Completed notes of the course

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Computational fluid dynamics . -- Legend New paragraph / new theorem Demonstration Definition Important CONSERVAtIOn LAWs MASS CONSERVATION INTEGraLForMI du = o 38dzt at 2. s s 2 3 t $5102dS : O WONERICau .SUERE CLTHEMATICAIL ' FARS IS HARD TO BE MANAGED MASS CONSERNATIOn IDIFFERENTIAL LAW ) 38dz = 44 Is st tJ 2."'se1d 2 ").055tar tredoz=0 78 tolre ):o DS + S0 m = o st Dt IF WE PASS FROM THE INTEGZAL TO THE BIFFERENTIAL LAW WE CAN NO CONCER DEAL WITH DISLONTINUITIES LIKE SHO WAVES CONTACT SURFACE SIIPIINE DISCONTINVITIES ADE NOT BIFFERENTIABLE COMPRESSIBLE INCOMPRESSIBLE FLOWS d I - o medoz variation OF THE VOLUME OVER TIMCJHE INTEGRaL OF THE DIVEREENCE OF VELOCITT iS THE dt fs It ] THE VOLwMt OF THE FLWID DOESN 'TCHANGE OVER tiracompressibie frow : m -- o NELOCITY FIELM THtYOF AN INCONPRESSIBLE FLOW IS SOLENOIDAL .KEEPN MIND THAT INCOMPRESSIBLEFLUIDS DON 'TEXIST :THETRE THERMOBYNAMICALTAND PH SICALLYMEANINGLESS MOMENTUM BALANCE IINTEOZAL ForMI ulalm = Ed£ doJsadranJsemoads= Js .2ds - fean." TS :SURFACE STRESS TENSOR 1 FIZ :VOLUME FERCES PRESSURE :TP=-PE Eo =88 grawit .: wiscous StrEsSES : IE MOMENTUM BALANCE (DIFFERENTIAL FORM ) J 19 u) f ( ee TPElo IE - S 5ot 1tuolgul tSeo 9=-. E-58.485 t+ sau st MASS CONSERWAtiOn e SDtr pt + - - - - c 0 IE- 5 8 VISCONS STRESS TENSOR sisu .,5E =IIL .HIPOTHESIS:ISOTZOPIC NEWTONIAN FLUID THE VISCOUSSTRESS TENSOR IS A LINEAR FUNCTIONOF THE STRAIN ZATE TENSOR - E 2 t - - ux u 1+= Z = ui + u 1! + +1 ou1,WIEre I M =MIT,P) DINAMIC WISCOSITT COEFFICIENT X= x1 x, P1 VOLME VISCOSITT COEFFICIENT -BULKVISLOSITY COEFFICIENT :neV = 3u +x . STOKES HIPOTHESIS :MVIO IT 'SVALID ONLT FOR FEW MOLECULES INOT VALID ,FOR EXAMOLE ,FOR CO 2) ENERGT BALANCE IINTEGRALFORM ) e INTERNAL ENEROT PER wir1asa .TOTALENEROT PER UNIT VOLUME :Et = get Su? SI ?:KINETIC…