Department of Mathematics

Indian Institute Of Technology Madras , Chennai
Dr. Sanyasiraju V S S Yedida
NAC 553



Computational Fluid Dynamics


044 - 2257 4621



Teaching :

MA5490 Fluid dynamics

Kinematics of Fluid flow, Laws of fluid motion, Inviscid incompressible flows, two and three-dimensional motions, inviscid compressible flows; Viscous incompressible flows, Navier-Stokes equations of motion and some exact solutions; Flows at small Reynolds numbers; Boundary layer theory.

MA5720 Numerical analysis of differential equations

Ordinary Differential Equations: Initial value problems- basic theory and application of multistep methods (explicit and implicit), stability analysis- zero stability, absolute stability, relative stability and intervals of stability, eigenvalue problems, predictor- corrector methods, Runge-Kutta methods, boundary value problems-shooting methods. Partial Differential Equations: (a) Parabolic Equations:Explicit and implicit finite difference approximations to one-dimensional heat equation, Alternating Direction Implicit (ADI) methods. (b) Hyperbolic equations and Characteristics: Numerical integration along a characteristic, equations, numerical solution by the method of characteristics, finite diference solution of second order wave equation. (c) Elliptic equations: finite difference methods in polar coordinates, techniques near curved boundaries, improvement of accuracy- direct and iterative schemes to solve systems, methods to accelerate the convergence. (d) Convergence, consistency and stability analysis.

MA5390 Ordinary Differential equations

Existence-Uniqueness for systems: Picard’s theorem, Non-local existence theorem. (6 lectures) Second Order Equations: General solution of homogeneous equations, Non-homogeneous equations, Wronskian, Method of variation of parameters, Sturm comparison theorem, Sturm separation theorem, Boundary value problems, Green's functions, Sturm-Liouville problems. (15 lectures) Series Solution of Second Order Linear Equations: ordinary points, regular singular points, Legendre polynomials and properties, Bessel functions and properties. (15 lectures) Systems of Differential Equations: Algebraic properties of solutions of linear systems, The eigenvalueeigenvector method of finding solutions, Complex eigenvalues, Equal eigenvalues, Fundamental matrix solutions, Matrix exponential. (4 lectures)

MA5890 Numerical Linar Algebra

Floating point arithmetic (1 lecture), stability of algorithms (2 lectures), conditioning of a problem (2 lectures), perturbation analysis (2 lectures), algorithmic complexity (1 lecture), Matrix decomposition including LU, Cholesky, QR, SVD, etc. (12 lectures), Iterative techniques mainly focussing on Krylov subspace methods including Lanczos, Arnoldi, Conjugate Gradient, GMRES, etc. (12 lectures), Preconditioning (2 lectures), structured matrix computations (4 lectures), designing matrix algorithms on modern computer architectures (3 lectures).

MA5892 Numerical Methods & Scientific Computing

Part 0 Introduction, Root finding: Fixed point iteration (Newton method, Secant mathod, etc.) – Part 1: Floating point arithmetic – Part 2: Orthogonal polynomials, Polynomial Interpolation and Approximation ∗ Weierstrass approximation theorem ∗ Minimax approximation ∗ Computing the best approximation ∗ Lebesgue constants ∗ Error analysis – Part 3: Numerical Differentiation ∗ Construction of finite difference schemes ∗ Pade Approximants ∗ Error analysis ∗ Non-uniform grids – Part 4: Numerical Integration ∗ Rectangular, Trapezoidal and Simpsons rule ∗ Romberg integration and Richardson extrapolation ∗ Gaussian quadrature ∗ Adaptive quadrature ∗ Error analysis – Part 5: Transform techniques ∗ Fourier, Laplace and Chebyshev transforms ∗ Fast algorithms for above

Recent Publications :

Stefan problem coupled with natural convection: An application to dissolution process

Authors : S. Nandi and Y.V.S.S. Sanyasiraju

Journal : Physics of Fluids

Volume :36 Page: 063601 DOI:

Year: 2023

A second order accurate fixed-grid method for multi-dimensional Stefan problem with moving phase change materials

Authors : S. Nandi and Y.V.S.S. Sanyasiraju

Journal : Applied Mathematics and Computation (Elsevier)

Volume :416 Page: 126719 DOI:

Year: 2022

Investigation on the performance of meshfree RBF based method for the solution of thin film flows over topographies through depth-averaged Momentum Integral Model

Authors : S K Pal, Y V S S Sanyasiraju, R Usha

Journal : Journal of Computational Science

Volume :63 Page: 101777 DOI:

Year: 2022

A consistent energy integral model for a film over a substrate featuring topographies

Authors : Sanjib Kr Pal, Y V S S Sanyasiraju & R Usha

Journal : International Journal for Numerical Methods for Fluids

Volume :93 Page: 3424–3446 DOI: 10.1002/fld.5040

Year: 2021

Upwind Biased Local RBF Scheme with PDE Centers for the Steady Convection Diffusion Equations with Continuous and Discontinuous Boundary Conditions

Authors : K. Monysekar and Y V S S Sanyasiraju

Journal : Communications in Computational Physics

Volume :27(2) Page: 460-479 DOI: 10.4208/cicp.OA-2018-0054

Year: 2020

An ADI based body-fitted method for Stefan problem in irregular geometries

Authors : Subhankar Nandi and Y V S S Sanyasiraju

Journal : International Journal of Thermal Sciences

Volume :150 Page: 106473 DOI: 10.1016/j.ijthermalsci.2020.106473

Year: 2020