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.