for 3D MHD simulations Ulyanov Artem LPI RAS Moscow a rtemulianovgmailcom RussianBritish Seminar of Young Scientists Dynamical plasma processes in the heliosphere from the Sun to the Earth ID: 653211
Download Presentation The PPT/PDF document "Inversed Lagrangian approach" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Inversed Lagrangian approach for 3D MHD simulations
Ulyanov Artem, LPI RAS, Moscowartem.ulianov@gmail.com
Russian-British Seminar of Young Scientists “Dynamical plasma processes in the heliosphere: from the Sun to the Earth”
18 - 21 September 2017, Irkutsk, RussiaSlide2
Hardware, software…
CPU
:
Intel core-i5 3.4
ГГц
Memory
:
8 Гб
Graphics
:
Nvidia
GeForce GTX 680 2
Гб
Python
2.7
GPGPU: OpenCL
Computation time (64x64x256 grid): approx. 15 min
Visualization
:
Matplotlib
, OpenGL,
OpenCV
http://github.com/temik42/Slide3
MHD equationsNon-ideal plasma
Ideal plasma
Slide4
Eulerian approach
(Here should be an image of a man sitting on a bank of a river and looking at passing boats)Slide5
Eulerian MHD
- total specific energy
- stress tensor
Advection equation:
Slide6
Eulerian numerical schemeSlide7
Langrangian
approach
(Here
should be a image of a man
sitting
on
a boat and drifting down a river)Slide8
Lagrangian approach
- trajectory of an “observer”,
-
initial coordinates,
If
is fixed in time:
Slide9
Lagrangian MHD
- initial density,
- initial
pressure,
- initial
field.
Slide10
Lagrangian numerical schemeSlide11
Inversed
Langrangian approach
(Here should be an image of a man jumping from boat to boat to stay at rest with respect to a bank of a river)Slide12
Inversed Lagrangian approach
If
x
is fixed:
Slide13
Inversed Lagrangian MHD
- initial density,
- initial
pressure,
- initial
field.
Slide14
Numerical inversed Lagrangian schemeSlide15
Tests!Slide16
Sod’s shock tube testSlide17
Theory
I, V – unperturbed regionsII – rarefaction waveIII – contact discontinuity
IV – shock waveSlide18
Approximate Riemann solver simulationSlide19
Inverted Lagrangian simulationSlide20
Grid deformationSlide21
Theory vs. Simulation
ParameterTheory
Simulation
Inaccuracy, %
P3
1.693
1.694
0.02
N3 (left)1.9941.9890.2N3 (right)1.4511.4590.4V30.4640.4680.5V4 (shock)1.4941.4870.5Slide22
Observations - high speed flows in coronal loopSlide23
Perturbation speeds:
Speeds of plasma and perturbation
Plasma speed:
Slide24
Acoustics (B=0)Slide25
Torsional wave propagation (
β = 0)
BSlide26
Shear wave diffraction (β = 0)
BSlide27
THANK YOU!