Difusão de Calor 2DP em Placa Plana sem Geração de Calor ******************************************************************************************************** Parâmetros Físicos ************************************************************************************* ******************************************************************************************************** 1.000000000000000E+00 = Lx: comprimento do domínio [m] 1.000000000000000E+00 = Ly: altura do domínio [m] ******************************************************************************************************** Parâmetros Numéricos *********************************************************************************** ******************************************************************************************************** 11 = Nx: número de nós da malha, direção x 11 = Ny: número de nós da malha, direção y 1000 = itmax: número máximo de iterações a ser efetuada -1.000000000000000E-10 = tol: tolerância máxima admitida 1000 = it: iterações realizadas 2.209343819004062E-14 = L1(it): norma L1 adimensionalizada na última iteração Norma L1 com base no campo inicial de temperaturas: 6.313751514675043E+01 Norma L2 com base no campo inicial de temperaturas: 5.000000000000000E+02 Norma L-infinito com base no campo inicial de temperaturas: 1.000000000000000E+01 * Problema térmico ************************************************************************************* iteração L1(it)/L1(0) L2(it)/L2(0) Linf(it)/Linf(0) 0 1.000000000000000E+00 1.000000000000000E+00 1.000000000000000E+00 50 3.331790267161921E-03 1.489326625346721E-06 5.545956398150586E-04 100 2.205315779926758E-05 6.526042157340074E-11 3.671330468701939E-06 150 1.459161652399554E-07 2.857032308991118E-15 2.429160019801202E-08 200 9.654637946708555E-10 1.250778147059889E-19 1.607268984571419E-10 250 6.388260876008916E-12 5.476029286296109E-24 1.063416021906960E-12 300 4.231902753860043E-14 2.409074523433490E-28 7.016609515630990E-15 350 4.668606490972269E-16 1.379335618730583E-31 3.552713678800501E-16 400 3.499256842574319E-16 1.264765898198875E-31 3.552713678800501E-16 450 3.499256842574319E-16 1.264765898198875E-31 3.552713678800501E-16 500 3.499256842574319E-16 1.264765898198875E-31 3.552713678800501E-16 550 3.499256842574319E-16 1.264765898198875E-31 3.552713678800501E-16 600 3.499256842574319E-16 1.264765898198875E-31 3.552713678800501E-16 650 3.499256842574319E-16 1.264765898198875E-31 3.552713678800501E-16 700 3.499256842574319E-16 1.264765898198875E-31 3.552713678800501E-16 750 3.499256842574319E-16 1.264765898198875E-31 3.552713678800501E-16 800 3.499256842574319E-16 1.264765898198875E-31 3.552713678800501E-16 850 3.499256842574319E-16 1.264765898198875E-31 3.552713678800501E-16 900 3.499256842574319E-16 1.264765898198875E-31 3.552713678800501E-16 950 3.499256842574319E-16 1.264765898198875E-31 3.552713678800501E-16 1000 3.499256842574319E-16 1.264765898198875E-31 3.552713678800501E-16 ******************************************************************************************************** Soluções para o campo de temperaturas ****************************************************************** ******************************************************************************************************** Posição x Posição y Temp. numérica Temp. analítica Erro numérico 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 2.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 3.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 4.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 5.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 6.000000000000001E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 7.000000000000001E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 8.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 9.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 1.000000000000000E-01 8.693374621814003E-03 8.545119855814076E-03 -1.482547659999271E-04 2.000000000000000E-01 1.000000000000000E-01 1.653578116534225E-02 1.625378384279016E-02 -2.819973225520848E-04 3.000000000000000E-01 1.000000000000000E-01 2.275955023684482E-02 2.237141422046285E-02 -3.881360163819694E-04 4.000000000000000E-01 1.000000000000000E-01 2.675545595605410E-02 2.629917470342836E-02 -4.562812526257426E-04 5.000000000000000E-01 1.000000000000000E-01 2.813235123006164E-02 2.765258872929755E-02 -4.797625007640846E-04 6.000000000000001E-01 1.000000000000000E-01 2.675545595605410E-02 2.629917470342836E-02 -4.562812526257426E-04 7.000000000000001E-01 1.000000000000000E-01 2.275955023684482E-02 2.237141422046285E-02 -3.881360163819694E-04 8.000000000000000E-01 1.000000000000000E-01 1.653578116534225E-02 1.625378384279016E-02 -2.819973225520848E-04 9.000000000000000E-01 1.000000000000000E-01 8.693374621814003E-03 8.545119855814080E-03 -1.482547659999237E-04 1.000000000000000E+00 1.000000000000000E-01 0.000000000000000E+00 3.386353585753484E-18 3.386353585753484E-18 0.000000000000000E+00 2.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 2.000000000000000E-01 1.823771732191377E-02 1.794056853353554E-02 -2.971487883782313E-04 2.000000000000000E-01 2.000000000000000E-01 3.469019980271017E-02 3.412498921971752E-02 -5.652105829926507E-04 3.000000000000000E-01 2.000000000000000E-01 4.774696382598294E-02 4.696901819829290E-02 -7.779456276900409E-04 4.000000000000000E-01 2.000000000000000E-01 5.612992235730994E-02 5.521539242322671E-02 -9.145299340832316E-04 5.000000000000000E-01 2.000000000000000E-01 5.901849300813835E-02 5.805689932951472E-02 -9.615936786236262E-04 6.000000000000001E-01 2.000000000000000E-01 5.612992235730994E-02 5.521539242322670E-02 -9.145299340832386E-04 7.000000000000001E-01 2.000000000000000E-01 4.774696382598294E-02 4.696901819829290E-02 -7.779456276900409E-04 8.000000000000000E-01 2.000000000000000E-01 3.469019980271017E-02 3.412498921971753E-02 -5.652105829926368E-04 9.000000000000000E-01 2.000000000000000E-01 1.823771732191377E-02 1.794056853353555E-02 -2.971487883782209E-04 1.000000000000000E+00 2.000000000000000E-01 0.000000000000000E+00 7.109684780214984E-18 7.109684780214984E-18 0.000000000000000E+00 3.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 3.000000000000000E-01 2.956729486313089E-02 2.912129146871406E-02 -4.460033944168364E-04 2.000000000000000E-01 3.000000000000000E-01 5.624033689760170E-02 5.539198802850194E-02 -8.483488690997632E-04 3.000000000000000E-01 3.000000000000000E-01 7.740818290706683E-02 7.624053086138576E-02 -1.167652045681075E-03 4.000000000000000E-01 3.000000000000000E-01 9.099877663906437E-02 8.962611933454341E-02 -1.372657304520963E-03 5.000000000000000E-01 3.000000000000000E-01 9.568177608787190E-02 9.423847878534339E-02 -1.443297302528512E-03 6.000000000000001E-01 3.000000000000000E-01 9.099877663906437E-02 8.962611933454341E-02 -1.372657304520963E-03 7.000000000000001E-01 3.000000000000000E-01 7.740818290706683E-02 7.624053086138576E-02 -1.167652045681075E-03 8.000000000000000E-01 3.000000000000000E-01 5.624033689760170E-02 5.539198802850195E-02 -8.483488690997562E-04 9.000000000000000E-01 3.000000000000000E-01 2.956729486313089E-02 2.912129146871407E-02 -4.460033944168294E-04 1.000000000000000E+00 3.000000000000000E-01 0.000000000000000E+00 1.154050398950868E-17 1.154050398950868E-17 0.000000000000000E+00 4.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 4.000000000000000E-01 4.379112523300811E-02 4.319988756247264E-02 -5.912376705354619E-04 2.000000000000000E-01 4.000000000000000E-01 8.329567001749896E-02 8.217106913901513E-02 -1.124600878483831E-03 3.000000000000000E-01 4.000000000000000E-01 1.146466542656184E-01 1.130987739487273E-01 -1.547880316891098E-03 4.000000000000000E-01 4.000000000000000E-01 1.347752252040088E-01 1.329555827588441E-01 -1.819642445164749E-03 5.000000000000000E-01 4.000000000000000E-01 1.417110580652205E-01 1.397977727725092E-01 -1.913285292711342E-03 6.000000000000001E-01 4.000000000000000E-01 1.347752252040088E-01 1.329555827588440E-01 -1.819642445164776E-03 7.000000000000001E-01 4.000000000000000E-01 1.146466542656184E-01 1.130987739487273E-01 -1.547880316891098E-03 8.000000000000000E-01 4.000000000000000E-01 8.329567001749896E-02 8.217106913901515E-02 -1.124600878483817E-03 9.000000000000000E-01 4.000000000000000E-01 4.379112523300811E-02 4.319988756247266E-02 -5.912376705354480E-04 1.000000000000000E+00 4.000000000000000E-01 0.000000000000000E+00 1.711972407874317E-17 1.711972407874317E-17 0.000000000000000E+00 5.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 5.000000000000000E-01 6.230153605140257E-02 6.157732441181586E-02 -7.242116395867193E-04 2.000000000000000E-01 5.000000000000000E-01 1.185045636737677E-01 1.171270312757562E-01 -1.377532398011500E-03 3.000000000000000E-01 5.000000000000000E-01 1.631075389338988E-01 1.612115282464125E-01 -1.896010687486294E-03 4.000000000000000E-01 5.000000000000000E-01 1.917444118461322E-01 1.895155176055455E-01 -2.228894240586671E-03 5.000000000000000E-01 5.000000000000000E-01 2.016120057649925E-01 1.992684076691934E-01 -2.343598095799121E-03 6.000000000000001E-01 5.000000000000000E-01 1.917444118461322E-01 1.895155176055455E-01 -2.228894240586671E-03 7.000000000000001E-01 5.000000000000000E-01 1.631075389338988E-01 1.612115282464126E-01 -1.896010687486266E-03 8.000000000000000E-01 5.000000000000000E-01 1.185045636737677E-01 1.171270312757562E-01 -1.377532398011472E-03 9.000000000000000E-01 5.000000000000000E-01 6.230153605140257E-02 6.157732441181587E-02 -7.242116395867054E-04 1.000000000000000E+00 5.000000000000000E-01 0.000000000000000E+00 2.440253581477619E-17 2.440253581477619E-17 0.000000000000000E+00 6.000000000000001E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 6.000000000000001E-01 8.691045529883450E-02 8.608234924199730E-02 -8.281060568371967E-04 2.000000000000000E-01 6.000000000000001E-01 1.653135096922704E-01 1.637383583691934E-01 -1.575151323077006E-03 3.000000000000000E-01 6.000000000000001E-01 2.275345259500771E-01 2.253665161469877E-01 -2.168009803089427E-03 4.000000000000000E-01 6.000000000000001E-01 2.674828774816286E-01 2.649342291034658E-01 -2.548648378162877E-03 5.000000000000000E-01 6.000000000000001E-01 2.812481413024852E-01 2.785683338099808E-01 -2.679807492504405E-03 6.000000000000001E-01 6.000000000000001E-01 2.674828774816286E-01 2.649342291034657E-01 -2.548648378162932E-03 7.000000000000001E-01 6.000000000000001E-01 2.275345259500771E-01 2.253665161469877E-01 -2.168009803089427E-03 8.000000000000000E-01 6.000000000000001E-01 1.653135096922704E-01 1.637383583691934E-01 -1.575151323076979E-03 9.000000000000000E-01 6.000000000000001E-01 8.691045529883450E-02 8.608234924199733E-02 -8.281060568371690E-04 1.000000000000000E+00 6.000000000000001E-01 0.000000000000000E+00 3.411365515574154E-17 3.411365515574154E-17 0.000000000000000E+00 7.000000000000001E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 7.000000000000001E-01 1.200267754516650E-01 1.191534683871887E-01 -8.733070644763724E-04 2.000000000000000E-01 7.000000000000001E-01 2.283044938464024E-01 2.266433650976087E-01 -1.661128748793650E-03 3.000000000000000E-01 7.000000000000001E-01 3.142341776925105E-01 3.119478301150961E-01 -2.286347577414416E-03 4.000000000000000E-01 7.000000000000001E-01 3.694044308278203E-01 3.667166680525826E-01 -2.687762775237690E-03 5.000000000000000E-01 7.000000000000001E-01 3.884148044816910E-01 3.855887234558147E-01 -2.826081025876337E-03 6.000000000000001E-01 7.000000000000001E-01 3.694044308278203E-01 3.667166680525825E-01 -2.687762775237801E-03 7.000000000000001E-01 7.000000000000001E-01 3.142341776925105E-01 3.119478301150961E-01 -2.286347577414416E-03 8.000000000000000E-01 7.000000000000001E-01 2.283044938464024E-01 2.266433650976087E-01 -1.661128748793622E-03 9.000000000000000E-01 7.000000000000001E-01 1.200267754516650E-01 1.191534683871887E-01 -8.733070644763169E-04 1.000000000000000E+00 7.000000000000001E-01 0.000000000000000E+00 4.721944007062502E-17 4.721944007062502E-17 0.000000000000000E+00 8.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 8.000000000000000E-01 1.648921526614232E-01 1.640816041815871E-01 -8.105484798361096E-04 2.000000000000000E-01 8.000000000000000E-01 3.136435125491636E-01 3.121017577221210E-01 -1.541754827042552E-03 3.000000000000000E-01 8.000000000000000E-01 4.316932601457424E-01 4.295712166760020E-01 -2.122043469740431E-03 4.000000000000000E-01 8.000000000000000E-01 5.074858636554509E-01 5.049912519429768E-01 -2.494611712474115E-03 5.000000000000000E-01 8.000000000000000E-01 5.336022149686384E-01 5.309792249888296E-01 -2.622989979808810E-03 6.000000000000001E-01 8.000000000000000E-01 5.074858636554509E-01 5.049912519429768E-01 -2.494611712474115E-03 7.000000000000001E-01 8.000000000000000E-01 4.316932601457424E-01 4.295712166760020E-01 -2.122043469740431E-03 8.000000000000000E-01 8.000000000000000E-01 3.136435125491636E-01 3.121017577221211E-01 -1.541754827042496E-03 9.000000000000000E-01 8.000000000000000E-01 1.648921526614232E-01 1.640816041815872E-01 -8.105484798360541E-04 1.000000000000000E+00 8.000000000000000E-01 0.000000000000000E+00 6.502405326690022E-17 6.502405326690022E-17 0.000000000000000E+00 9.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 9.000000000000000E-01 2.258983226448643E-01 2.253375761602225E-01 -5.607464846417720E-04 2.000000000000000E-01 9.000000000000000E-01 4.296841435430864E-01 4.286175403466702E-01 -1.066603196416216E-03 3.000000000000000E-01 9.000000000000000E-01 5.914094866858447E-01 5.899414333299805E-01 -1.468053355864196E-03 4.000000000000000E-01 9.000000000000000E-01 6.952435486796025E-01 6.935177484552916E-01 -1.725800224310903E-03 5.000000000000000E-01 9.000000000000000E-01 7.310223280819608E-01 7.292077143395160E-01 -1.814613742444737E-03 6.000000000000001E-01 9.000000000000000E-01 6.952435486796025E-01 6.935177484552916E-01 -1.725800224310903E-03 7.000000000000001E-01 9.000000000000000E-01 5.914094866858447E-01 5.899414333299805E-01 -1.468053355864196E-03 8.000000000000000E-01 9.000000000000000E-01 4.296841435430864E-01 4.286175403466702E-01 -1.066603196416160E-03 9.000000000000000E-01 9.000000000000000E-01 2.258983226448643E-01 2.253375761602226E-01 -5.607464846416610E-04 1.000000000000000E+00 9.000000000000000E-01 0.000000000000000E+00 8.929924002364643E-17 8.929924002364643E-17 0.000000000000000E+00 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 1.000000000000000E+00 3.090169943749474E-01 3.090169943749475E-01 5.551115123125783E-17 2.000000000000000E-01 1.000000000000000E+00 5.877852522924731E-01 5.877852522924731E-01 0.000000000000000E+00 3.000000000000000E-01 1.000000000000000E+00 8.090169943749475E-01 8.090169943749475E-01 0.000000000000000E+00 4.000000000000000E-01 1.000000000000000E+00 9.510565162951535E-01 9.510565162951535E-01 0.000000000000000E+00 5.000000000000000E-01 1.000000000000000E+00 1.000000000000000E+00 1.000000000000000E+00 0.000000000000000E+00 6.000000000000001E-01 1.000000000000000E+00 9.510565162951535E-01 9.510565162951535E-01 0.000000000000000E+00 7.000000000000001E-01 1.000000000000000E+00 8.090169943749475E-01 8.090169943749475E-01 0.000000000000000E+00 8.000000000000000E-01 1.000000000000000E+00 5.877852522924733E-01 5.877852522924731E-01 -1.110223024625157E-16 9.000000000000000E-01 1.000000000000000E+00 3.090169943749475E-01 3.090169943749476E-01 5.551115123125783E-17 1.000000000000000E+00 1.000000000000000E+00 1.224606353822377E-16 1.224606353822377E-16 0.000000000000000E+00 Temperatura média (analítica): 1.858539204602858E-01 Temperatura média (numérica): 1.869150256758170E-01 Erro numérico: -1.061105215531127E-03 ******************************************************************************************************** Soluções para o campo de deslocamentos ***************************************************************** ******************************************************************************************************** Posição x Posição y Deslocamento x Deslocamento y 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 2.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 3.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 4.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 5.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 6.000000000000001E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 7.000000000000001E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 8.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 9.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 1.000000000000000E-01 -4.390607258437563E-04 -6.928204090078919E-04 2.000000000000000E-01 1.000000000000000E-01 -5.707677281161493E-04 -1.179124982114611E-03 3.000000000000000E-01 1.000000000000000E-01 -4.936119170752412E-04 -1.523074132549842E-03 4.000000000000000E-01 1.000000000000000E-01 -2.807487473379164E-04 -1.731954398240018E-03 5.000000000000000E-01 1.000000000000000E-01 3.113096787378692E-19 -1.802282089954137E-03 6.000000000000001E-01 1.000000000000000E-01 2.807487473379171E-04 -1.731954398240018E-03 7.000000000000001E-01 1.000000000000000E-01 4.936119170752417E-04 -1.523074132549842E-03 8.000000000000000E-01 1.000000000000000E-01 5.707677281161499E-04 -1.179124982114611E-03 9.000000000000000E-01 1.000000000000000E-01 4.390607258437564E-04 -6.928204090078920E-04 1.000000000000000E+00 1.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 2.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 2.000000000000000E-01 -6.830221134392091E-04 -1.250702197052056E-03 2.000000000000000E-01 2.000000000000000E-01 -9.277331043544007E-04 -2.212375486354306E-03 3.000000000000000E-01 2.000000000000000E-01 -8.222098891641510E-04 -2.906774239057045E-03 4.000000000000000E-01 2.000000000000000E-01 -4.735274544271883E-04 -3.330596741564128E-03 5.000000000000000E-01 2.000000000000000E-01 5.606150329967066E-19 -3.473477440873697E-03 6.000000000000001E-01 2.000000000000000E-01 4.735274544271893E-04 -3.330596741564128E-03 7.000000000000001E-01 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9.000000000000000E-01 1.803505803537581E-03 -4.052483231740079E-03 8.000000000000000E-01 9.000000000000000E-01 2.102175634566211E-03 -2.835575990741658E-03 9.000000000000000E-01 9.000000000000000E-01 1.633712290356309E-03 -1.357287945832937E-03 1.000000000000000E+00 9.000000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E-01 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 2.000000000000000E-01 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 3.000000000000000E-01 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 4.000000000000000E-01 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 5.000000000000000E-01 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 6.000000000000001E-01 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 7.000000000000001E-01 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 8.000000000000000E-01 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 9.000000000000000E-01 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E+00 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 Tempo de processamento (em segundos): .390