4.1 Eigenvalues and Optimization I cannot believe that I have managed to teach three lectures on spectral graph theory without giving the characterization of eigenvalues as solutions to optimization problems. It is one of the most useful ways of understanding eigenvalues of symmetric matrices. To begin, let A be a symmetric matrix with eigenvalues α1 ≥ α2 ≥ · · · ≥ αn, and corresponding orthono...

General positive-definite and monotonic limiters are described for use with unrestricted-Courant-number flux-form transport schemes. These limiters are tested using a time-split multidimensional transport scheme. The importance of minimizing the splitting errors associated with the time-split operator and of the consistency between the transport scheme and the discrete continuity equation is de...

The numerical errors associated with explicit upstream finite difference solutions of two-dimensional advectionedispersion equation with linear sorption are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation. The numerical truncation errors are defined using Peclet and Courant numbers in the X and Y direction, a sink/sou...

Six state-of-the-art large-eddy simulation codes were compared in Fedorovich et al. (Preprints, 16th American Meteorological Society Symposium on Boundary Layers and Turbulence, 2004b) for three airflow configurations in order to better understand the effect of wind shear on entrainment dynamics in the convective boundary layer CBL). One such code was the University of Oklahoma large-eddy simul...

The binary bracket of a Courant algebroid structure on (E,〈⋅,⋅〉) can be extended to n-ary Γ(E), yielding multi-Courant algebroid. These brackets form Poisson algebra and were defined, in an algebraic setting, by Keller Waldmann. We construct higher geometric version Keller-Waldmann define algebroids. As structures seen as degree 3 functions graded symplectic manifold 2, n≥3 that manifold.

In this paper, we report an extension of the Space-time Conservation Element-Solution Element (CE/SE) framework based viscous flow solver. The formulation of the Courant Number Insensitive Scheme (CNIS) is explained. The developed solver is validated through simulation of 2-D problems, such as, driven cavity, and external flow over a circular cylinder. Verifications are also conducted to study ...