered
FISHPAK on Hydra
Natural Flow Upper b.c.

2D Staggered
Accretion Upper b.c.
Top-Down, Dirichlet-Dirichlet, P'=0

2D Staggered
FISHPAK vs. PETSc
Top-Down, Dirichlet-Dirichlet, P'=0

2D Staggered
Top-Down, Dirichlet-Dirichlet, P'=0
Naturally Adiabatic

2D Staggered
Top-Down, Conserv, Periodic
5 cm/z, 100x100

2D Staggered
Conservative, Periodic
5 cm/z, 100x100

2D Staggered
Continuity Equation Residual
5 cm/z, 100x100

2D Staggered
Reflecting
5 cm/z, 101x100

2D Staggered
Convective Terms
5 cm/z, 100x100

2D Staggered
pre-3rd burst, 1.e17
5 cm/z, 100x100

2D Staggered
pre-3rd burst, 6.e15
10 cm/z

2D Staggered
pre-3rd burst, 3.e16
Uniform He4

2D Staggered
pre-3rd burst, 1.e17
VERY HOT MODEL

2D Staggered
pre-3rd burst, 3.e16
He4 Perturbation

2D Staggered
pre-3rd burst, 3.e16
Artificial Adiabaticity
Small domain

2D Staggered
pre-3rd burst, 6.e15
WENO comp advect
Small domain

2D Staggered
pre-3rd burst, 6.e15
Upwind comp advect
Small domain

2D Staggered
pre-3rd burst, 6.e15
Upwind comp advect

2D Staggered
pre-3rd burst, 6.e15
WENO comp advect

2D Staggered
pre-3rd burst, 1.e16
pre-3rd burst, 1.e15
pre-2nd burst, 1.e16

Initial Conditions
5 cm/z Diffusional-Thermal

2D Staggered
K bot-up
50x90 Domain,
Extrap b.c.

2D Staggered
K bot-up
50x100 Domain,
Extrap b.c.

2D Staggered
K bot-up
Small Domain,
Extrap upper b.c.

2D Staggered
K bot-up
Extrap upper b.c.

2D Staggered
K bot-up
Small Domain

2D Staggered
noK / K bot-up
50 cm sigma

2D Staggered
K NO perturbation
5 cm/z, dt=2.e-6

2D Staggered
K wide perturbation
5 cm/z, dt=2.e-6

2D Staggered
noK / K bot-up
5 cm/z, dt=2.e-6

2D Periodic Function TEST

2D Staggered
noK / K (bot-up, top-down)
5 cm/z, dt=2.e-6

Perturbations
no-K, 5 cm/z, dt=2.e-6

Perturbations
K, 5 cm/z, dt=2.e-6

1D BURST
K Predict-Corrector
5 cm/z Comparison, dt=2.e-6 vs 2.e-7

1D BURST
K
NO Predict-Corrector 5.00 cm/z, dt=2.e-6

1D BURST
K
Predict-Corrector 5.00 cm/z, dt=2.e-6

1D BURST
K Comparison
Predict-Correct vs. None 1.25 vs 5.00 cm/z, dt=2.e-7

1D BURST
Predictor-Corrector, K
1.25 vs 5.00 cm/z, dt=2.e-7

1D BURST
Predictor-Corrector, no-K
1.25 vs 5.00 cm/z, dt=2.e-7

1D BURST
Comparison no-K, K
analyt drdt, dt=2.e-7, smoothed no-K

1D BURST
No Smoothing
5 cm/z, dt=2.e-7, K

1D BURST
No Smoothing
5 cm/z, dt=2.e-7, no-K

1D BURST
Smoothing 0.5, 5 loops
5 cm/z, dt=2.e-7, no-K

1D BURST
Smoothing 0.5, 10 loops
dt=2.e-7, no-K

1D BURST
Smoothing 0.5, 5 loops
dt=2.e-7, no-K

1D BURST
Analytical d(rho)/dt
dt=2.e-7, K & no-K

1D BURST
Numerical d(rho)/dt
dt=2.e-7, K & no-K

Force, K vs. no-K
1.25 cm/z, staggered

d(rho)/dt Numer vs Analyt
5 cm/z, no-K, staggered

1D BURST
5 cm/z, no-K, staggered

1D BURST
1.25 cm/z, K & no-K, staggered

1D Convective
5 cm/z, Stagger Compare

1D Convective
1 cm/z, no-K, Staggered

1D Convective
no-K, Staggered, NRTridag

1D Cos Test
Num Recipes Tridag vs ESSL
1.e10 vs 1.e0

1D Convective
Diff: cntrl vs WENO
Rho': ave vs cntrl

1D Convective
K-relaxed init cond

1D Convective
split b.c. momentum EQ

1D Cos Test
ESSL vs PETSc Tridiag

1D Radiative
no-K, Smoothing

1D Convective
no-K, Smoothing

2D Convective
no-K, glitch

2D Radiative
K, bottom-up

1D Radiative
no-K vs K

2D PETSc unsplit No-K
dbl vs quad precision

2D IMSL g-split K
dbl vs quad precision

2D IMSL g-split K
Straight Sum vs
Trapezoidal Rule

2D PETSc unsplit K
Straight Sum vs
Trapezoidal Rule

2D PETSc no-K
unsplit vs g-split

g-split, 2D
PETSc vs IMSL
K and no-K

1D g-split, no-K, IMSL

g-split, 2D full K, IMSL
Bottom-Up vs Top-Down K

IDEAL 1D BURST
g-split, 2D full K, IMSL

1D g-split, no-K, PETSc

2D PETSc vs IMSL
K and no-K

1D no-K, IMSL

1D BURST
2D full K, IMSL

2D Sin-Cos Test
PETSc vs. IMSL

2D K vs. no-K

Cause of 2D Instability

Serial 2D Code

2D code, 1D burst (restr)

2D K vs gK order

2D Sin-Cos Test

1D BURST
2D vs 1D Code

1D BURST
CFL=0.5(!!)

1D BURST
BC Comparison:

1D BURST Dir-Neum, RHS_ave NOT subtracted:

1D BURST
Neum-Neum, RHS_ave subtracted:

1D BURST
Dir-Neum, RHS_ave subtracted:

RHS_ave: subtract or not?

ABOVE: Back to 1D Re-Test

Initial Conditions

GIFs / Animations

Therm Diffusion

Oscillations

Glitches

EPX

Diagnostics

Original NS Problem

GIFs / Animations

Charts

Diagnostics

Etc ...