FLOWPRB Tests for the FLOW routines. TEST02 R = 0.0000000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.1000 0.1000 1.0000 -0.0000 -0.2296 0.3296 0.2000 0.2000 1.0000 -0.0000 -0.4535 0.6535 0.3000 0.3000 1.0000 -0.0000 -0.6662 0.9662 0.4000 0.4000 1.0000 -0.0000 -0.8625 1.2625 0.5000 0.5000 1.0000 -0.0000 -1.0376 1.5376 0.6000 0.6000 1.0000 -0.0000 -1.1872 1.7872 0.7000 0.7000 1.0000 0.0000 -1.3075 2.0075 0.8000 0.8000 1.0000 -0.0000 -1.3956 2.1956 0.9000 0.9000 1.0000 0.0000 -1.4493 2.3493 1.0000 1.0000 1.0000 0.0000 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.5657 -0.3861 0.0000 0.0000 0.1000 0.1566 1.5463 -0.3861 -0.2296 -0.0000 0.2000 0.3093 1.4889 -0.7627 -0.4535 0.0000 0.3000 0.4543 1.3947 -1.1205 -0.6662 -0.0000 0.4000 0.5882 1.2662 -1.4507 -0.8625 0.0000 0.5000 0.7076 1.1064 -1.7452 -1.0376 0.0000 0.6000 0.8095 0.9193 -1.9967 -1.1872 -0.0000 0.7000 0.8914 0.7095 -2.1989 -1.3075 0.0000 0.8000 0.9514 0.4822 -2.3470 -1.3956 0.0000 0.9000 0.9879 0.2430 -2.4372 -1.4493 -0.0000 1.0000 1.0000 0.1211 -2.4372 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.5657 -0.3861 0.0000 0.0000 0.1000 0.1566 1.5463 -0.3861 -0.2296 -0.0000 0.2000 0.3093 1.4889 -0.7627 -0.4535 0.0000 0.3000 0.4543 1.3947 -1.1205 -0.6662 0.0000 0.4000 0.5882 1.2662 -1.4507 -0.8625 -0.0000 0.5000 0.7076 1.1064 -1.7452 -1.0376 -0.0000 0.6000 0.8095 0.9193 -1.9966 -1.1872 0.0000 0.7000 0.8914 0.7095 -2.1989 -1.3075 -0.0000 0.8000 0.9514 0.4822 -2.3470 -1.3956 0.0000 0.9000 0.9879 0.2430 -2.4372 -1.4493 -0.0000 1.0000 1.0000 0.1211 -2.4372 1.0000 0.0000 R = 0.10000000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.1000 0.1000 1.0000 -0.0000 -0.2053 0.3153 0.2000 0.2000 1.0000 -0.0000 -0.4073 0.6273 0.3000 0.3000 1.0000 -0.0000 -0.6026 0.9326 0.4000 0.4000 1.0000 -0.0000 -0.7878 1.2278 0.5000 0.5000 1.0000 -0.0000 -0.9591 1.5091 0.6000 0.6000 1.0000 -0.0000 -1.1125 1.7725 0.7000 0.7000 1.0000 0.0000 -1.2439 2.0139 0.8000 0.8000 1.0000 -0.0000 -1.3494 2.2294 0.9000 0.9000 1.0000 0.0000 -1.4251 2.4151 1.0000 1.0000 1.0000 0.0000 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.5353 -0.3690 0.0000 0.0000 0.1000 0.1535 1.5169 -0.3690 -0.2053 0.0131 0.2000 0.3034 1.4624 -0.7210 -0.4073 0.0340 0.3000 0.4460 1.3738 -1.0510 -0.6026 0.0589 0.4000 0.5781 1.2535 -1.3552 -0.7878 0.0832 0.5000 0.6967 1.1041 -1.6312 -0.9591 0.1015 0.6000 0.7990 0.9287 -1.8776 -1.1125 0.1081 0.7000 0.8824 0.7301 -2.0942 -1.2439 0.0966 0.8000 0.9450 0.5113 -2.2820 -1.3494 0.0607 0.9000 0.9847 0.2751 -2.4430 -1.4251 -0.0061 1.0000 1.0000 0.1529 -2.4430 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 -0.0000 1.5636 -0.3849 0.0000 -0.0000 0.1000 0.1564 1.5443 -0.3849 -0.2053 0.0009 0.2000 0.3089 1.4871 -0.7597 -0.4073 0.0024 0.3000 0.4538 1.3933 -1.1154 -0.6026 0.0042 0.4000 0.5875 1.2654 -1.4438 -0.7878 0.0059 0.5000 0.7069 1.1063 -1.7373 -0.9591 0.0069 0.6000 0.8088 0.9200 -1.9890 -1.1125 0.0067 0.7000 0.8909 0.7109 -2.1928 -1.2439 0.0053 0.8000 0.9510 0.4841 -2.3436 -1.3494 0.0028 0.9000 0.9877 0.2451 -2.4370 -1.4251 -0.0000 1.0000 1.0000 0.1232 -2.4370 1.0000 0.0000 R = 1.00000000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.1000 0.1000 1.0000 -0.0000 0.0131 0.1869 0.2000 0.2000 1.0000 -0.0000 0.0082 0.3918 0.3000 0.3000 1.0000 -0.0000 -0.0308 0.6308 0.4000 0.4000 1.0000 -0.0000 -0.1156 0.9156 0.5000 0.5000 1.0000 -0.0000 -0.2522 1.2522 0.6000 0.6000 1.0000 -0.0000 -0.4402 1.6402 0.7000 0.7000 1.0000 0.0000 -0.6721 2.0721 0.8000 0.8000 1.0000 -0.0000 -0.9339 2.5339 0.9000 0.9000 1.0000 0.0000 -1.2066 3.0066 1.0000 1.0000 1.0000 0.0000 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 -0.0000 1.3329 -0.2212 0.0000 -0.0000 0.1000 0.1333 1.3218 -0.2212 0.0131 0.0751 0.2000 0.2644 1.2909 -0.3958 0.0082 0.2017 0.3000 0.3915 1.2438 -0.5475 -0.0308 0.3616 0.4000 0.5131 1.1812 -0.7034 -0.1156 0.5314 0.5000 0.6277 1.1015 -0.8913 -0.2522 0.6800 0.6000 0.7334 0.9999 -1.1408 -0.4402 0.7662 0.7000 0.8277 0.8686 -1.4856 -0.6721 0.7331 0.8000 0.9071 0.6958 -1.9700 -0.9339 0.5022 0.9000 0.9669 0.4644 -2.6583 -1.2066 -0.0358 1.0000 1.0000 0.3315 -2.6583 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.4683 -0.3103 0.0000 0.0000 0.1000 0.1468 1.4528 -0.3103 0.0131 0.0367 0.2000 0.2906 1.4077 -0.5908 0.0082 0.1006 0.3000 0.4284 1.3355 -0.8535 -0.0308 0.1778 0.4000 0.5577 1.2372 -1.1139 -0.1156 0.2493 0.5000 0.6758 1.1122 -1.3861 -0.2522 0.2936 0.6000 0.7801 0.9590 -1.6776 -0.4402 0.2908 0.7000 0.8676 0.7759 -1.9835 -0.6721 0.2293 0.8000 0.9353 0.5628 -2.2786 -0.9339 0.1171 0.9000 0.9802 0.3236 -2.5059 -1.2066 -0.0019 1.0000 1.0000 0.1983 -2.5059 1.0000 0.0000 R = 10.0000000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.1000 0.1000 1.0000 -0.0000 2.1975 -1.0975 0.2000 0.2000 1.0000 -0.0000 4.1630 -1.9630 0.3000 0.3000 1.0000 -0.0000 5.6878 -2.3878 0.4000 0.4000 1.0000 -0.0000 6.6071 -2.2071 0.5000 0.5000 1.0000 -0.0000 6.8164 -1.3164 0.6000 0.6000 1.0000 -0.0000 6.2824 0.3176 0.7000 0.7000 1.0000 0.0000 5.0465 2.6535 0.8000 0.8000 1.0000 -0.0000 3.2209 5.5791 0.9000 0.9000 1.0000 0.0000 0.9777 8.9223 1.0000 1.0000 1.0000 0.0000 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 0.6776 1.1892 0.0000 0.0000 0.1000 0.0678 0.7371 1.1892 2.1975 -0.4411 0.2000 0.1474 0.8793 1.6553 4.1630 -1.0640 0.3000 0.2436 1.0395 1.5490 5.6878 -1.3626 0.4000 0.3553 1.1739 1.1393 6.6071 -0.9412 0.5000 0.4784 1.2625 0.6326 6.8164 0.3348 0.6000 0.6078 1.2989 0.0944 6.2824 2.3148 0.7000 0.7382 1.2728 -0.6157 5.0465 4.4718 0.8000 0.8624 1.1359 -2.1232 3.2209 5.3140 0.9000 0.9654 0.6880 -6.8336 0.9777 -0.2039 1.0000 1.0000 0.3463 -6.8336 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 0.5376 1.6688 0.0000 0.0000 0.1000 0.0538 0.6210 1.6688 2.1975 -0.1411 0.2000 0.1242 0.8384 2.6800 4.1630 -0.3175 0.3000 0.2214 1.1111 2.7732 5.6878 -0.2327 0.4000 0.3464 1.3516 2.0371 6.6071 0.4588 0.5000 0.4918 1.4931 0.7932 6.8164 1.8114 0.6000 0.6450 1.4963 -0.7291 6.2824 3.2857 0.7000 0.7910 1.3264 -2.6702 5.0465 3.5664 0.8000 0.9103 0.9309 -5.2401 3.2209 0.9232 0.9000 0.9772 0.4484 -4.4095 0.9777 -0.0284 1.0000 1.0000 0.2279 -4.4095 1.0000 0.0000 TEST03 R = 0.0000000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.1000 0.1000 1.0000 -0.0000 -0.2296 0.3296 0.2000 0.2000 1.0000 -0.0000 -0.4535 0.6535 0.3000 0.3000 1.0000 -0.0000 -0.6662 0.9662 0.4000 0.4000 1.0000 -0.0000 -0.8625 1.2625 0.5000 0.5000 1.0000 -0.0000 -1.0376 1.5376 0.6000 0.6000 1.0000 -0.0000 -1.1872 1.7872 0.7000 0.7000 1.0000 0.0000 -1.3075 2.0075 0.8000 0.8000 1.0000 -0.0000 -1.3956 2.1956 0.9000 0.9000 1.0000 0.0000 -1.4493 2.3493 1.0000 1.0000 1.0000 0.0000 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.5657 -0.3861 0.0000 0.0000 0.1000 0.1566 1.5463 -0.3861 -0.2296 0.0000 0.2000 0.3093 1.4889 -0.7627 -0.4535 -0.0000 0.3000 0.4543 1.3947 -1.1205 -0.6662 0.0000 0.4000 0.5882 1.2662 -1.4507 -0.8625 -0.0000 0.5000 0.7076 1.1064 -1.7452 -1.0376 0.0000 0.6000 0.8095 0.9193 -1.9967 -1.1872 -0.0000 0.7000 0.8914 0.7095 -2.1989 -1.3075 -0.0000 0.8000 0.9514 0.4822 -2.3470 -1.3956 0.0000 0.9000 0.9879 0.2430 -2.4372 -1.4493 -0.0000 1.0000 1.0000 0.1211 -2.4372 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.5657 -0.3861 0.0000 0.0000 0.1000 0.1566 1.5463 -0.3861 -0.2296 0.0000 0.2000 0.3093 1.4889 -0.7627 -0.4535 -0.0000 0.3000 0.4543 1.3947 -1.1205 -0.6662 -0.0000 0.4000 0.5882 1.2662 -1.4507 -0.8625 0.0000 0.5000 0.7076 1.1064 -1.7452 -1.0376 -0.0000 0.6000 0.8095 0.9193 -1.9967 -1.1872 -0.0000 0.7000 0.8914 0.7095 -2.1989 -1.3075 0.0000 0.8000 0.9514 0.4822 -2.3470 -1.3956 -0.0000 0.9000 0.9879 0.2430 -2.4372 -1.4493 0.0000 1.0000 1.0000 0.1211 -2.4372 1.0000 0.0000 R = 0.10000000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.1000 0.1000 1.0000 -0.0000 -0.2053 0.3153 0.2000 0.2000 1.0000 -0.0000 -0.4073 0.6273 0.3000 0.3000 1.0000 -0.0000 -0.6026 0.9326 0.4000 0.4000 1.0000 -0.0000 -0.7878 1.2278 0.5000 0.5000 1.0000 -0.0000 -0.9591 1.5091 0.6000 0.6000 1.0000 -0.0000 -1.1125 1.7725 0.7000 0.7000 1.0000 0.0000 -1.2439 2.0139 0.8000 0.8000 1.0000 -0.0000 -1.3494 2.2294 0.9000 0.9000 1.0000 0.0000 -1.4251 2.4151 1.0000 1.0000 1.0000 0.0000 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.5353 -0.3690 0.0000 0.0000 0.1000 0.1535 1.5169 -0.3690 -0.2053 0.0131 0.2000 0.3034 1.4624 -0.7210 -0.4073 0.0340 0.3000 0.4460 1.3738 -1.0510 -0.6026 0.0589 0.4000 0.5781 1.2535 -1.3552 -0.7878 0.0832 0.5000 0.6967 1.1041 -1.6312 -0.9591 0.1015 0.6000 0.7990 0.9287 -1.8776 -1.1125 0.1081 0.7000 0.8824 0.7301 -2.0942 -1.2439 0.0966 0.8000 0.9450 0.5113 -2.2820 -1.3494 0.0607 0.9000 0.9847 0.2751 -2.4430 -1.4251 -0.0061 1.0000 1.0000 0.1529 -2.4430 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.5636 -0.3849 0.0000 0.0000 0.1000 0.1564 1.5443 -0.3849 -0.2053 0.0009 0.2000 0.3089 1.4871 -0.7597 -0.4073 0.0024 0.3000 0.4538 1.3933 -1.1154 -0.6026 0.0042 0.4000 0.5875 1.2654 -1.4438 -0.7878 0.0059 0.5000 0.7069 1.1063 -1.7372 -0.9591 0.0069 0.6000 0.8088 0.9200 -1.9890 -1.1125 0.0067 0.7000 0.8909 0.7109 -2.1929 -1.2439 0.0053 0.8000 0.9510 0.4841 -2.3437 -1.3494 0.0028 0.9000 0.9877 0.2451 -2.4370 -1.4251 -0.0000 1.0000 1.0000 0.1232 -2.4370 1.0000 0.0000 R = 1.00000000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.1000 0.1000 1.0000 -0.0000 0.0131 0.1869 0.2000 0.2000 1.0000 -0.0000 0.0082 0.3918 0.3000 0.3000 1.0000 -0.0000 -0.0308 0.6308 0.4000 0.4000 1.0000 -0.0000 -0.1156 0.9156 0.5000 0.5000 1.0000 -0.0000 -0.2522 1.2522 0.6000 0.6000 1.0000 -0.0000 -0.4402 1.6402 0.7000 0.7000 1.0000 0.0000 -0.6721 2.0721 0.8000 0.8000 1.0000 -0.0000 -0.9339 2.5339 0.9000 0.9000 1.0000 0.0000 -1.2066 3.0066 1.0000 1.0000 1.0000 0.0000 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.3329 -0.2212 0.0000 0.0000 0.1000 0.1333 1.3218 -0.2212 0.0131 0.0751 0.2000 0.2644 1.2909 -0.3958 0.0082 0.2017 0.3000 0.3915 1.2438 -0.5475 -0.0308 0.3616 0.4000 0.5131 1.1812 -0.7034 -0.1156 0.5314 0.5000 0.6277 1.1015 -0.8913 -0.2522 0.6800 0.6000 0.7334 0.9999 -1.1408 -0.4402 0.7661 0.7000 0.8277 0.8686 -1.4856 -0.6721 0.7331 0.8000 0.9071 0.6958 -1.9700 -0.9339 0.5022 0.9000 0.9669 0.4644 -2.6583 -1.2066 -0.0358 1.0000 1.0000 0.3315 -2.6583 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.4683 -0.3103 0.0000 0.0000 0.1000 0.1468 1.4528 -0.3103 0.0131 0.0367 0.2000 0.2906 1.4077 -0.5908 0.0082 0.1006 0.3000 0.4284 1.3355 -0.8535 -0.0308 0.1778 0.4000 0.5577 1.2372 -1.1139 -0.1156 0.2493 0.5000 0.6758 1.1122 -1.3861 -0.2522 0.2936 0.6000 0.7801 0.9590 -1.6776 -0.4402 0.2908 0.7000 0.8676 0.7759 -1.9835 -0.6721 0.2293 0.8000 0.9353 0.5628 -2.2786 -0.9339 0.1171 0.9000 0.9802 0.3236 -2.5059 -1.2066 -0.0019 1.0000 1.0000 0.1983 -2.5059 1.0000 0.0000 R = 10.0000000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.1000 0.1000 1.0000 -0.0000 2.1975 -1.0975 0.2000 0.2000 1.0000 -0.0000 4.1630 -1.9630 0.3000 0.3000 1.0000 -0.0000 5.6878 -2.3878 0.4000 0.4000 1.0000 -0.0000 6.6071 -2.2071 0.5000 0.5000 1.0000 -0.0000 6.8164 -1.3164 0.6000 0.6000 1.0000 -0.0000 6.2824 0.3176 0.7000 0.7000 1.0000 0.0000 5.0465 2.6535 0.8000 0.8000 1.0000 -0.0000 3.2209 5.5791 0.9000 0.9000 1.0000 0.0000 0.9777 8.9223 1.0000 1.0000 1.0000 0.0000 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 0.6776 1.1892 0.0000 0.0000 0.1000 0.0678 0.7371 1.1892 2.1975 -0.4411 0.2000 0.1474 0.8793 1.6553 4.1630 -1.0640 0.3000 0.2436 1.0395 1.5490 5.6878 -1.3626 0.4000 0.3553 1.1739 1.1393 6.6071 -0.9412 0.5000 0.4784 1.2625 0.6326 6.8164 0.3348 0.6000 0.6078 1.2989 0.0944 6.2824 2.3148 0.7000 0.7382 1.2728 -0.6157 5.0465 4.4718 0.8000 0.8624 1.1359 -2.1232 3.2209 5.3140 0.9000 0.9654 0.6880 -6.8336 0.9777 -0.2039 1.0000 1.0000 0.3463 -6.8336 1.0000 0.0000 Finite difference approximation: ____X____ ____U____ __Ux_____ ___Uxx___ ___RHS___ __Resid__ 0.0000 0.0000 0.5376 1.6688 0.0000 0.0000 0.1000 0.0538 0.6210 1.6688 2.1975 -0.1411 0.2000 0.1242 0.8384 2.6800 4.1630 -0.3175 0.3000 0.2214 1.1111 2.7732 5.6878 -0.2327 0.4000 0.3464 1.3516 2.0371 6.6071 0.4588 0.5000 0.4918 1.4931 0.7932 6.8164 1.8114 0.6000 0.6450 1.4963 -0.7291 6.2824 3.2857 0.7000 0.7910 1.3264 -2.6702 5.0465 3.5664 0.8000 0.9103 0.9309 -5.2401 3.2209 0.9232 0.9000 0.9772 0.4484 -4.4095 0.9777 -0.0284 1.0000 1.0000 0.2279 -4.4095 1.0000 0.0000 FLOWPRB Normal end of FLOW tests.