计算流体力学（传热传质）patankar02

Back to: steady 1D heat conduction,Discretization,Discretization equation,conductances,heat generation,Source term linearization,for example when S=f(T),Nonlinearity,for example when k=f(T),the answer is iteration,Interpolation of interfacial conductivity,First guess:,Interpolation of interfacial conductivity,remember all we need is the flux,Interpolation of interfacial conductivity,remember the first guess:,for:,which one is correct?,Grid spacing,Uniform easy to set-up computationally expensive Non-uniform harder to set-up needs iteration computationally economicalBlock grids? Multi-grids?,Boundary conditions,1. Given boundary temperature simple2. Given boundary heat fluxa) as a constant b) specified via a heat transfer coefficient and the temperature of the surrounding fluid,Boundary conditions,Boundary conditions,Boundary conditions,if qB specified as a constant then:,Boundary conditions,if qB specified via a heat transfer h coefficient and the temperature of the surrounding fluid Tf :,Solution of the linear algebraic equations,Possibilities Iteration Gaussian elimination Tri-Diagonal-Matrix-Algorithm TDMA,change of notation,TDMA,what happens when a boundary temperature is given ?,TDMA,TDMA,TDMA algorithm,Calculate: P1=b1/a1 and Q1=d1/a1 Use recurrence relations to get Pi and Qi for i=2,3N.Set TN =QN Use recurrence relations to get