NCMW  Finite Volume and Spectral Methods for Hyperbolic Problems(2023)
Speakers and Syllabus
Syllabus to be covered in terms of modules of 6 lectures each :
S.No 
Name of the Speakers with their Affiliation 
No. of Lectures 
Detailed Syllabus 
1 
G. D. Veerappa Gowda 
6 
Scalar conservation laws Weak solutions, RankineHugoniot condition, vanishing viscosity and entropy condition, convex and nonconvex problems, Riemann problem and structure of solutions, Godunov method, monotone schemes, TVD condition and high resolution methods 
2

Harish Kumar Dept. of Mathematics, IIT Delhi

6

Numerical methods for hyperbolic PDE Hyperbolic system of conservation laws, linear equations, characteristics and Riemann problem, finite volume method, high resolution methods, convergence, accuracy and stability, variable coefficients, nonconservative problems, nonlinear PDE and methods, nonlinear systems, approximate Riemann solvers, multidimensional problems

3 
Praveen Chandrashekar

10 

4

Konduri Aditya

6

Numerical methods for compressible flow solvers Introduction and background: Numerical schemes: Solvers: Research topics: 
5

Jim Thomas Centre for Applicable Mathematics, TIFR,Bangalore

6

Spectral methods for linear and nonlinear PDE Brief review of python, solvers for ordinary differential equations, introduction to Fast Fourier Transform (FFT), computing derivatives using FFT, solving linear partial differential equations using the spectral method, dealiasing and hyperdissipation, the pseudospectral method, solution of Burgers and Euler equations, Chebyshev and Legendre basis for nonperiodic boundary conditions, overview of spectral methods for arbitrary boundary conditions and geometry. 
References:

Godlewski E. and PA. Raviart, Hyperbolic systems of conservation laws, Mathematiques et Applications, Ellipses, Paris, 1991.

Godlewski E. and PA. Raviart, Numerical approximation of hyperbolic systems of conservation laws, Springer, 1996.

R. J. LeVeque, Numerical Methods for Conservation Laws, Birkhauser Verlag, 1992.

R. J. LeVeque, FiniteVolume methods for hyperbolic problems, Cambridge Univ. Press, 2004.

D. I. Ketcheson, R. J. LeVeque, M. J. del Razo, Riemann problems and Jupyter solutions, SIAM, 2020.

E. F. Toro, Riemann solvers and numerical methods for fluid dynamics, Springer, 2009.

Ferziger, Joel H., Milovan Perić, and Robert L. Street. Computational methods for fluid dynamics. Vol. 3. Berlin: springer, 2002.

Anderson, Dale, John C. Tannehill, and Richard H. Pletcher. Computational fluid mechanics and heat transfer. Taylor & Francis, 2016.

Patankar, Suhas V., and D. Brian Spalding. "A calculation procedure for heat, mass and momentum transfer in threedimensional parabolic flows." In Numerical prediction of flow, heat transfer, turbulence and combustion, pp. 5473. Pergamon, 1983.
Names of the tutors with their affiliation:

Arpit Babbar, TIFRCAM, Bangalore

Aadi Bhure, TIFRCAM, Bangalore

Rajendra Rajpoot, TIFRCAM, Bangalore

Dipti Parida, TIFRCAM, Bangalore

Shubham Kumar Goswami, CDS, IISc, Bangalore

Raj Maddipati, CDS, IISc, Bangalore
Time Table
Tentative timetable, mentioning names of the speakers and tutors with their affiliation:

Day
Date
Lecture 1
(9.30–11.00)
Tea
Lecture 2
(11.30–1.00)
Lunch
Lecture 3
(2.00–3.30)
Tea
Lecture 4
(4.005.30)
Snacks
(name of the speaker)
(name of the speaker)
(name of the speaker)
(Name of the tutor)
Mon
4/12/23
VG
PC
VG
VG/ABR/ABE
Tues
5/12/23
VG
PC
VG
PC
Wed
6/12/23
VG
PC
VG
PC/ABR/ABE
Thu
7/12/23
PC
HK
PC
HK
Fri
8/12/23
HK
PC
HK
PC/ABR/ABE
Sat
Sun
Mon
11/12/23
PC
HK
PC
HK/ABR/ABE
Tues
12/12/23
KA
JT
KA
PC/ABR/ABE
Wed
13/12/23
KA
JT
KA
JT/RR/DP
Thu
14/12/23
KA
JT
KA
KA/SKG/RM
Fri
15/12/23
JT
JT
JT
JT/RR/DP
Full forms for the abbreviations of speakers and tutors:
VG: G. D. Veerappa Gowda, HK: Harish Kumar, PC: Praveen Chandrashekar, KA: Konduri Aditya, JT: Jim Thomas, ABR: Arpit Babbar, ABE: Aadi Bhure, RR: Rajendra Rajpoot, DP: Dipti Parida, SKG: Shubham Kumar Goswami, RM: Raj Maddipati