Scalar transport using AWCM.
Research interest
- Turbulence.
- Atmospheric modelling.
- High performance computing.
Current teaching
FALL 2008
Past teaching
Mathematics 745, Fall 2006
Mathematical and Computational Fluid DynamicsMathematics 2T03, Winter, 2006
Numerical Linear Algebra
Syllabus: Mathematical Introduction to Fluid Mechanics;
Euler and Navier-Stokes equations; Mathematical properties of these systems of equations; boundary conditions, potential and rotational flow; representation of the equations in different coordinate systems; shocks, boundary layers and turbulence; limits of small and large Reynolds number
Computational Fluid Dynamics;
techniques for the numerical solution; finite volume techniques; equations with discontinuities; efficient treatment of boundary layers and high Reynolds number flows; fundamental aspects such as local and global truncation error, consistency, convergence, stability, non-uniform grids and numerical oscillations; staggered grid discretization of the incompressible Navier--Stokes equations; pressure correction scheme.
Introduction to MatLab; Numerical solution of linear systems of equations; matrix and vector norms; sensitivity, conditioning, convergence and complexity; direct and iterative methods for linear systems; eigenvalues and eigenvectors; least squares; QR factorization; Householder transformation.
Mathematics 3C03, Winter 2005
Mathematical Physics I
differential equations in physics and engineering; vector spaces and linear operators; Eigenvalue problems; Normal mode solutions; Diagonalization and quadratic forms; Ordinary differential equations; Linear equations with constant coefficients; General first- and second-order equations; Power series solutions about ordinary and regular singular points; Sturm–Liouville theory; Orthogonal polynomials; Sturm–Liouville eigenvalue problems; Fourier series expansions; Solution of partial differential equations by separation of variables; Wave and heat equation; Laplace’s equation; Schrdinger equation; Classification of partial differential equations; Solution of partial differential equations by Laplace transform and by Fourier transform