Computational Fluid Dynamics 2

Apply periodic outlet boundary conditions to impose a fully developed inlet profile for channel flow, iterating with a zero streamwise gradient at the outlet until the flow fully develops.

Modify code to implement periodic inlet-outlet boundary conditions and a mass-conserving outlet velocity. Increase iterations to drive a fully developed flow, cycling through the domain while resolving the transverse direction.

Visualize pressure boundary conditions in channel flow using ParaView, revealing a centerline pressure distribution that forms a nearly linear profile in fully developed flow and a constant centerline velocity.

Apply a symmetry boundary on the top line, halve the channel grid, remove the upper wall, and set the top boundary velocity equal to interior values after extrapolation.

Explore symmetry boundary condition results by analyzing the cemetery plane for channel flow, with velocity reaching about 1.4976 along the center line and a matching pressure drop.

Blend first order upwind with second order central interpolation to improve convection term accuracy and introduce a deferred correction scheme for the x and y momentum equations.

Add unsteady terms to the neighbor Stoke solver for channel flow on a 300 by 60 mesh with 1200 time steps, using small iterations and higher-order terms to preserve vortices.

Analyze the flow behind a square cylinder in a channel, revealing vortex shedding and instabilities. The lecture emphasizes using higher-order upwinding to reduce artificial diffusion and preserve vortices.

Explore mesh clustering toward walls or the domain center, study the updated momentum equations and control volumes, and learn how nonuniform delta y affects indexing and code.

Add the energy equation to the code, discretize with second-order central differences, apply first-order upwind for cell-centered temperatures, and couple to momentum while handling temperature-dependent properties and buoyancy via Boussinesq.

Examine the driven cavity with a heated top wall and zero-temperature side walls, where a clockwise vortex convects heat, shaping temperature contours with no energy and momentum coupling.

Explore the Boussinesq approximation for buoyancy, treating density as constant in unsteady and convection terms and variable only in the buoyancy term, for small temperature differences.

Explore how the Boussinesq approximation drives buoyancy-induced flow in a cavity with a heated bottom plate, forming a central plume and rotating vortices, with flow depending on chosen parameters.

Explore pressure-driven flow in a duct, where inlet boundary conditions create high and low pressures that drive symmetric flow and mass flux governed by pressure gradients.

Explore a pair of parallel jets entering the lower domain, which attract, merge into a single jet that exits the domain, with a runnels number around twenty-three and magnitude contours.

Explore the viscous sublayer and log layer of a turbulent boundary layer, including y+ definitions and the choice between resolving the sublayer with dense grids or using log-law wall functions.

Derives a wall function under near-wall equilibrium by equating production and dissipation of turbulent kinetic energy, using log-layer relations to express wall shear stress and velocity scales.

Compare velocity profiles in channel flow normalized by the center line, using y/h, K Epsilon and DC models, noting developing flow and terminal viscosity, and discuss K Epsilon limitations.