The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

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Numerical Heat Transfer And Fluid Flow

Most numerical integration techniques consist of approximating the integrand by a polynomial in a region or regions and then integrating the polynomial exactly. Often a complicated integrand can be factored into a non-negative ''weight'' function and another function better approximated by a polynomial, thus $\int_{a}^{b} g(t)dt = \int_{a}^{b} \omega (t)f(t)dt \approx \sum_{i=1}^{N} w_i f(t_i)$. Hopefully, the quadrature rule ${\{w_j, t_j\}}_{j=1}^{N}$ corresponding to the weight function $\omega$(t) is available in tabulated form, but more likely it is not. We present here two algorithms for generating the Gaussian quadrature rule defined by the weight function when: a) the three term recurrence relation is known for the orthogonal polynomials generated by $\omega$(t), and b) the moments of the weight function are known or can be calculated.

Calculation of Gauss quadrature rules.

Turbulence, Coherent Structures, Dynamical Systems and SymmetryP. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley, 2nd ed., Cambridge University Press, Cambridge, England, U.K., 2012, 386 pp., $90

50 years of Computational Wind Engineering: Past, present and future

This article reviews the state-of-the-art numerical calculation of wind turbine wake aerodynamics. Different computational fluid dynamics techniques for modeling the rotor and the wake are discussed. Regarding rotor modeling, recent advances in the generalized actuator approach and the direct model are discussed, as far as it attributes to the wake description. For the wake, the focus is on the different turbulence models that are employed to study wake effects on downstream turbines.

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Review of computational fluid dynamics for wind turbine wake aerodynamics

This report reviews the available literature on the aerodynamics of wind turbines and wind farms. Firstly, two introductory chapters are devoted to the physics of the flow around a wind turbine and the existing engineering models for blade and wake aerodynamics. The focus of this work is however on the numerical modeling of wakes. The difficulties in solving the Navier-Stokes equations are discussed, and the different existing models for the description of the rotor and the wake are mentioned, along with problems associated with the choice of turbulence models and inflow conditions. The purpose of this overview is to include the latest developments in the numerical computation of wind turbine aerodynamics.

Benjamin Sanderse

Papers

Review of computational fluid dynamics for wind turbine wake aerodynamics

Aerodynamics of wind turbine wakes

Accuracy analysis of explicit Runge-Kutta methods applied to the incompressible Navier-Stokes equations

Energy-conserving Runge-Kutta methods for the incompressible Navier-Stokes equations

Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods