NCMW - System of Conservation Laws : Theory and Numerics

Speakers and 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

 

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