# Lecture Objectives: Review discretization methods for advection diffusion equation Accuracy Numerical Stability Unsteady-state CFD Explicit vs. Implicit.

## Presentation on theme: "Lecture Objectives: Review discretization methods for advection diffusion equation Accuracy Numerical Stability Unsteady-state CFD Explicit vs. Implicit."— Presentation transcript:

Lecture Objectives: Review discretization methods for advection diffusion equation Accuracy Numerical Stability Unsteady-state CFD Explicit vs. Implicit method HW2 Turbulence

I) X direction If Vx > 0, If Vx < 0, Convection term - Upwind-scheme: W P dxw dxe E and a) and Dx Diffusion term: w e b) When mesh is uniform: DX = dxe = dxw Assumption: Source is constant over the control volume c) Source term:

Dx N Dx N+1 Different notation: Dx General equation

1D example multiple (N) volumes
N unknowns 1 2 3 i N-1 N Equation for volume 1 N equations Equation for volume 2 …………………………… Equation matrix: For 1D problem 3-diagonal matrix

3D problem Equation in the general format: H N W P E S L
Wright this equation for each discretization volume of your discretization domain A F 60,000 elements 60,000 cells (nodes) N=60,000 x = 60,000 elements 7-diagonal matrix This is the system for only one variable ( ) When we need to solve p, u, v, w, T, k, e, C system of equation is very larger

Boundary conditions for CFD application - indoor airflow
Real geometry Model geometry Where are the boundary Conditions?

CFD ACCURACY Depends on airflow in the vicinity of Boundary conditions
1) At air supply device 2) In the vicinity of occupant 3) At room surfaces Detailed modeling limited by computer power

Surface boundaries thickness mm for forced convection Wall surface W use wall functions to model the flow in the vicinity of surface Using relatively large mesh (cell) size.

Airflow at air supply devices
momentum sources Complex geometry - Δ~10-4m We can spend all our computing power for one small detail

Diffuser jet properties
High Aspiration diffuser D D L L How small cells do you need? We need simplified models for diffusers

Simulation of airflow in In the vicinity of occupants
How detailed should we make the geometry? Peter V. Nielsen