A new strategy for adapting time-step in the Local Time Stepping … · 2017-05-10 · Quang Huy...

P Extended reserves | Clean refining | Fuel-efficient vehicles | Diversified fuels | Controlled CO2

MAMCDP 2009 Workshop - Université Pierre et Marie Curie

A new strategy for adapting time-step in the Local Time Stepping Method applied to

hyperbolic PDEs

Équipe de Recherche Technologique: Frédéric Coquel, Marie Postel (LJLL) Quang Huy Tran (IFP)

Quang Long Nguyen

Outline

Context Mathematical model and numerical scheme Multiresolution (MR) Local Time Stepping (LTS) Conclusion

Outline

Context

Transportation of hydrocarbons: oil and gas numerical simulation of two-phase flows in pipelines over a long

time-range Characteristics

Closure laws: costly to evaluate Time varying boundary conditions: inflow and outflow Pipeline's geometry: horizontal, slugging, severe slugging (gravity) fronts separating the oil and gas propagate along the pipeline

Goals Model the problem Improve the simulations Speed up the computation thanks to the Multiresolution and Local Time Stepping methods

Outline

Mathematical model

Drift-Flux Model

Closure laws Thermodynamics and Hydrodynamics :

nonlinear and costly

Numerical scheme

Finite volume method with Riemann solver Explicit Lagrange-Projection scheme under the form

Under the CFL condition

The positivity of the scheme is preserved

Outline

Multiresolution (MR)

Idea The mesh size depends on the local

smoothness of the solution adaptive grid The adaptive grid adapts dynamically

as the solution evolves in time grid prediction by detecting the

displacement and the formation of the singularities

Advantages Well adapted to our problem Reduce the number of calls to the

expensive closure laws gain in CPU time

Uniform

Adaptive

Adaptive Multiresolution (MR)

Multiscale representation Mean value interpolation of the solution A. Cohen, S.M. Kaber, S. Müller and M. Postel, Math. Comp., 72

(2003), pp. 183–225

1. Encoding

2. Decoding h

h/2 level k-2

level k-1 level k

level k+1

Multiresolution (MR) Thresholding algorithm

Details

Level dependent threshold parameter

Prediction (Harten's heuristic) Mark the neighborhoods of if

Mark the higher levels if

The adaptive grid is updated at each time step graded to ensure optimal complexity of the encoding/decoding

algorithm

Numerical results (MR) Problem of shock tube flow

4000.4−10

5400.2−10

Uniform solution versus MR solution Adaptive tree

Convergence of the Multiresolution method

Outline

Local Time Stepping (LTS)

Remark on MR Same time-step for all cells

Principle of the LTS Time-step adapted to mesh size

Advantage Further reduction of calls to closure

laws increase gain in CPU time

Adaptive Mesh Refinement

Local time stepping

Local Time Stepping (LTS) Computation of the time-step

Definitions Macro time-step: corresponds to the biggest cells Micro time-step: corresponds to the smallest cells

The micro time-steps decrease during each macro time-step They are updated along with the solution while ensuring the

stability condition

The micro time-steps decrease during each macro time-step They are updated along with the solution while ensuring the

stability condition The first micro time-step

The others

where is the updated solution at time

The macro time-step

Local Time Stepping (LTS) Synchronization in transition zones

S. Müller and Y. Stiriba, J. Sci. Comput., 30 (2007), pp. 493–531

LP conservative scheme Outside of transition zones

In transition zones

Example of a mesh with 3 levels (K = 3) The solution is updated at each micro time step

0 0 1 2

Example of a mesh with 3 levels (K = 3) Synchronisation of the at the macro time step

Numerical results (LTS) Problem of shock tube flow

Numerical results - Convergence

Numerical results - Pipeline

Pipeline with slope of 30 degrees

Sensors along the pipeline

Time-steps’ evolution

Performance

Comparison between two types of hydrodynamics laws

ratio UNI/MR ratio MR/LTS

N(K) Simple law Realistic law Simple law Realistic law

rCPU rNbLaw rCPU rNbLaw rCPU rNbLaw rCPU rNbLaw

256(5) 2,98 2,90 3,17 3,07 6,61 11,67 10,41 10,82

512(6) 4,19 4,64 5,02 4,85 7,77 18,79 16,13 17,06

1024(7) 5,47 6,99 7,48 7,13 8,39 29,20 24,58 25,88

Outline

Conclusion

Speed up the simulations thanks to the Multiresolution method Analysis of the local regularity of the solution Dyadic grid hierarchy Threshold parameter + prediction

Increase the performance by using the Local Time Stepping method coupled with MR Time-step adapted to the mesh size Faster, less calls to closure laws A new strategy to compute the time-step

The more expensive the closure laws are, the better the CPU gain is

References [1] N. Adrianov, F. Coquel, M. Postel, Q-H. Tran A relaxation multi-resolution scheme for accelerating realistic two-phase

flows calculations in pipelines [2] A. Cohen, M.S. Kaber, S. Müller, M. Postel Fully adaptive multiresolution finite volume schemes for conservation laws [3] F. Coquel, Q-L. Nguyen, M. Postel, Q-H. Tran Local time stepping applied to implicit-explicit methods for hyperbolic systems [4] A. Harten Multiresolution algorithms for the numerical solutions of hyperbolic

conservation laws [5] S. Müller, Y. Stiriba Fully adaptive multiscale schemes for conservation laws employing

locally varying time stepping

http://www.ann.jussieu.fr/ERTint/

Thank you for your attention

Numerical method

Relaxation to treat the nonlinearities Replacing and by two new variables and Relaxation system

Hyperbolic system with linearly degenerate eigenfields

Subcharacteristic conditions

Numerical method

Lagrange-Projection decomposition Based on ALE (Arbitrary Lagrange-Euler) formalism

3-step resolution

Numerical method

3-step resolution

Numerical method

3-step resolution

Numerical method

3-step resolution

Numerical method

3-step resolution

Numerical method

3-step resolution

Numerical method

3-step resolution

Evolution of the adaptive tree

Local Time Stepping (LTS) 1st strategy

Constant micro time-step during the whole simulation by using the smallest time-step issued from a uniform simulation

Local Time Stepping (LTS) 2nd strategy

Constant micro time-step during each macro time-step by satisfying the very first stability conditions at time

The first strategy stable but expensive as the time-step is very small needs to do simulation with a uniform grid first

The second strategy not sure to be stable as the solution evolves in time, i.e

after every micro time-step

A new strategy ??? ensure the stability

LTS-fix

A new strategy for adapting time-step in the Local Time Stepping … · 2017-05-10 · Quang Huy...

Documents

Transcript of A new strategy for adapting time-step in the Local Time Stepping … · 2017-05-10 · Quang Huy...

Thibault de Poyferré & Quang-Huy Nguyen - arXiv · 2018-10-11 · Thibault de Poyferré & Quang-Huy Nguyen Abstract. — We consider in this article the system of gravity-capillary

REGULATIONS ON ENERGY EFFICIENCY & CONSERVATION OF VIETNAM Cu Huy Quang, Officer of EECO - MOIT.

SOFTWARE ARCHITECTURE AND DESIGN TEAM 3 – K15T1 Hanh Luong – Leader – T095095 Hao Tran – T094442 Huy Nguyen – T094016 Hieu Le – T093798 Quang Nguyen –

Big case TET - quynh phuong, minh hoang, thai hoang, quang huy

IFP Booklet

Man Quang Huy Faculty of Geography VNU - University of Science Hanoi, Vietnam Email: mqhuy@vnu.edu.vnmqhuy@vnu.edu.vn.

Nonlinear Time-Dependent Behavior of Composite Steel ... · Nonlinear time-dependent behavior of composite steel-concrete beams Quang-Huy Nguyen 1 Not a Member, ASCE and Mohammed

Asian Cities Climate Resilience - pubs.iied.org.pubs.iied.org/pdfs/10724IIED.pdfQuy Nhon University for their support in conducting the fieldwork. Special thanks go to man Quang Huy

Thibault de Poyferré & Quang-Huy Nguyen · 2 THIBAULT DE POYFERRÉ & QUANG-HUY NGUYEN 1. Introduction Weconsiderthesystemofgravity-capillarywavesdescribingthemotionof ...

IFP - Fixedindeco-breakers.com/wp-content/uploads/2016/09/16-04-G-P...2016/09/16 · IFP 8 X IFP 13 X IFP 19 X IFP 28 X IFP 35 X IFP 45 X 6 ÷ 18 tons 750 Kg 650 mm 1700 mm 980 mm

IFP, IFP PRO, IFP ETH - support.industry.siemens.com · IFP, IFP PRO, IFP ETH Operating Instructions 11/2017 A5E31298376-AH Overview 1 Safety information 2 Installing and connecting

Truong Quang Huy - Visual Art - extended essayhuyartportfolio.weebly.com/uploads/5/8/5/9/58595685/truong_quang... · Extended Essay: Visual Art Australian ... 6-8 Impressionism ...

SDN-BASED CONFIGURATION SOLUTION FOR IEEE …SDN-BASED CONFIGURATION SOLUTION FOR IEEE 802.1 TIME SENSITIVE NETWORKING (TSN) SIWAR BEN HADJ SAID, QUANG HUY TRUONG, AND MICHAEL BOC

Truong Quang Huy - Visual Art - extended essay · Title: Microsoft Word - Truong Quang Huy - Visual Art - extended essay.docx Created Date: 10/7/2015 1:15:15 AM

Assignment Tet - Minh Quang, Thai Hoang, Minh Hoang, Hoang Yen, Quang Huy

Nguyen Quang Huy MARKETING COMMUNICATION PLAN FOR …

Islam - hse.ru Islam VIET NAM’S LESSON FOR CHINA: AN EXAMINATION ... Vu Huy, Trinh Quang Long, Steve Parker, Adam McCarty, Jonathan Pincus, Eric Ramstetter, Shoichi ...

Energy Consumption Measurements as a Basis for ......Energy Consumption Measurements as a Basis for Computational Ofﬂoading for Android Smartphones Quang-Huy Nguyen, Johannes Blobel

ABSTRACT - Institut des actuaires - Accueil€¦ · Dissertation ISFA – Nguyen Quang Huy Page 4 Acknowledgements I would like to express my appreciation and gratitude to my supervisors,

Migration, Resilience and Global Change in the Coastal Zone POLICY IMPLICATIONS FOR COMMUNAL TRENDS 1 Nguyen Huu Ninh, 1 Luong Quang Huy and 2 Mick Kelly.