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
Centre for Applicable Mathematics, TIFR, Bangalore

6

Scalar conservation laws

Weak solutions, Rankine-Hugoniot condition, vanishing viscosity and entropy condition, convex and non-convex 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, non-conservative problems, nonlinear PDE and methods, nonlinear systems, approximate Riemann solvers, multidimensional problems

 

3

Praveen Chandrashekar
Centre for Applicable Mathematics, TIFR, Bangalore

 

10

4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Konduri Aditya
Dept. of Computational and Data Science, IISc, Bangalore

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Numerical methods for compressible flow solvers

Introduction and background:
(1) Governing equations: Burgers’ equation. Conservation of mass, momentum, energy, and scalars.
(2) Flow regimes: subsonic and supersonic, non-reacting and reacting.

Numerical schemes:
(1) Introduction to finite volume and discontinuous-Galerkin methods
(2) Numerical fluxes
(4)Time integration: multi-step (Adams-Bashforth scheme),multi-stage (low-storage Runge-Kutta schemes)
(5)Numerical properties: stability, consistency, accuracy, spectral resolution

Solvers:
(1) One-dimensional Burgers’ equation solver:implementations for smooth solutions and shocks
(2) One-dimensional compressible flow solver: schemes, algorithms,implementation
(3) Extension of the compressible flow solver to reacting flows

Research topics:
(1) Asynchronous computing: concept,asynchrony-tolerant schemes, and implementation
(2) Multi physics compressible flow solvers: challenges, advances and opportunities

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, de-aliasing and hyper-dissipation, the pseudo-spectral method, solution of Burgers and Euler equations, Chebyshev and Legendre basis for non-periodic boundary conditions, overview of spectral methods for arbitrary boundary conditions and geometry.

 

References:

  1. Godlewski E. and P-A. Raviart, Hyperbolic systems of conservation laws, Mathematiques et Applications, Ellipses, Paris, 1991.

  2. Godlewski E. and P-A. Raviart, Numerical approximation of hyperbolic systems of conservation laws, Springer, 1996.

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

  4. R. J. LeVeque, Finite-Volume methods for hyperbolic problems, Cambridge Univ. Press, 2004.

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

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

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

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

  9. Patankar, Suhas V., and D. Brian Spalding. "A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows." In Numerical prediction of flow, heat transfer, turbulence and combustion, pp. 54-73. Pergamon, 1983.

 

Names of the tutors with their affiliation:

  1. Arpit Babbar, TIFR-CAM, Bangalore

  2. Aadi Bhure, TIFR-CAM, Bangalore

  3. Rajendra Rajpoot, TIFR-CAM, Bangalore

  4. Dipti Parida, TIFR-CAM, Bangalore

  5. Shubham Kumar Goswami, CDS, IISc, Bangalore

  6. Raj Maddipati, CDS, IISc, Bangalore

 

Time Table

Tentative time-table, 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

(4.00-5.30)

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

 

 

 

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