Solução Numérica de Difusão de Calor 2D em regime permanente, em meio com prop. constantes, utilizando malha não-ortogonal Problema resolvido: 1 - Laplace linear Solução analítica: T(x,y) = x*y Malha utilizada gerada por segmentos de reta M01.txt = nome_entrada: nome do arquivo com dados sobre a malha empregada 4 = N1: Número de volumes (reais) na direção ksi 2 = N2: Número de volumes (reais) na direção eta 8 = Nt: Número total de volumes (reais) 10000 = itsolver: Número de iterações internas do solver 1000 = itmax: Número máximo de iterações externas Métricas de malha de todos os volumes (inclusive fictícios) - derivadas (i) x_ksi_e(i) y_ksi_e(i) x_ksi_n(i) y_ksi_n(i) x_eta_e(i) y_eta_e(i) x_eta_n(i) y_eta_n(i) 1 0.0000E+00 0.0000E+00 0.0000E+00 -5.0000E-01 2.5000E-01 0.0000E+00 0.0000E+00 0.0000E+00 2 0.0000E+00 0.0000E+00 0.0000E+00 -5.0000E-01 2.5000E-01 1.2500E-01 2.5000E-01 6.2500E-02 3 0.0000E+00 0.0000E+00 0.0000E+00 -5.0000E-01 2.5000E-01 2.5000E-01 2.5000E-01 1.8750E-01 4 0.0000E+00 0.0000E+00 5.0000E-01 0.0000E+00 1.2500E-01 2.5000E-01 1.8750E-01 2.5000E-01 5 0.0000E+00 0.0000E+00 5.0000E-01 0.0000E+00 0.0000E+00 2.5000E-01 6.2500E-02 2.5000E-01 6 0.0000E+00 0.0000E+00 5.0000E-01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.2500E-01 7 0.0000E+00 -4.3750E-01 0.0000E+00 -3.7500E-01 2.5000E-01 0.0000E+00 0.0000E+00 0.0000E+00 8 0.0000E+00 -4.3750E-01 0.0000E+00 -3.7500E-01 2.5000E-01 1.2500E-01 2.5000E-01 6.2500E-02 9 2.1875E-01 -2.1875E-01 0.0000E+00 -3.7500E-01 2.5000E-01 2.5000E-01 2.5000E-01 1.8750E-01 10 4.3750E-01 0.0000E+00 3.7500E-01 0.0000E+00 1.2500E-01 2.5000E-01 1.8750E-01 2.5000E-01 11 4.3750E-01 0.0000E+00 3.7500E-01 0.0000E+00 0.0000E+00 2.5000E-01 6.2500E-02 2.5000E-01 12 0.0000E+00 0.0000E+00 3.7500E-01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.2500E-01 13 0.0000E+00 -3.1250E-01 0.0000E+00 -2.5000E-01 2.5000E-01 0.0000E+00 0.0000E+00 0.0000E+00 14 0.0000E+00 -3.1250E-01 0.0000E+00 -2.5000E-01 2.5000E-01 1.2500E-01 2.5000E-01 6.2500E-02 15 1.5625E-01 -1.5625E-01 0.0000E+00 -2.5000E-01 2.5000E-01 2.5000E-01 2.5000E-01 1.8750E-01 16 3.1250E-01 0.0000E+00 2.5000E-01 0.0000E+00 1.2500E-01 2.5000E-01 1.8750E-01 2.5000E-01 17 3.1250E-01 0.0000E+00 2.5000E-01 0.0000E+00 0.0000E+00 2.5000E-01 6.2500E-02 2.5000E-01 18 0.0000E+00 0.0000E+00 2.5000E-01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.2500E-01 19 0.0000E+00 -1.2500E-01 0.0000E+00 0.0000E+00 2.5000E-01 0.0000E+00 0.0000E+00 0.0000E+00 20 0.0000E+00 -1.2500E-01 0.0000E+00 0.0000E+00 2.5000E-01 1.2500E-01 0.0000E+00 0.0000E+00 21 6.2500E-02 -6.2500E-02 0.0000E+00 0.0000E+00 2.5000E-01 2.5000E-01 0.0000E+00 0.0000E+00 22 1.2500E-01 0.0000E+00 0.0000E+00 0.0000E+00 1.2500E-01 2.5000E-01 0.0000E+00 0.0000E+00 23 1.2500E-01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 2.5000E-01 0.0000E+00 0.0000E+00 24 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 Métricas de malha de todos os volumes (inclusive fictícios) - componentes do tensor métrico e jacobianos (i) alpha(i) gama(i) beta_e(i) beta_n(i) Jp(i) Je(i) Jn(i) 1 0.0000E+00 2.5000E-01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 2 0.0000E+00 2.5000E-01 0.0000E+00 -3.1250E-02 0.0000E+00 0.0000E+00 9.1429E+00 3 0.0000E+00 2.5000E-01 0.0000E+00 -9.3750E-02 0.0000E+00 0.0000E+00 9.1429E+00 4 0.0000E+00 2.5000E-01 0.0000E+00 9.3750E-02 0.0000E+00 0.0000E+00 9.1429E+00 5 0.0000E+00 2.5000E-01 0.0000E+00 3.1250E-02 0.0000E+00 0.0000E+00 9.1429E+00 6 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 7 6.2500E-02 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 9.1429E+00 0.0000E+00 8 7.8125E-02 1.4063E-01 -5.4688E-02 -2.3438E-02 9.1429E+00 9.1429E+00 1.0971E+01 9 1.2500E-01 1.4063E-01 0.0000E+00 -7.0313E-02 9.1429E+00 9.1429E+00 1.0971E+01 10 7.8125E-02 1.4063E-01 5.4688E-02 7.0313E-02 9.1429E+00 9.1429E+00 1.0971E+01 11 6.2500E-02 1.4063E-01 0.0000E+00 2.3438E-02 9.1429E+00 9.1429E+00 1.0971E+01 12 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 13 6.2500E-02 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.2800E+01 0.0000E+00 14 7.8125E-02 6.2500E-02 -3.9063E-02 -1.5625E-02 1.2800E+01 1.2800E+01 1.2800E+01 15 1.2500E-01 6.2500E-02 0.0000E+00 -4.6875E-02 1.2800E+01 1.2800E+01 1.2800E+01 16 7.8125E-02 6.2500E-02 3.9063E-02 4.6875E-02 1.2800E+01 1.2800E+01 1.2800E+01 17 6.2500E-02 6.2500E-02 0.0000E+00 1.5625E-02 1.2800E+01 1.2800E+01 1.2800E+01 18 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 19 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 20 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 21 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 22 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 23 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 24 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 Coeficientes e termos-fontes de todos os volumes (inclusive fictícios) (i) ap(i) ae(i) aw(i) an(i) as(i) ane(i) anw(i) ase(i) asw(i) bp(i) 1 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 2 1.0000E+00 0.0000E+00 0.0000E+00 -1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 3 1.0000E+00 0.0000E+00 0.0000E+00 -1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 4 1.0000E+00 0.0000E+00 0.0000E+00 -1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 5 1.0000E+00 0.0000E+00 0.0000E+00 -1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 6 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 7 1.0000E+00 -1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 2.5000E-01 8 5.1143E+00 7.0714E-01 5.7857E-01 1.6679E+00 2.1607E+00 1.8929E-01 -6.4286E-02 -1.9643E-01 7.1429E-02 0.0000E+00 9 5.6857E+00 1.1214E+00 7.3571E-01 1.4179E+00 2.4107E+00 1.9286E-01 -3.1786E-01 -2.1429E-01 3.3929E-01 0.0000E+00 10 5.6857E+00 7.3571E-01 1.1214E+00 1.4179E+00 2.4107E+00 -3.1786E-01 1.9286E-01 3.3929E-01 -2.1429E-01 0.0000E+00 11 5.1143E+00 5.7857E-01 7.0714E-01 1.6679E+00 2.1607E+00 -6.4286E-02 1.8929E-01 7.1429E-02 -1.9643E-01 0.0000E+00 12 1.0000E+00 0.0000E+00 -1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 2.5000E-01 13 1.0000E+00 -1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 7.5000E-01 14 4.1429E+00 9.8571E-01 8.1429E-01 9.2500E-01 1.4179E+00 1.7500E-01 -5.0000E-02 -1.8929E-01 6.4286E-02 0.0000E+00 15 4.9429E+00 1.5571E+00 1.0429E+00 6.7500E-01 1.6679E+00 1.5000E-01 -2.7500E-01 -1.9286E-01 3.1786E-01 0.0000E+00 16 4.9429E+00 1.0429E+00 1.5571E+00 6.7500E-01 1.6679E+00 -2.7500E-01 1.5000E-01 3.1786E-01 -1.9286E-01 0.0000E+00 17 4.1429E+00 8.1429E-01 9.8571E-01 9.2500E-01 1.4179E+00 -5.0000E-02 1.7500E-01 6.4286E-02 -1.8929E-01 0.0000E+00 18 1.0000E+00 0.0000E+00 -1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 7.5000E-01 19 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 20 1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 -1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 8.7500E-01 21 1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 -1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 6.2500E-01 22 1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 -1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 6.2500E-01 23 1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 -1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 8.7500E-01 24 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 Campo de temperaturas (volumes reais) X [m] Y[m] Temp. numérica [°C] Temp. analítica [°C] 0.000000000000000E+00 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 7.500000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 2.500000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 2.500000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 7.500000000000000E-01 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 0.000000000000000E+00 1.250000000000000E-01 1.000000000000000E+00 1.250000000000000E-01 1.250000000000000E-01 1.190476190476190E-01 7.797619047619047E-01 8.811920092852650E-02 9.282879818594099E-02 1.190476190476190E-01 3.392857142857143E-01 3.356279790369549E-02 4.039115646258502E-02 3.392857142857143E-01 1.190476190476190E-01 3.356279790369549E-02 4.039115646258502E-02 7.797619047619047E-01 1.190476190476190E-01 8.811920092852651E-02 9.282879818594099E-02 1.000000000000000E+00 1.250000000000000E-01 1.250000000000000E-01 1.250000000000000E-01 3.750000000000000E-01 1.000000000000000E+00 3.750000000000000E-01 3.750000000000000E-01 3.666666666666667E-01 8.416666666666667E-01 3.067173119087882E-01 3.086111111111111E-01 3.666666666666667E-01 5.250000000000000E-01 1.797139376685393E-01 1.925000000000000E-01 5.250000000000000E-01 3.666666666666667E-01 1.797139376685394E-01 1.925000000000000E-01 8.416666666666667E-01 3.666666666666667E-01 3.067173119087882E-01 3.086111111111111E-01 1.000000000000000E+00 3.750000000000000E-01 3.750000000000000E-01 3.750000000000000E-01 5.000000000000000E-01 1.000000000000000E+00 5.000000000000000E-01 5.000000000000000E-01 5.000000000000000E-01 8.750000000000000E-01 4.375000000000000E-01 4.375000000000000E-01 5.000000000000000E-01 6.250000000000000E-01 3.125000000000000E-01 3.125000000000000E-01 6.250000000000000E-01 5.000000000000000E-01 3.125000000000000E-01 3.125000000000000E-01 8.750000000000000E-01 5.000000000000000E-01 4.375000000000000E-01 4.375000000000000E-01 1.000000000000000E+00 5.000000000000000E-01 5.000000000000000E-01 5.000000000000000E-01 1.368304266546746E-01 = Tm_num: Temperatura média numérica [°C] 1.458333333333333E-01 = Tm_an: Temperatura média analítica [°C]