Presentation on theme: "Lecture Objectives: Review discretization methods for advection diffusion equation Accuracy Numerical Stability Unsteady-state CFD Explicit vs. Implicit."— Presentation transcript:
1 Lecture Objectives:Review discretization methods for advection diffusion equationAccuracyNumerical StabilityUnsteady-state CFDExplicit vs. Implicit methodHW2Turbulence
2 Steady–state 1D example I)X directionIf Vx > 0,If Vx < 0,Convection term - Upwind-scheme:WPdxwdxeEanda)andDxDiffusion term:web)When mesh is uniform:DX = dxe = dxwAssumption:Source is constant over the control volumec)Source term:
4 1D example multiple (N) volumes N unknowns123iN-1NEquation for volume 1NequationsEquation for volume 2……………………………Equation matrix:For 1D problem3-diagonal matrix
5 3D problem Equation in the general format: H N W P E S L Wright this equation for each discretization volumeof your discretization domainAF60,000 elements60,000 cells (nodes)N=60,000x=60,000 elements7-diagonal matrixThis is the system for onlyone variable ( )When we need to solve p, u, v, w, T, k, e, Csystem of equation is very larger
6 Boundary conditions for CFD application - indoor airflow Real geometryModel geometryWhere are the boundaryConditions?
7 CFD ACCURACY Depends on airflow in the vicinity of Boundary conditions 1) At air supply device2) In the vicinity of occupant3) At room surfacesDetailed modelinglimited bycomputer power
8 Surface boundariesthicknessmmfor forcedconvectionWall surfaceW use wall functions to model the flow in the vicinity of surfaceUsing relatively large mesh (cell) size.
9 Airflow at air supply devices momentum sourcesComplex geometry - Δ~10-4mWe can spend all ourcomputing power for one small detail
10 Diffuser jet properties High Aspiration diffuserDDLLHow small cells do you need?We need simplified models for diffusers
11 Simulation of airflow in In the vicinity of occupants How detailed should we make the geometry?Peter V. Nielsen
12 General Transport Equation Unsteady-state HNEquation in the algebraic format:WPESLWe have to solve the system matrix for each time step !Transient term:Are these values for step or + ?Unsteady-state 1-DIf: - explicit method- + - implicit method
13 General Transport Equation unsteady-state 1-D Fully explicit method:Implicit method:Value form previous time step (known value)Make the difference between- Calculation for different time step- Calculation in iteration step