Computational modeling of multiscale flows - C-SWARM

Computational modeling of
multiscale flows
T. Grenga, S. Paolucci
Department of Aerospace & Mechanical Engineering
Center for Shock Wave-processing
of Advanced Reactive Materials
(C-SWARM)
WCCM XI - ECCM V - ECFD VI - Barcelona 21 July 2014
Motivation
“a single overarching grand challenge: the development of a validated,
predictive, multi-scale, combustion modeling capability to optimize the
design and operation of evolving fuels in advanced engines”,
Basic Research Needs for Clean and Efficient Combustion of 21-st
Century Transportation Fuels, DOE 2007
Models need to simulate the intricate coupling between
the fluid mechanics and chemistry
Multi-scales problems require
• advanced computational approaches
• high performance computing
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
2
Introduction
The model includes detailed
chemical kinetics, multicomponent diffusion
Problems are typically
multidimensional and contain
a wide range of spatial and
temporal scales
An adaptive method is applied
to the simulation of
compressible adaptive flows
“Research needs for future internal
combustion engines”,
Physics Today, Nov. 2008, pp. 47-52
The method resolves the range of spatial scales
present, while greatly reducing computational cost
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
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Governing Equations
∂ρ
∂t
∂ρui
∂t
∂ρE
∂t
∂ρYk
∂t
∂
=−
(ρui )
∂xi
∂
∂τij
=−
(ρuj ui + pδij ) +
∂xj
∂xj
∂
∂
=−
(uj (ρE + p)) +
(uj τji − qi )
∂xj
∂xi
∂
∂ji,k
=−
(ui ρYk ) −
+ Mk ω̇k ,
k = 1, . . . , K − 1
∂xi
∂xi
ρ-density, ui -velocity vector, p-pressure, E-specific total energy, Yk -mass fraction of species k, τij -viscous stress tensor, qi -heat flux, ji,k -species mass flux,
Mk - molecular mass of species k, and ω̇k -production rate of species k
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
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Governing Equations
�
�
�
�
∂ul
∂ui
∂uj
2
τij = µ
+
δij
+ κ− µ
∂xj
∂xi
3
∂xl
�
K �
�
∂T
RT
hk ji,k −
qi = −λ
+
DTk di,k
∂xi
Mk X k
k=1
ji,k
ρYk
=
M Xk
K
�
j=1
j�=k
Mj Dkj di,j
DTk ∂T
−
T ∂xi
k=1
∂Xk
1 ∂p
di,k =
+ (Xk − Yk )
∂xi
p ∂xi
�
�
K
I
K
�
� � ��
�
�
�
��
�
f
νki
r
νki
νki − νki
ki
ω̇k =
[Xk ] − ki
[Xk ]
i=1
1
E = e + ui ui
2
ρRT
p=
M
K
�
Yk = 1
k=1
k=1
e-internal energy, T -temperature, R-universal gas constant, M -mixture molecular mass, µ-shear viscosity, κ-bulk viscosity, λ-thermal conductivity, hk -enthalpy
of species k, Xk -mole fraction of species k, di,k -diffusion driving force, DkT thermal diffusion coefficients, Dij -ordinary multicomponent diffusion coefficients,
�
��
νki and νki -product and reactant stoichiometric coefficients in reaction i, kif and
kir forward and reverse reaction rate constants
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
5
Wavelet Adaptive Multiresolution
Representation (WAMR) Method
l - l0
It is a dynamically spatially
6
adaptive multi-scale method
Collocation points are
4
associated with wavelets
2
Wavelet amplitudes reflect the
local regularity of functions
0
1.0
High resolution grid with small
0.5
number of points
y
Solutions are automatically verified
Method is parallelized with MPI approach
1.0
0.5
0.0 0.0
x
S. Paolucci, Z. Zikoski, D. Wiraseat, WAMR: An adaptive method for the simulation of compressible
reacting flow. Part I. Accuracy and efficiency of algorithm, J. Comp. Phys., 272 (2014), pp. 814-841
S. Paolucci, Z. Zikoski, T. Grenga, WAMR: An adaptive method for the simulation of compressible
reacting flow. Part II. The parallel algorithm, J. Comp. Phys., 272 (2014), pp. 842-864
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
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WAMR Method
Sparse wavelet representation (SWR)
u (x) =
J
�
�
u0,k Φ0,k (x) +
J−1
�
�
dj,λ Ψj,λ (x)
j=0 {λ : |dj,λ |≥ε}
k
��
�
uJ
ε
��
�
RεJ
Density
Pressure
Temperature
order 1/6
−2
−d/p
Max error
−3
10
(i) J
Dx uε �V,∞
1
−4
10
−5
10
−6
10
Error of derivative approximation
�∂ u/∂x −
dj,λ Ψj,λ (x),
10
Number of collocation points
i
0
−1
�u − uJε �∞ ≤ C1 ε
i
�
10
Error in SWR:
�
j=0 {λ : |dj,λ |<ε}
10
Threshold parameter: ε
NE ≤ C2 ε
+
J−1
�
≤
−6
10
−5
10
−4
10
−3
ε
10
−2
10
−1
10
− min((p−i),n)/2
CNE
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
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WAMR: 3D Shock-Bubble interaction (SBI)
Problem Description
• Domain
[0, 3]×[0, 0.4]×[0, 0.4] cm
• Ambient Mixture
YN2=0.868, YO2=0.232
P=101.3 kPa
T=1000 K
• Bubble
YH2=0.990
r=0.1 cm at x=0.5cm
• Loaded by Shock
Ms = 1.5 at x=0.3 cm
• Wavelet parameter
ε=10-2
p=4
[Nx× Ny × Nz]coarse=[60×8×8]
J=6
Δxmin= 7.81 µm
• Time integration
Runge-Kutta-Fehlberg 45
εrel=10-3, εabs=10-10
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
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WAMR: 3D SBI - Results
3
Density [g/cm ]
Temperature [K]
1000
1100
1200
1300
1400
1500
4.0e-4
1600
5.0e-4
6.0e-4
7.0e-4
8.0e-4
0µs
2.5µs
5µs
10µs
18.75µs
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
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WAMR: 3D SBI - Results
HO2
Velocity [cm/s]
20000
40000
60000
80000
4.0e-5
100000
6.0e-5
8.0e-5
1.0e-4
1.2e-4
0µs
2.5µs
5µs
10µs
18.75µs
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
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WAMR: 3D SBI - Results 10μs
H2
5.00e-02
4.00e-02
3.00e-02
2.00e-02
1.00e-02
H2O2
1.60e-08
1.20e-08
8.00e-09
4.00e-09
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
HO2
1.00e-05
8.00e-06
6.00e-06
4.00e-06
2.00e-06
H2O
2.80e-05
2.00e-05
1.20e-05
4.00e-06
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WAMR: 3D SBI - Results 15.5μs
H2
2.80e-02
H2
2.40e-02
2.80e-02
2.00e-02
2.40e-02
2.00e-02
1.60e-02
1.60e-02
1.20e-02
1.20e-02
8.00e-03
8.00e-03
4.00e-03
4.00e-03
HO2
1.40e-04
1.00e-04
6.00e-05
2.00e-05
H2O2
1.60e-06
1.20e-06
8.00e-07
4.00e-07
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
H2O
4.40e-03
3.20e-03
2.00e-03
8.00e-04
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WAMR: 3D SBI - Results 18.75μs
H2
1.00e-02
HO2
1.20e-04
7.00e-03
1.00e-04
4.00e-03
8.00e-05
1.00e-03
6.00e-05
H2O2
8.00e-05
6.00e-05
4.00e-05
2.00e-05
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
H2O
1.00e-01
7.00e-02
4.00e-02
1.00e-02
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WAMR: 3D SBI - Results
H2
1.0e-4
10µs
1.0e-3
1.0e-2
12.5µs
15.5µs
18.75µs
O2
1.6e-1
1.8e-1
2.0e-1
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
2.2e-1
14
WAMR: 3D SBI - Results
H
1.0e-5
10µs
1.0e-4
12.5µs
1.0e-3
18.75µs
15.5µs
O
1.0e-5
1.0e-4
1.0e-3
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
1.0e-2
15
WAMR: 3D SBI - Results
OH
1.0e-5
10µs
1.0e-4
1.0e-3
12.5µs
1.0e-2
18.75µs
15.5µs
H2O
1.0e-4
1.0e-3
1.0e-2
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
1.0e-1
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WAMR: 3D SBI - Results
7
−7
10
10
Grid points
Time step [s]
6
10
−8
10
5
10
4
10
0
0.2
0.4
0.6
0.8
1
1.2
Time [s]
1.4
1.6
• Runtime
~2.58 × 10^5 CPU-hr
1024 maximum cores
• Equivalent uniform grid
109 points (7.81 µm)
−9
10
1.8 2
−5
x 10
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
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Conclusions
The WAMR method
•
•
•
•
provides a robust spatial adaption strategy
minimizes the number of degrees of freedom
provides a verified solutions
MPI parallelization with good scaling up to 1024
cores
The SBI problem
• has been solved with high accuracy (7.81 µm)
• a wide range of spatial and temporal scales has
been captured
• interaction between advection, diffusion and
reaction has been shown
T. Grenga, S. Paolucci — University of Notre Dame (C-SWARM) — Computational modeling of multiscale flows
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Center for Shock Wave-processing of Advanced Reactive Materials
(C-SWARM)
Computational modeling of
multiscale flows
T. Grenga, S. Paolucci
Department of Aerospace & Mechanical Engineering
University of Notre Dame
WCCM XI - ECCM V - ECFD VI - Barcelona 21 July 2014