Solução Numérica de Difusão de Calor 2D em regime permanente, em meio com prop. constantes, utilizando malha não-ortogonal Problema resolvido: 2 - Poisson senoidal Solução analítica: T(x,y) = sin(pi*x/2)*sin(pi*y/2) Malha utilizada gerada através da solução de eqs. elípticas E01.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 2.8123E-01 1.7080E-01 2.6562E-01 8.5402E-02 3 0.0000E+00 0.0000E+00 0.0000E+00 -5.0000E-01 3.9064E-01 3.9064E-01 3.3594E-01 2.8072E-01 4 0.0000E+00 0.0000E+00 5.0000E-01 0.0000E+00 1.7080E-01 2.8123E-01 2.8072E-01 3.3594E-01 5 0.0000E+00 0.0000E+00 5.0000E-01 0.0000E+00 0.0000E+00 2.5000E-01 8.5402E-02 2.6562E-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 1.5616E-02 -4.1460E-01 3.1232E-02 -3.2920E-01 2.5000E-01 0.0000E+00 0.0000E+00 0.0000E+00 8 3.5160E-02 -4.0234E-01 3.1232E-02 -3.2920E-01 2.8123E-01 1.7080E-01 2.5000E-01 6.2500E-02 9 2.2239E-01 -2.2239E-01 1.0941E-01 -2.8016E-01 3.9064E-01 3.9064E-01 2.5000E-01 1.8750E-01 10 4.0234E-01 -3.5160E-02 2.8016E-01 -1.0941E-01 1.7080E-01 2.8123E-01 1.8750E-01 2.5000E-01 11 4.1460E-01 -1.5616E-02 3.2920E-01 -3.1232E-02 0.0000E+00 2.5000E-01 6.2500E-02 2.5000E-01 12 0.0000E+00 0.0000E+00 3.2920E-01 -3.1232E-02 0.0000E+00 0.0000E+00 0.0000E+00 1.2500E-01 13 1.5616E-02 -2.8960E-01 0.0000E+00 -2.5000E-01 2.5000E-01 0.0000E+00 0.0000E+00 0.0000E+00 14 3.5160E-02 -2.7734E-01 0.0000E+00 -2.5000E-01 2.1877E-01 7.9196E-02 2.3438E-01 3.9598E-02 15 1.5989E-01 -1.5989E-01 0.0000E+00 -2.5000E-01 1.0936E-01 1.0936E-01 1.6406E-01 9.4278E-02 16 2.7734E-01 -3.5160E-02 2.5000E-01 0.0000E+00 7.9196E-02 2.1877E-01 9.4278E-02 1.6406E-01 17 2.8960E-01 -1.5616E-02 2.5000E-01 0.0000E+00 0.0000E+00 2.5000E-01 3.9598E-02 2.3438E-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 2.1877E-01 7.9196E-02 0.0000E+00 0.0000E+00 21 6.2500E-02 -6.2500E-02 0.0000E+00 0.0000E+00 1.0936E-01 1.0936E-01 0.0000E+00 0.0000E+00 22 1.2500E-01 0.0000E+00 0.0000E+00 0.0000E+00 7.9196E-02 2.1877E-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 -4.2701E-02 0.0000E+00 0.0000E+00 8.9720E+00 3 0.0000E+00 2.5000E-01 0.0000E+00 -1.4036E-01 0.0000E+00 0.0000E+00 6.8306E+00 4 0.0000E+00 2.5000E-01 0.0000E+00 1.4036E-01 0.0000E+00 0.0000E+00 6.8306E+00 5 0.0000E+00 2.5000E-01 0.0000E+00 4.2701E-02 0.0000E+00 0.0000E+00 8.9720E+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 3.9040E-03 0.0000E+00 0.0000E+00 8.9720E+00 0.0000E+00 8 1.0827E-01 1.0935E-01 -5.8833E-02 -1.2767E-02 8.9720E+00 7.9013E+00 1.1786E+01 9 3.0520E-01 9.0462E-02 0.0000E+00 -2.5179E-02 6.8306E+00 6.8306E+00 1.3693E+01 10 1.0827E-01 9.0462E-02 5.8833E-02 2.5179E-02 6.8306E+00 7.9013E+00 1.3693E+01 11 6.2500E-02 1.0935E-01 -3.9040E-03 1.2767E-02 8.9720E+00 8.9720E+00 1.1786E+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 3.9040E-03 0.0000E+00 0.0000E+00 1.4600E+01 0.0000E+00 14 5.4131E-02 6.2500E-02 -1.4272E-02 -9.8995E-03 1.4600E+01 1.7578E+01 1.4600E+01 15 2.3919E-02 6.2500E-02 0.0000E+00 -2.3569E-02 2.0556E+01 2.0556E+01 2.0556E+01 16 5.4131E-02 6.2500E-02 1.4272E-02 2.3569E-02 2.0556E+01 1.7578E+01 2.0556E+01 17 6.2500E-02 6.2500E-02 -3.9040E-03 9.8995E-03 1.4600E+01 1.4600E+01 1.4600E+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 3.9018E-01 8 4.9479E+00 7.9728E-01 6.1891E-01 1.4137E+00 2.1180E+00 1.5383E-01 -2.8859E-02 -2.1199E-01 8.7022E-02 1.0086E-01 9 5.8865E+00 1.9312E+00 1.0089E+00 1.1225E+00 1.8239E+00 8.6195E-02 -2.0241E-01 -2.3969E-01 3.5590E-01 9.9813E-02 10 5.8865E+00 1.0089E+00 1.9312E+00 1.1225E+00 1.8239E+00 -2.0241E-01 8.6195E-02 3.5590E-01 -2.3969E-01 9.9813E-02 11 4.9479E+00 6.1891E-01 7.9728E-01 1.4137E+00 2.1180E+00 -2.8859E-02 1.5383E-01 8.7022E-02 -2.1199E-01 1.0086E-01 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 3.9018E-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 1.1111E+00 14 4.0652E+00 9.5002E-01 9.1395E-01 9.8944E-01 1.2118E+00 9.8851E-02 -2.1883E-02 -1.0034E-01 2.3367E-02 1.8394E-01 15 3.9667E+00 5.2661E-01 9.1658E-01 1.2220E+00 1.3014E+00 1.2112E-01 -1.8384E-01 -8.6195E-02 1.4891E-01 1.1524E-01 16 3.9667E+00 9.1658E-01 5.2661E-01 1.2220E+00 1.3014E+00 -1.8384E-01 1.2112E-01 1.4891E-01 -8.6195E-02 1.1524E-01 17 4.0652E+00 9.1395E-01 9.5002E-01 9.8944E-01 1.2118E+00 -2.1883E-02 9.8851E-02 2.3367E-02 -1.0034E-01 1.8394E-01 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 1.1111E+00 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 1.3870E+00 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 1.1759E+00 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 1.1759E+00 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 1.3870E+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 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 1.950903220161283E-01 1.950903220161283E-01 1.245103211371699E-01 7.851336686066227E-01 1.683732245176298E-01 1.833717620741932E-01 1.614227177551684E-01 3.713213592176116E-01 1.187716610518432E-01 1.381593715705538E-01 3.713213592176116E-01 1.614227177551684E-01 1.187716610518432E-01 1.381593715705538E-01 7.851336686066227E-01 1.245103211371699E-01 1.683732245176299E-01 1.833717620741932E-01 1.000000000000000E+00 1.250000000000000E-01 1.950903220161283E-01 1.950903220161283E-01 3.750000000000000E-01 1.000000000000000E+00 5.555702330196022E-01 5.555702330196022E-01 3.770139073521797E-01 8.569981647306846E-01 5.494298216011643E-01 5.441743235437047E-01 4.111154415305109E-01 5.878161708725669E-01 4.627938838192472E-01 4.800242156577778E-01 5.878161708725669E-01 4.111154415305109E-01 4.627938838192473E-01 4.800242156577778E-01 8.569981647306846E-01 3.770139073521797E-01 5.494298216011643E-01 5.441743235437047E-01 1.000000000000000E+00 3.750000000000000E-01 5.555702330196022E-01 5.555702330196022E-01 5.000000000000000E-01 1.000000000000000E+00 7.071067811865475E-01 7.071067811865475E-01 5.000000000000000E-01 8.750000000000000E-01 6.935199226610737E-01 6.935199226610737E-01 5.000000000000000E-01 6.250000000000000E-01 5.879378012096793E-01 5.879378012096793E-01 6.250000000000000E-01 5.000000000000000E-01 5.879378012096793E-01 5.879378012096793E-01 8.750000000000000E-01 5.000000000000000E-01 6.935199226610737E-01 6.935199226610737E-01 1.000000000000000E+00 5.000000000000000E-01 7.071067811865475E-01 7.071067811865475E-01 2.568049280032752E-01 = Tm_num: Temperatura média numérica [°C] 2.701898230462340E-01 = Tm_an: Temperatura média analítica [°C]