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)

Recent Publications :

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