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Shanghai Jiao Tong University 压力振荡产生的原因
压力梯度
压力Poisson方程源项
自由面判断
1
Shanghai Jiao Tong University
Tanaka et al. Journal of Computational Physics, 2010, 229(11): 4279-4290.
压力梯度改进方法
'
0 2 ( ) (| |)| |
j ii j i j i
j i j i
P PDP Wn
r r r rr r
0 2 ( ) (| |)| |
j ii j i j i
j i j i
P PDP Wn
r r r rr r
原始MPS方法
改进方法:
2
Shanghai Jiao Tong University 压力Poisson方程源项
* 02 1
2 0(1 )
k i
i in n
P Vt t n
* 02 1
2 0
k i
in nP
t n
原始MPS方法
混合源项法:
3
Tanaka et al. Journal of Computational Physics, 2010, 229(11): 4279-4290.
Shanghai Jiao Tong University 对压力梯度的测试
静水问题
4
液舱几何模型(单位: mm)
Shanghai Jiao Tong University算例 压力梯度 压力Poisson方程源项 自由面判断
Case A1 原始方法 原始方法 原始方法
Case A2 改进方法 原始方法 原始方法
Case A3 原始方法 改进方法 原始方法
Case A4 改进方法 改进方法 原始方法
A3
A1 A2
A4
5
Shanghai Jiao Tong University
理论值 Case A1 Case A2Case A3 Case A4
6
Shanghai Jiao Tong University 压力振荡现象与缓解方法
剧烈晃荡问题
7
sin( )x a t 液舱运动方式:
0.02 m a ,2 tanhn
g hL L
n , 其中:
液舱几何尺寸(单位:mm)
Shanghai Jiao Tong University
实验
Case 1Case 2
8
压力振荡现象与缓解方法
Case 1 Case 2
Shanghai Jiao Tong University
9
压力场
自由面粒子
粒子数密度场
流场瞬间
Shanghai Jiao Tong University 自由面判断
原始MPS方法中自由面判断准则:* 0 in n
10
其中: 为粒子数密度, 为一个参数, 为初始粒子数密度。0nn
粒子数密度场
Shanghai Jiao Tong University 自由面判断
新的自由面判断方法
0
1 ( ) ( )| |i i j ij
j i i j
D Wn
F r r r
r r
表征邻居粒子的不对称性
11
F
Shanghai Jiao Tong University 自由面判断
新的自由面判断准则:
12
0| | | |F F i
其中: 是一参数, 等于初始时刻自由面上粒子的 。 0| |F | |F
| |F 粒子数密度场场
Shanghai Jiao Tong University
13
原始自由面判断法计算结果
新的自由面判断法计算结果
Shanghai Jiao Tong University
算例 压力梯度压力Poisson方
程源项自由面判断
Case A1 原始方法 原始方法 原始方法
Case A2 改进方法 原始方法 原始方法
Case A3 原始方法 改进方法 原始方法
Case A4 原始方法 原始方法 改进方法
Case A5 改进方法 改进方法 原始方法
Case A6 改进方法 改进方法 改进方法
14
Shanghai Jiao Tong University
15
Case A1 Case A2 Case A3
Case A4 Case A5 Case A6
Shanghai Jiao Tong University实验 Case A1Case A2
实验 Case A4Case A3
实验 Case A5Case A6
16
Shanghai Jiao Tong University
17
算例 压力梯度压力Poisson方程
源项自由面判断
Case A1 原始方法 原始方法 原始方法
Case A2 改进方法 原始方法 原始方法
Case A3 原始方法 改进方法 原始方法
Case A4 原始方法 原始方法 改进方法
Case A5 改进方法 改进方法 原始方法
Case A6 改进方法 改进方法 改进方法
改进的MPS方法
Shanghai Jiao Tong University
已有的改进的压力梯度和压力Poisson方程源项能够改善
压力场,但在流动剧烈时改善效果不好
在剧烈流动问题中,自由面误判成为导致压力振荡的重
要因素
本文提出的新的自由面判断方法,能够较大程度地提高
自由面的判断精度
结合新的自由面判断方法、守恒型压力梯度和混合源项
法,构建的改进的MPS方法,较好地抑制了压力振荡现
象
18
Shanghai Jiao Tong University 并行计算及效率分析
并行策略
动态负载平衡
并行性能测试
基于GPU的并行加速
19
Shanghai Jiao Tong University 并行策略
粒子分解法
区域分解法
20
Shanghai Jiao Tong University 基于背景网格的区域分解法
21
Shanghai Jiao Tong University 基于背景网格的区域分解法
Node 0 Node 1 Node 2 Node 3
22
Shanghai Jiao Tong University 负载平衡
t=0.9 s
t=0.0 s初始时
一段时间后
23
Shanghai Jiao Tong University
Node 0 Node 1 Node 2 Node 3
n0 n1 n2 n3 n4 n5 n6 n7 n8 n9
_ _ /N proc N total np
_N proc_N total
np
每个进程中的粒子数
整个计算域的粒子数
进程数
动态负载平衡
其中:
24
Shanghai Jiao Tong University
Node0 Node1 Node2 Node 3
n0 n1 n2 n3 n4 n5 n6 n7 n8 n9
_ _ /N proc N total np
_N proc_N total
np
每个进程中的粒子数
整个计算域的粒子数
进程数
其中:
动态负载平衡
25
Shanghai Jiao Tong University 动态负载平衡
静态负载平衡
动态负载平衡
26
Shanghai Jiao Tong University 加速比对比
静态与动态负载平衡时的加速比
27
Shanghai Jiao Tong University 并行性能测试
三维溃坝几何尺寸
28
Shanghai Jiao Tong University
粒子总数 742 914
测试环境天津国家超算中心
CPU为Intel Xeon 5670
29
Shanghai Jiao Tong University 加速比
30
Shanghai Jiao Tong University 并行性能分析
每个时间步的计算:
粒子搜寻
压力Poisson方程(PPE)求解
其他步骤
31
Shanghai Jiao Tong University 基于GPU的并行加速
ALU
Tesla C1060 结构
32
Shanghai Jiao Tong University
CULA的特点:
1. 较高的计算效率
2. 支持多种平台,Linux,Windows和Mac OS
33
Shanghai Jiao Tong University
1. 定义一个CULA求解计划
2. 将稀疏矩阵进行压缩,并与求解计划关联
3. 设置求解条件,包括收敛残差、最大迭代次数等参数
4. 在GPU上执行求解计划
5.将GPU上计算结果传回CPU
实现过程
34
Shanghai Jiao Tong University GPU加速比分析
算例 Case 1 Case 2 Case 3 Case 4
粒子总数 49 563 136 059 270 435 742 914
粒子间距 (m) 0.03 0.02 0.015 0.01
35
Spee
d-up
Shanghai Jiao Tong University
一种基于背景网格的区域分解法
开发了动态负载平衡功能,获得了较好的并行效率
压力Poisson方程是MPS的并行效率瓶颈
GPU能较好地加速压力Poisson方程求解效率,在MPS的
并行计算中具有很大的潜力
36
Shanghai Jiao Tong University
Parallel computation
GPU acceleration
Overlapping technique
Multi-resolution technique
Acceleration techniques
加速方法
Shanghai Jiao Tong University
GPU acceleration for Poission equation
GPU 加速
Shanghai Jiao Tong UniversityGPU 加速
ALU
Tesla C1060
Shanghai Jiao Tong University
Static balance
Dynamic balance
Parallel computation with dynamic load balance
并行计算动态负载平衡技术
Shanghai Jiao Tong University并行计算动态负载平衡技术
Shanghai Jiao Tong University
Coarse particles
Fine particles
Overlapping region
Overlapping Particle technique
重叠粒子技术
Shanghai Jiao Tong University
溃坝波Overlapping region
重叠粒子技术
Shanghai Jiao Tong University
Overlapping region
重叠粒子技术
Shanghai Jiao Tong University重叠粒子技术
Shanghai Jiao Tong University
Cases Initial particle space (m)
Coarse 0.005
OPT 0.0025
Fine 0.0025
Overlapping region
重叠粒子技术
波浪在斜坡上破碎过程
Shanghai Jiao Tong University
47
Overlapping Region
MLParticle-SJTU
MLParticle-SJTU
重叠粒子技术
Shanghai Jiao Tong University
Coarse
OPT Fine
OPT
Coarse
Fine
重叠粒子技术
Shanghai Jiao Tong University
Coarse
OPT Fine
Coarse
OPT Fine
重叠粒子技术
Shanghai Jiao Tong University重叠粒子技术
Shanghai Jiao Tong University
Multi-resolution MPS The influence domain of particle i contains particles j
but not vice versa if these two interaction particles have
different interaction radiuses.
多分辨率粒子技术
Shanghai Jiao Tong University
The cut-off radiuses for particle interaction models
between two neighbor particles i and j are replaced by
following equations respectively:
+2
ei ej
e
r rr
_ _
_
+2
ei lap ej lap
e lap
r rr
_e lapr_e lapr
多分辨率粒子技术
Shanghai Jiao Tong University
20
j i jj i j ii
ij i
P P LDP Wn L
r r r r
r r
2
0
2j j
j ii j
j i ijiji
i j
m mL LD W
mmnL L
Modified pressure gradient model and PPE
Where: L is the particle diameter
jkj ij
i j
Lr r
L L
j
e kj e ij
i j
Lr r
L L
iik ij
i j
Lr r
L L
i
e ik e ij
i j
Lr r
L L
多分辨率粒子技术
Shanghai Jiao Tong University
Computational model
Cases Initial particle space (m) Description
A1 0.005 Single-MPSA2 0.02/0.01/0.005 Multi-MPS
Computational parameters
多分辨率粒子技术
Shanghai Jiao Tong University
溃坝波
MLParticle-SJTU
多分辨率粒子技术
Shanghai Jiao Tong University
Single-MPS
Single-MPS
Multi-MPS
Multi-MPS
Comparisons of dam-break flows at gt H
Comparisons of dam-break flows at gt H
*H is initial water height
多分辨率粒子技术
Shanghai Jiao Tong University
P1* P2
Pressure
*The numerical results are evaluated at the bottom of the probe P1
多分辨率粒子技术
Shanghai Jiao Tong University
Water height
多分辨率粒子技术
Shanghai Jiao Tong University
Computation time
多分辨率粒子技术
Shanghai Jiao Tong University
涌潮波
Shanghai Jiao Tong University涌潮波
Shanghai Jiao Tong University
Undulation bore flows
Shanghai Jiao Tong University
Undulation bore flows
Shanghai Jiao Tong University
Undulation bore flows
Shanghai Jiao Tong University
VOF MLParticle-SJTU
Undulation bore flows
Shanghai Jiao Tong University
Breaking bore flows
Shanghai Jiao Tong University
Breaking bore flows
Shanghai Jiao Tong University
Breaking bore flows
Breaking bore flows
Shanghai Jiao Tong University
VOF MLParticle-SJTU
Breaking bore flows
Shanghai Jiao Tong University
溃坝波
Shanghai Jiao Tong University
Case 1 Case 2 Case 3 Case 4
Number of particles
49 563 136 059 270 435 742 914
r 0.03 0.02 0.015 0.01
溃坝波
Shanghai Jiao Tong University
MLParticle-SJTU
溃坝波
Shanghai Jiao Tong University
Case 1
Case 2
Case 3
Case 4
溃坝波
Shanghai Jiao Tong UniversityCase 4Case 3Case 2Case 1
EXPCase 4SPHFluent
t /g H
t /g H
溃坝波
Shanghai Jiao Tong University
MLParticle-SJTU
溃坝波与障碍物相互作用
Shanghai Jiao Tong University
Exp. (Kleefsman, 2005)MLParticle-SJTUVOF (Kleefsman, 2005)
H2
H4
溃坝波与障碍物相互作用
Shanghai Jiao Tong University
Exp.MLParticle-SJTUOriginal MPSVOFP1
P5
溃坝波与障碍物相互作用
Shanghai Jiao Tong University
MPS MLParticle-SJTU
(a1) t=0.35 s (b1) t=0.35 s
(a2) t=0.70 s (b2) t=0.70 s
溃坝波与障碍物相互作用
Shanghai Jiao Tong University
甲板上浪
Shanghai Jiao Tong University
1.035
waveMaker
2.0 3.5
7.0
0.248 0.198
verticalWall
• Wave length 2m
• Wave height 0.16m
0.2275m
r=0.08m FPSO
PR1 dist from deck=12mmPR2 dist from deck=32mm
Computational model
Cases Initial particle space (m)
Number of particles
Single-MPS 0.02 19, 000Multi-MPS 0.02/0.01/0.005 88, 000
Computational parameters
甲板上浪
Shanghai Jiao Tong University
Multi-MPS
MLParticle-SJTU
MLParticle-SJTU
甲板上浪
Shanghai Jiao Tong University
Experiment Multi-MPS Single-MPS
dp = 0.02m*
*dp is initial particle space
甲板上浪
Shanghai Jiao Tong University
Experiment Multi-MPS Single-MPS
dp = 0.02m
甲板上浪
Shanghai Jiao Tong University
P1
甲板上浪
Shanghai Jiao Tong University
P2
甲板上浪
Shanghai Jiao Tong University
物体出入水
Shanghai Jiao Tong University
Computational model
Cases Initial particle space (m) Description
C1 0.0025 Single-MPSC2 0.01/0.005/0.0025 Multi-MPS
Computational parameters
物体出入水
Shanghai Jiao Tong University
Multi-MPS
MLParticle-SJTU
物体出入水
Shanghai Jiao Tong University
Exp.
Single-MPS Multi-MPS
t = 0.315s
物体出入水
Shanghai Jiao Tong University
Exp.
Single-MPS Multi-MPS
t = 0.390s
物体出入水
Shanghai Jiao Tong University
Exp.
Single-MPS Multi-MPS
t = 0.410s
物体出入水
Shanghai Jiao Tong University
Exp.
Single-MPS Multi-MPS
t = 0.50s
物体出入水
Shanghai Jiao Tong University
Penetration depths
物体出入水
Shanghai Jiao Tong University
MLParticle-SJTU
物体出入水
Shanghai Jiao Tong University楔形物体出入水
Shanghai Jiao Tong University
计算工况:
Cases α (deg) β (deg) H (m) mass (kg) g (m/s2) ρ (kg/m3) dp
Case1 30 0 0.5 85.375 9.8 1000 0.0125
Case2 30 10 0.5 85.375 9.8 1000 0.0125
Case3 30 20 0.5 85.375 9.8 1000 0.0125
1 m
H
β
α
3 m
Water
楔形物体出入水
Shanghai Jiao Tong University
case1
楔形物体出入水
Shanghai Jiao Tong University
case2
楔形物体出入水
Shanghai Jiao Tong University
case3
楔形物体出入水
Shanghai Jiao Tong University
0.2 0.25 0.3 0.35 0.4 0.45 0.5-20
-10
0
10
20
30
40
50
60
Time(s)
Pres
sure
(Pa)
Exp.Case1
Impact pressure (point 1)
楔形物体出入水
Shanghai Jiao Tong University
0.2 0.25 0.3 0.35 0.4 0.45 0.5-10
0
10
20
30
40
50
60
70
80
Time(s)
Pres
sure
(Pa)
Case1Case2Case3
Impact pressure (point 1)
楔形物体出入水
Shanghai Jiao Tong University
0.2 0.25 0.3 0.35 0.4 0.45 0.5-10
0
10
20
30
40
50
60
Time(s)
Forc
e(N
)
Exp.-Force sensor2Case1-Force sensor2
Impact force
楔形物体出入水
Shanghai Jiao Tong University
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
Time(s)
Velo
city
(m/s
)
Exp.Case1
楔形物体出入水
Shanghai Jiao Tong University
液舱晃荡
Shanghai Jiao Tong University
d h Excitation frequency Amplitude
0.25 m 0.0575 m 4.49 rad/s 0.05 m
Unit: m
Summary report of sloshing model test for rectangular model. Kang DH&Lee YB ,2005.
液舱晃荡
Shanghai Jiao Tong University
MLParticle-SJTU
液舱晃荡
Shanghai Jiao Tong University
MLParticle-SJTU
液舱晃荡
Shanghai Jiao Tong University
EXP.
MLParticle-SJTU
Comparison of free-surface profiles between experiment and numerical simulation
Summary eport of sloshing model test for rectangular model, Kang DH&Lee YB ,2005.
液舱晃荡
Shanghai Jiao Tong University
(m) (m) (m) (°) (°) (°)Case A 0.02 0 0 0 0 0Case B 0 0 0 4 0 0Case C 0.02 0 0 4 0 0Case D 0.02 0.02 0.005 4 4 2
The translating motions of excitation are:
sin
y sin
sin
The rotating motions of excitation are:
sin
sin
sin
液舱晃荡
Shanghai Jiao Tong University
Case A
Case DCase C
Case BMLParticle-SJTU
液舱晃荡
Shanghai Jiao Tong University
Case A
EXP.:
MLParticle-SJTU:
( =4.34rad/s)
MLParticle-SJTU
Shanghai Jiao Tong University
Case B
EXP.:
( =4.87rad/s)
MLParticle-SJTU:
MLParticle-SJTU
Shanghai Jiao Tong Universitynaoe-FOAM-SJTU 2.0
Tank Sloshing
MLParticle-SJTU
液舱晃荡
Shanghai Jiao Tong Universitynaoe-FOAM-SJTU 2.0
Tank Sloshing
MLParticle-SJTU
液舱晃荡
Shanghai Jiao Tong University
f=0.95Hz f=1.0Hz
f=1.05Hz f=1.1HzMLParticle-SJTU
液舱晃荡
Shanghai Jiao Tong University
MLParticle-SJTU
液舱晃荡
Shanghai Jiao Tong University
Pressure
P1 P2
P3 P4
P5 P6MLParticle-SJTU
液舱晃荡
Shanghai Jiao Tong University
Tank Sloshing with Baffle Plate
MLParticle-SJTU
液舱晃荡
Shanghai Jiao Tong University
h=0.15 m h=0.12 m
h=0.08 m
MLParticle-SJTU
Sloshing Flows
Shanghai Jiao Tong University
MLParticle-SJTU
液舱晃荡
Shanghai Jiao Tong University液舱晃荡
Shanghai Jiao Tong University
有网格求解器naoe-FOAM-SJTU和无网格求 解
器MLParticle-SJTU都可以有效求解自由面剧烈
流动问题
有网格方法数值计算值相对稳定,但处理自由面
变形和动边界问题较为复杂
无网格方法计算量大,计算值容易发生振荡,但
处理自由面变形和动边界问题较为直接和简单
结 论
Shanghai Jiao Tong University 展望
处理外流场问题可以与网格类方法相结合,远场
基于网格法进行计算,进场采用粒子法,可考虑
将MLParticle-SJTU与naoeFOAM结合起来,充
分发挥两个求解器各自的特点
可以推广应用到更为复杂的流动问题,如带锚链
的海洋平台在波浪中的运动或实际船型如DTMB 5415、KCS等的操纵性和耐波性问题
123
Shanghai Jiao Tong University
展 望
124
C FT C: naoe-FOAM-SJTU
T: Matching zoneF: MLParticle-SJTU
有网格方法与无网格方法结合
Shanghai Jiao Tong University
LNG tank in waves without liquid
展 望
Shanghai Jiao Tong University
LNG tank in waves with liquid
展 望
Shanghai Jiao Tong University
Particle solver
(MLParticle-SJTU)
展 望
Shanghai Jiao Tong University
What is CFD
Shanghai Jiao Tong University
What is CFD
Shanghai Jiao Tong University
What is CFD
Shanghai Jiao Tong University
What is CFD
Shanghai Jiao Tong University
What is CFD
Shanghai Jiao Tong University What is CFD
Shanghai Jiao Tong University
What is CFD
Shanghai Jiao Tong University What is CFD