System of Conservation Laws : Theory and Numerics

Convener(s)
Name: Shyam Sundar Ghoshal Ujjwal Koley
Mailing Address:

TIFR Centre for Applicable Mathematics

Sharada Nagar, Chikkabommasandra,

Bengaluru, 560065

TIFR Centre for Applicable Mathematics

Sharada Nagar, Chikkabommasandra,

Bengaluru, 560065
Email:

ghoshal@tifrbng.res.in

ujjwal@tifrbng.res.in

The aim of this workshop is to give a broad overview to the Ph.d students and young researchers in the field of conservation laws. In general, a complete mathematical understanding for system of conservation laws are largely unavailable, therefore there is a huge scope for researchers to enter in this field. The main topics we cover are scalar conservation laws, theory of Lax-Oleinik, Kruzkov’s entropy condition, uniquesness proof via doubling the variable, introduction to the hyperbolic system of conservation laws, Lax theory of Riemann problem for system, front tracking algorithm and interaction estimates for system of conservation laws, non conservative product in the sense of Volpert and its generalizations, Riemann problem for non conservative hyperbolic system, first order and higher order numerical methods for scalar conservation laws, numerical methods for Euler equation, approximate Riemann solvers and other techniques to construct numerical flux, ENO and WENO schemes, discontinuous Galerkin method.

 There will be a careful selection process and we expect to invite around 30 participants throughout the country. It is expected from the participants to have a good background in Analysis.

Please Note:  Participants have to arrange for their own travel.

Dates: 

Monday, August 5, 2019 - 09:00 to Saturday, August 17, 2019 - 18:00

Venue: 

Venue Address: 

TIFR Centre for Applicable Mathematics
Sharada Nagar, Chikkabommasandra

Venue State: 

Venue City: 

PIN: 

560065

Chrono Order: 

320

Syllabus: 

Name of the Speakers with their affiliation.

No. of Lectures

Detailed Syllabus

Prof. Adimurthi (TIFR-CAM)

6

Method of Characteristics. Weak solution for scalar conservation laws. Rankine-Hugoniot condition. Entropy condition. Lax-Oleinik theory. Introduction to Kruzkov theory and uniquenss for scalar law.

Prof. Praveen Chandrashekar

(TIFR-CAM)

6

Numerical methods for non-linear systems like Euler equations. Approximate Riemann solvers and other techniques to construct numerical flux. High order methods based on ENO and WENO schemes. Discontinuous Galerkin Method.

Dr. Shyam Ghoshal

(TIFR-CAM)

6

Introduction to front tracking approximations for scalar laws. Introduction to wave front tracking algorithm for system of conservation laws. Global existence of solution via front tracking. Interaction estimates.

Prof. G D Veerappa Gowda

(TIFR-CAM)

6

Solution for one dimesional Riemann Problem for scalar laws. First order Schemes. Introduction to higher order schemes. Upwind schemes of Van-Leer, ENO Schemes, Central Schemes.

Prof. K T Joseph

(TIFR-CAM)

6

Review of functions of bounded variation in one space variable. Completion of graph of a BV function. Nonconservative product, in the sense of Volpert and its generalizations. Stability under graph convergence. Applications to Riemann problem for nonconservative
hyperbolic systems. Illustrations by examples from continuum mechanics.

Dr. Ujjwal Koley

(TIFR-CAM)

6

Introduction to the hyperbolic system of conservation laws. Riemann invariants. Riemann problem for systems of conservation laws: Rarefaction waves, Shock curves, Entropy condition.

 References:

  1. Alberto Bressan, Hyperbolic System of Conservation laws. The One Dimensional Cauchy Problem. Oxford Lecture Series in Mathematics and its Applications,20. Oxford University Press, Oxford, 2000.

  2. C. Dafermos, Hyberbolic Conservation Laws in Continuum Physics, Springer-Verlag, Heidelberg (2000).

  3. E. Godlewski and P. A. Raviart, Numerical Approximation of Hyperbolic System of Conservation Laws, Springer-Verlag, New York, 1996.

  4. E. Godlewski and P. A. Raviart, Hyperbolic System of Conservation Laws, Collection Mathematiques et Applications de las SMAI, Ellipses, Paris (1991).

  5. L.C. Evans, Partial Differetial Equations, Graduate Studies in Mathematics, Vol 19, AMS 1998.

  6. H. Holden and N. H. Risebro, Front Tracking for Hyperbolic System of Conservation Laws, Springer, 2015.

  7. P. D. Lax, Hyperbolic Systems of Conservation Laws. II. Comm. Pure. Appl. Math. 10, 1957, 537-566.

  8. R. J Leveque, Numerical Methods for Conservation Laws, 2nd edition, Birkhauser, 2005.

  9. J.P.Raymond, A new definition of nonconservative product and weak stability results, Bulletino UMI (1996) 681-699.

  10. J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer Verlag, New York (1983).

  11. A.I.Volpert, The space BV and quasilinear equations, Math.Sbornik, 73 (1967) 225-267.

  12. G.Dal Maso, P.G.LeFloch and F.Murat, Definition and weak stability of nonconservative products, J.Math.Pures Appl. 74 (1995) 483-548.

 

Names of the tutors with their affiliation : 

  1. Ganesh Vaidya, Phd student, TIFR-CAM

  2. Abhishek, Phd student, TIFR-CAM

  3. Saibal Khan, Phd student, TIFR-CAM

  4. Neeraj singh, Phd student, TIFR-CAM

  5. Abhishek Das, Phd student, TIFR-CAM

  6. Animesh Jana, Phd student, TIFR-CAM

Time Table: 

WEEK I

Day

Date

Lecture 1

(9.30–11.00)

Tea

(11.05–11.25)

Lecture 2

(11.30–1.00)

Lunch

(1.05–1.55)

Lecture 3

(2.00–3.30)

Tea

(3.35-3.55)

Discussion

(4.00-5.00)

Snacks

5.05-5.35

 

 

(name of the speaker)

 

(name of the speaker)

 

(name of the speaker)

 

(Name of the tutor)

 

Mon

5th Aug, 2019

Adimurthi

 

G D Veerappa Gowda

 

Adimurthi

 

Ganesh Vaidya

 

Tues

6th Aug, 2019

G D Veerappa Gowda

 

Adimurthi

 

G D Veerappa Gowda

 

Ganesh Vaidya

 

Wed

7th Aug, 2019

Adimurthi

 

G D Veerappa Gowda

 

Adimurthi

 

Abhishek

 

Thu

8th Aug, 2019

G D Veerappa Gowda

 

Adimurthi

 

G D Veerappa Gowda

 

Abhishek

 

Fri

9th Aug, 2019

Praveen C

 

Ujjwal Koley

 

Praveen C

 

Saibal Khan

 

Sat

10th Aug, 2019

Ujjwal Koley

 

Praveen C

 

Ujjwal Koley

 

Saibal Khan

 

 

WEEK I I

Day

Date

Lecture 1

(9.30–11.00)

Tea

(11.05–11.25)

Lecture 2

(11.30–1.00)

Lunch

(1.05–1.55)

Lecture 3

(2.00–3.30)

Tea

(3.35-3.55)

Discussion

(4.00-5.00)

Snacks

5.05-5.35

 

 

(name of the speaker)

 

(name of the speaker)

 

(name of the speaker)

 

(Name of the tutor)

 

Mon

12th Aug, 2019

Praveen C

 

Ujjwal Koley

 

Praveen C

 

Neeraj Singh

 

Tues

13th Aug, 2019

Ujjwal Koley

 

Praveen C

 

Ujjwal Koley

 

Neeraj Singh

 

Wed

14th Aug, 2019

Shyam Ghoshal

 

K T Joseph

 

Shyam Ghoshal

 

Abhishek Das

 

Thu

15th Aug, 2019

K T Joseph

 

Shyam Ghoshal

 

K T Joseph

 

Abhishek Das

 

Fri

16th Aug, 2019

Shyam Ghoshal

 

K T Joseph

 

Shyam Ghoshal

 

Animesh Jana

 

Sat

17th Aug, 2019

K T Joseph

 

Shyam Ghoshal

 

K T Joseph

 

Animesh Jana

 

Selected Applicants: 

Sr.n SID Full Name Gender Affiliation Position in College/ University University/Institute M.Sc./ M.A. Year of Passing M.Sc ./M.A Ph.D. Deg Date
1 25123 Ms Jisha Cr Female SRM institute of science and technologgy phd calicut university 2013  
2 25511 Mr. Gopikrishnan C R Male Indian Institute of Technology Bombay PhD IISER Thiruvananthapuram 2015  
3 26224 Mr. Vikas Kumar Jayswal Male SRM Institute of Science and Technology PhD M.Sc. 2014  
4 26544 Mr. Mayank Singh Male IIT Roorkee PhD IIT ROORKEE 2014  
5 26645 Mr. Akshay Kumar Male University of Hyderabad PhD Banaras Hindu University 2017  
6 26863 Mr. Prashant Kumar Pandey Male Srm Institute Of Science And Technology PhD IIT MADRAS 2013  
7 27111 Mr. Bharat Soni Male Indian Institute of Technology Roorkee Research Scholar Thapar University 2017  
8 27149 Mr. Prabhat Mishra Male SRM Institute of Science & Technology, Kattankulathur (Chennai) PhD South Asian University, New Delhi 2015  
9 27619 Mr. Surya Narayan Maharana Male IIT Ropar Ph.D. South Asian Univerysity, New Delhi 2016  
10 27681 Ms. Pratibha Verma Female Indian Institute of Technology Roorkee PhD M.Sc. 2015  
11 27843 Mr. Ritesh Singla Male IIT Delhi PhD Student Tata Institute of Fundamental Research 2018  
12 28151 Mr. Manoj Kumar Male Indian Institute of Technology Mandi PhD Indian Institute of Technology Ropar 2018  
13 28160 Dr Samala Rathan Male IIT Bombay Postdoctoral fellow IIT Kharagpur 2013 21/12/2018
14 28209 Mr. Sudhir Singh Male National Institute of technology PhD student Udai Pratap Autonomous college, Varanasi M.Sc 2016  
15 28337 Mr. Joydev Halder Male University of Hyderabad PhD Student University of Hyderabad 2017  
16 28402 Ms. Pooja Gupta Female Indian Institute Of Technology ( Banaras Hindu University ) PhD Banaras Hindu University, Varanasi 2015  
17 28403 Mr. Rahul Kumar Chaturvedi Male Indian Institute of Technology (Banaras Hindu University) Varanasi Ph.D. DDU Gorakhpur University Gorakhpur 2015  
18 28404 Mr Shobhit Kumar Srivastava Male IIT(BHU) PhD DDU Gorakhpur University Gorakhpur 2014  
19 28436 Mr. Lokesh Kumar Gurjar Male IIT ROORKEE PhD National Institute Of Technology Warangal 2018  
20 28463 Ms. Divya Joseph Kayyunnapara Female Visvesvaraya Technological University, Belgaum PhD Student Bangalore University 2014  
21 28533 Mr. Anupam Sen Male Indian Institute of Technology Kharagpur Research Scholar IIT Bombay 2014  
22 28578 Mr. Rahul Barthwal Male Indian Institute of Technology Kharagpur Research Scholar MNNIT ALLAHABAD 2017  
23 28617 Mr Minhajul Islam Male Indian Institute of Technology Kharagpur PhD student Indian Institute of Technology Kharagpur 2014  
24 28683 Ms. Nikita Madaan Female Thapar Institute of Engineering and Technology, Patiala PhD Thapar university patiala 2016  
25 28685 Mr. Ankit Bhojak Male IIT Kanpur PhD Student IIT Kanpur 2016  
26 28703 Mr Ramesh Chandra Sau Male IISc Bangalore Int. PhD IISc, Bangalore 2016  
27 28705 Mr. Ravishankar Kapildev Yadav Male Indian Institute of Science Education and Research PhD Maharaja Sayajirao University of Baroda 2016  
28 28722 Mr. Anurag Kumar Male University of Delhi PhD South Asian University 2015  
29 28784 Mr. Rahul Biswas Male Indian Institute Of Science Ph.D. student Indian Institute of Science 2016  
30 28647 Mr Raghav Singhal Male Indian Institute of Technology Guwahati PhD Indian Institute of Technology Guwahati 2018 18/07/2018
31 28666 Mr. Tanay Kumar Karmakar Male Indian Institute of Technology, Hyderabad M.Sc Student Indian Institute of Technology, Hyderabad. Awaiting Result  

 Waitlisted Candidates

Sr.n SID Full Name Gender Affiliation Position in College/University University/Institute M.Sc./M.A. Year of Passing M.Sc./M.A Ph.D. Degree Date
1 28749 Mr. Anand Bharadwaj S Male Indian Institute of Technology Madras PhD Indian Institute of Technology Madras    
2 28639 Ms. Sweta Sinha Female Thapar Institute of Engineering and Technolgy, Patiala PhD(JRF) NIT Rourkela 2015  
3 28108 Mr. Abhrojyoti Sen Male National Institute of Science Education and Research PhD TIFR-CAM 2015  
4 25021 Ms Pavithra Kumar Female Anna University Ph.D RIASM University Of Madras 2014  
5 25520 Mrs Aishwarya L Female Anna University PhD Anna University 2017  
6 25009 Ms S Yaazhini Female Anna University PH.D Central University Of Tamilnadu 2016  
7 27267 Mr. Prashant F Dharwad Male Karnatak University Ph.D Student Karnatak University, Dharwad. 2018  

 

 

 

 

 

How to Reach: 

How to reach TIFR, Bangalore

* From Bangalore Internation Airport (Distance 28km)

You can hire a City taxi or private taxi from Airport to TIFR , Yelahanka new town.
Landmark : Yelahanka new town Dairy Circle

* From Bangalore City Railway Station or Majestic Bus Stand (Distance 16km)

You can hire a City Taxi or Auto Rickshaw and ask drop for Yelahanka new town. The fare for City Taxi will be approximately Rs.400. For Auto Rickshaw fare will be approximately Rs.200.

You can also use BMTC Bus service to reach TIFR. You can board into following buses which comes to Yelahanka new town bus stand.

Buses to Yelahanka new town : 402B, 402D, 284D

TIFR CAM is located walkable distance from Yelahanka new town bus stand.

You may also visit the link below https://www.math.tifrbng.res.in/contact-us for links to the route maps.

School Short Name: 

scltn

Last Date Application: 

Friday, May 31, 2019

List of Conveners: 

Shyam Sundar Ghoshal
Ujjwal Koley

School Type: 

NCMW