Finite Volume Method for 1-D Diffusion

du ou = cliji - 241-1,1 + Uitz, AX2 2x2 Portes posing work) 2 29/01/2008 Mon-tay Fioite Volume method for 1-D Diffision Derivation of the disordiged equation 2. 1. Application of the discretized quaton to a difference problem. ( 1D only) N w E Ct Node Cosedoong one- dimensional (Exw) (on)e w e w op E W P E sw e XA neat) Ax : AyaAc-1 Q) dx d (k. dI dx ) + S = O. (iii us (dx) (5%) (1) iu + >k (is-il) 17 A w. 'e W P E.S.ils (ihill AX CA is

jik Integrating are interesting the gives in the equation. Isnaded vegion y e (K. dT d ) + S dn In Ssd. - 2 diw KiC - T.p.)- Kw (Tp-Tw) + SAX 20 - 3 (Sxile (on)w KeJe-KeJP kist (dx) $ TE ke) Tp (ve ke + (an)w the in) + Tw ( (dnyw kw ) + SAX (n)e onle [AA=b] ke E/S + the ko Tp = Key / TE H Kw TW + SAX + (5) awTwat b Finite Volume + representation apTp Method (First order Frite difference d (at + a) ( mtl MY Jxlax with dT = Tity; -Ti-w m 1/2 An da 2AX 4x tqps Aa dT = TE-TN - In 2AX K dT of / In (k.dI), Kr dI E - dr Iw 2 ax NK ke TE TP (52) N

Here we have to food 2 move nodes. ww w D2 P A2 E CE what EE second order foste differex dx d (K.dI)-0 =0. 2 (AX) f of TE= Tp + (ar (dr ) P Ax + ST) 2! Tw = TP + at + IT one Ip (An) 21 - a G (p) & TE - Tw = 2AX TE Tw CITY F 2AD 8/8 on P + Tp= TE - Tw 2AX t The (R. dT K di dn di Iw = da ) 2AX K. TEE-II Tp-Two 2AX 242. 24x K. (TEE- - 4(An)2 unit with on d (K. dig n = K [TEE- 2Tpt TWW JA 4 (Ans2 at It rss its col It XA So