{"id": "example_airfoil", "title": "Example: inviscid NACA 0012", "description": "NACA 0012 at Mach 0.5 and 2 degrees on a 48 x 12 curved O-mesh, p = 3. Outputs, adjoint derivatives, adjoint-based error estimates and surface distributions.", "passed": true, "checks": [{"name": "converged", "value": true, "expected": "true", "passed": true}, {"name": "cl near compressible thin-aerofoil value", "value": 0.28268689801822905, "expected": "0.228 \u2026 0.317", "passed": true}, {"name": "spurious inviscid drag |cd|", "value": 0.00019844886647335871, "expected": "< 1e-3", "passed": true}, {"name": "lift-curve slope per radian", "value": 8.12012890264927, "expected": "6.5 \u2026 9.0", "passed": true}], "charts": [{"id": "cp", "type": "line", "title": "Surface pressure coefficient", "xlabel": "x / c", "ylabel": "\u2212cp", "xscale": "linear", "yscale": "linear", "series": [{"name": "upper surface", "x": [0.0, 0.0, 0.00025004178768770087, 0.001713021262396932, 0.0032699717661079475, 0.0032699717661079475, 0.005323913559431058, 0.009694759205373639, 0.013039447075451328, 0.013039447075451328, 0.01687188762038368, 0.024096544857764794, 0.029187606085500726, 0.029187606085500726, 0.0347511492989901, 0.04474027024349551, 0.051514743288339666, 0.051514743288339666, 0.05874058440926271, 0.07137063284412526, 0.07974473728383603, 0.07974473728383603, 0.08854351378670079, 0.10365829294446685, 0.11352846559395052, 0.11352846559395052, 0.12379136234203184, 0.14120394660183788, 0.15244812228691815, 0.15244812228691815, 0.1640482172573093, 0.1835432638682221, 0.19602238501491207, 0.19602238501491207, 0.20881621895281427, 0.230152631193971, 0.24371236756404344, 0.24371236756404344, 0.25754171815425914, 0.28045562699631127, 0.29492828430106643, 0.29492828430106643, 0.30962212291537444, 0.33383015030879987, 0.34903674409706004, 0.34903674409706004, 0.36441335091824156, 0.389616114351185, 0.405368583523584, 0.405368583523584, 0.4212377948881946, 0.447123609872712, 0.4632271424475832, 0.4632271424475832, 0.4793927026144056, 0.505641437312181, 0.5218968796801187, 0.5218968796801187, 0.5381588679398088, 0.5644459022568908, 0.5806522221285496, 0.5806522221285496, 0.5968095252382241, 0.6228097654263616, 0.6387665380140359, 0.6387665380140359, 0.6546193373800034, 0.6800112364957047, 0.6955211231818872, 0.6955211231818872, 0.7108733660313631, 0.7353429005313424, 0.750214089370382, 0.750214089370382, 0.7648759133510086, 0.7881204666451785, 0.8021690445161701, 0.8021690445161701, 0.8159591257381328, 0.8376912306719402, 0.8507434577462454, 0.8507434577462454, 0.8634912532285802, 0.8834421472111189, 0.8953366056060118, 0.8953366056060118, 0.9068844623945951, 0.9248074112059639, 0.9353970012518373, 0.9353970012518373, 0.945602106125429, 0.9612754552975558, 0.9704292147306974, 0.9704292147306974, 0.9791653603828883, 0.9923952764171531, 1.0, 1.0], "y": [-0.8744186457206053, -0.8666790758750142, -0.6297477344974318, -0.14733504534674413, 0.1392328599326298, 0.14060440747118808, 0.3702836464618713, 0.6403876585649053, 0.7435070472888574, 0.7428665559702337, 0.8163683416102883, 0.8853813444047667, 0.9054444944174449, 0.9057146036203019, 0.9164664800495945, 0.9181832931192444, 0.913179890196882, 0.9129504103122628, 0.9047864066762292, 0.8866669328284598, 0.8737969950304798, 0.873580904347774, 0.8595734774168831, 0.8351338889386843, 0.8195220576112323, 0.8193488904786017, 0.8032515024241826, 0.7763858172081504, 0.7596166656681032, 0.7594668464519501, 0.7424395786771294, 0.714430470736592, 0.6969606654467322, 0.6970921311714102, 0.6794796102965694, 0.6509581206068011, 0.6333967770105264, 0.6332860266863376, 0.6156752803474506, 0.5871416405062853, 0.5695699390608908, 0.5696569693270206, 0.55212395761564, 0.524042005655355, 0.5068475374020718, 0.5069097826042501, 0.48983206962963166, 0.4626030922513822, 0.44605159492845203, 0.4460126881468458, 0.429637307074227, 0.4035537436780423, 0.387736647113905, 0.3877174609031009, 0.3721104186115536, 0.3473211747379157, 0.332295159755839, 0.33229968910057384, 0.3174887705887919, 0.2939826267846941, 0.27971837555068557, 0.27972284606473696, 0.26564918374438573, 0.24325339866756135, 0.22960937390149372, 0.2296174294488722, 0.21611103708928248, 0.19449873169678167, 0.1812511836797812, 0.18124394417708434, 0.16805395917635124, 0.14675143688542303, 0.13356301638807722, 0.13356657603203725, 0.12032783232484245, 0.09870746622943294, 0.08515899527388715, 0.08515835426161278, 0.07141580276026716, 0.04864410456851065, 0.03414842836083398, 0.03415412200825241, 0.019260049462682005, -0.005887215974538229, -0.022226260287411925, -0.022252908883574563, -0.03931628112560226, -0.06910955726895907, -0.08913707642595448, -0.0897226765490382, -0.11036938797503115, -0.15159682316164425, -0.1737670788334693, -0.18106514643543647, -0.2226133697742414, -0.31153316680032095, -0.28285450064039885, -0.26339456780222736]}, {"name": "lower surface", "x": [0.00025004178768770207, 0.0017130212623969535, 0.003269971766107982, 0.003269971766107982, 0.005323913559431077, 0.009694759205373608, 0.013039447075451328, 0.013039447075451328, 0.016871887620383805, 0.02409654485776485, 0.029187606085500726, 0.029187606085500726, 0.03475114929899011, 0.04474027024349561, 0.05151474328833979, 0.05151474328833979, 0.05874058440926279, 0.07137063284412516, 0.07974473728383603, 0.07974473728383603, 0.0885435137867011, 0.1036582929444669, 0.11352846559395052, 0.11352846559395052, 0.12379136234203186, 0.14120394660183808, 0.15244812228691837, 0.15244812228691837, 0.16404821725730942, 0.18354326386822195, 0.19602238501491207, 0.19602238501491207, 0.20881621895281471, 0.2301526311939711, 0.24371236756404344, 0.24371236756404344, 0.25754171815425925, 0.28045562699631144, 0.29492828430106677, 0.29492828430106677, 0.3096221229153746, 0.3338301503087998, 0.34903674409706004, 0.34903674409706004, 0.36441335091824206, 0.38961611435118515, 0.405368583523584, 0.405368583523584, 0.42123779488819474, 0.4471236098727122, 0.46322714244758334, 0.46322714244758334, 0.4793927026144057, 0.5056414373121809, 0.5218968796801184, 0.5218968796801184, 0.5381588679398094, 0.5644459022568908, 0.5806522221285496, 0.5806522221285496, 0.5968095252382242, 0.6228097654263619, 0.6387665380140359, 0.6387665380140359, 0.6546193373800038, 0.6800112364957045, 0.695521123181887, 0.695521123181887, 0.7108733660313635, 0.7353429005313423, 0.750214089370382, 0.750214089370382, 0.7648759133510088, 0.7881204666451789, 0.8021690445161704, 0.8021690445161704, 0.8159591257381331, 0.83769123067194, 0.8507434577462454, 0.8507434577462454, 0.8634912532285808, 0.8834421472111187, 0.8953366056060118, 0.8953366056060118, 0.9068844623945953, 0.9248074112059641, 0.9353970012518376, 0.9353970012518376, 0.9456021061254292, 0.9612754552975556, 0.9704292147306974, 0.9704292147306974, 0.9791653603828887, 0.992395276417153], "y": [-1.019427813869485, -1.0479863837153642, -0.9630493596127172, -0.9688651312190366, -0.8482701147058078, -0.640161949370933, -0.522970847791103, -0.5217925760768978, -0.41605115696317174, -0.27023282379622593, -0.196492832470339, -0.19621301496744437, -0.1316970031912259, -0.04519587339621456, -0.001028429893370486, -0.000877567150714853, 0.037544787725573237, 0.08948971114227078, 0.11638755683092317, 0.11622396041838812, 0.13957621634022388, 0.17085217964584132, 0.18691110703558422, 0.1867725712942354, 0.20048930517622665, 0.21828471479105005, 0.22705550225278248, 0.22693477022311548, 0.23405501968922238, 0.24242418089639006, 0.24600832335578104, 0.24590182160295448, 0.24828111122974406, 0.2498202702202148, 0.249625730301962, 0.2495348234147876, 0.24845874104705157, 0.24503925957907313, 0.2421133765426644, 0.24204061140955968, 0.23848622000331599, 0.23155907392570896, 0.22672459834000946, 0.2266714499875686, 0.2214106700759917, 0.21212217348400042, 0.20602696347204663, 0.20599294601154927, 0.19962875902288957, 0.1888593753409431, 0.18197515764742445, 0.1819924776482651, 0.17495334919363703, 0.1633315947179632, 0.1560299380190271, 0.15602539268809412, 0.14864079642937256, 0.13655409673150842, 0.12901286193076267, 0.129009350122681, 0.12141703114846703, 0.1090263382855543, 0.101294226383291, 0.10130104055052058, 0.09351230421275858, 0.08076972162833229, 0.07278029321878066, 0.07278636436825092, 0.06469991054506163, 0.051363817940639045, 0.04293075077347197, 0.042928192129063625, 0.034323290871920875, 0.019958972135964537, 0.010762775213137843, 0.010761078595523443, 0.0012774515012186072, -0.014784588482778638, -0.025225240976882723, -0.025231355827125768, -0.036138821939048604, -0.05496824658040378, -0.06749079491663856, -0.06746280005092409, -0.08074809639687963, -0.10442484399719376, -0.12067532006021509, -0.1211640539179566, -0.1381590648600879, -0.17292726875441478, -0.19835674324396724, -0.1939994920648136, -0.23409709036886373, -0.3144281580352821]}]}, {"id": "history", "type": "history", "title": "Residual history", "xlabel": "nonlinear iteration", "ylabel": "|Rw|", "xscale": "linear", "yscale": "log", "series": [{"name": "p-multigrid Newton\u2013Krylov", "x": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], "y": [0.25452570882836245, 0.28622338089936156, 0.11197023657147456, 0.07539318201899205, 0.05655083778075168, 0.04459675904590409, 0.03606154795295917, 0.02655588062592622, 0.01642375089451567, 0.007524015519911779, 0.003303096560402598, 0.0008986753909041476, 0.0001115272015653774, 3.394212147613e-06, 3.0041496151411755e-08, 2.343314046915277e-10, 1.8255744571527087e-12]}]}, {"id": "shape_sensitivity", "type": "line", "title": "Shape sensitivity of lift: d cl / d y of each surface node", "xlabel": "x / c", "ylabel": "d cl / d y_node", "xscale": "linear", "yscale": "linear", "series": [{"name": "upper surface", "x": [0.0, 9.759519334470054e-05, 0.0008181257950519322, 0.002238925387669003, 0.0032699717661079475, 0.004495001564073969, 0.007347951503475161, 0.010892510154034148, 0.013039447075451328, 0.015376761441562952, 0.020326848070255005, 0.02595132995293762, 0.029187606085500726, 0.032608299275620194, 0.03959430449661754, 0.047229151217154104, 0.051514743288339666, 0.05597651133019762, 0.0649120386867837, 0.07446282951639413, 0.07974473728383603, 0.08519240115346725, 0.09596694430073052, 0.10731556388444172, 0.11352846559395052, 0.11989465361887171, 0.1323749629640594, 0.14538106206226384, 0.15244812228691815, 0.15965410333671234, 0.17368583394705664, 0.18818856514521035, 0.19602238501491207, 0.20397904217509386, 0.21938866257330703, 0.23520866949410987, 0.24371236756404344, 0.2523213002517052, 0.26891823849292873, 0.28585987391025414, 0.29492828430106643, 0.304083025192351, 0.32166202568186025, 0.3395157711048487, 0.34903674409706004, 0.35862407581663613, 0.37696773772135533, 0.3955127945254887, 0.405368583523584, 0.41526993881252094, 0.434151404673624, 0.4531584247340723, 0.4632271424475832, 0.47332007049363556, 0.49250583178995627, 0.5117397538472422, 0.5218968796801187, 0.5320565604762155, 0.5513093454418478, 0.5705323021222791, 0.5806522221285496, 0.5907530101312969, 0.6098347181135293, 0.6288089776530618, 0.6387665380140359, 0.648683516011682, 0.6673581620798409, 0.6858490683708455, 0.6955211231818872, 0.7051316471549626, 0.7231682805439552, 0.7409471551451067, 0.750214089370382, 0.7593993052395966, 0.7765748655355508, 0.7934218357554667, 0.8021690445161701, 0.810815358019828, 0.826917433765158, 0.8426241518446591, 0.8507434577462454, 0.8587439392691012, 0.8735733948711224, 0.8879456146357794, 0.8953366056060118, 0.9025923125859393, 0.9159657510418545, 0.9288257301591698, 0.9353970012518373, 0.9418182018099995, 0.9535702327915516, 0.9647589309238735, 0.9704292147306974, 0.975936497392504, 0.9859217826407147, 0.9953008283091606, 1.0], "y": [0.005749244847537235, -0.0781155291940082, -0.0122766333188256, -0.029851388544808163, -0.079092700599289, -0.016165684170987814, 0.0537891459783792, 0.11541331043006423, 0.013884435612385582, 0.10748638928633497, 0.0957088333590636, 0.06277788287539514, 0.019620585140036742, 0.05150917126399365, 0.06255160092198903, 0.05030629734092019, 0.021343649638167404, 0.05464319929689147, 0.07153800644506536, 0.05568152317480707, 0.02287402330258673, 0.05775636369139934, 0.07671186309767888, 0.06027658872956327, 0.02596654492560848, 0.06067119006696219, 0.07850502204741285, 0.06115969198508975, 0.02415254994038207, 0.06217672572250332, 0.08224695392215167, 0.06376721194197263, 0.024896350207831416, 0.06480014925469374, 0.08592269754285994, 0.0667460965191174, 0.025766219669323284, 0.06788002201659386, 0.09026755097061817, 0.07031751271665221, 0.026863604311346524, 0.07167507191067227, 0.09563257632454418, 0.07473431824642252, 0.028309402333665704, 0.07643580978300474, 0.10237627281215479, 0.08029564708979986, 0.03024139246030494, 0.08248053293179985, 0.11096449852507853, 0.08739787599359862, 0.03282849215028946, 0.0902450259505476, 0.12204265314875773, 0.09659407243305289, 0.03629524180567851, 0.10035187790984261, 0.13654513990560438, 0.10869239282263819, 0.04096533756638462, 0.11372924737270784, 0.1558868944440176, 0.12493126430178761, 0.04733876415064496, 0.13182773523928412, 0.18232376360319374, 0.14731511884607373, 0.056240189753046, 0.15704729634582082, 0.2196861891437318, 0.17931271727566345, 0.06913381777126947, 0.1936530453903932, 0.27502691204129764, 0.2274703942496381, 0.08886412445660986, 0.24996721807590747, 0.362832083344234, 0.3056908967660416, 0.12166922359092562, 0.34439196221190077, 0.5178961666550186, 0.44901908519152706, 0.18756867710258018, 0.5178263302280401, 0.8545649541024212, 0.7923041399522872, 0.11692304618898323, 1.4255307783286326, 1.3514441397849033, 0.6189343998532169, 3.408586820221206, 3.9174585240659265, 13.699943889277353, 8.278170693545682, -93.47091835719434]}, {"name": "lower surface", "x": [9.759519334470054e-05, 0.000818125795051941, 0.002238925387669031, 0.003269971766107982, 0.004495001564073992, 0.007347951503475161, 0.010892510154034113, 0.013039447075451328, 0.015376761441563067, 0.02032684807025509, 0.025951329952937665, 0.029187606085500726, 0.032608299275620194, 0.0395943044966176, 0.04722915121715422, 0.05151474328833979, 0.0559765113301977, 0.0649120386867837, 0.07446282951639403, 0.07974473728383603, 0.08519240115346752, 0.09596694430073073, 0.10731556388444176, 0.11352846559395052, 0.11989465361887171, 0.13237496296405948, 0.1453810620622641, 0.15244812228691837, 0.15965410333671246, 0.17368583394705664, 0.1881885651452102, 0.19602238501491207, 0.2039790421750942, 0.21938866257330733, 0.23520866949410998, 0.24371236756404344, 0.2523213002517052, 0.26891823849292884, 0.28585987391025436, 0.29492828430106677, 0.30408302519235114, 0.32166202568186025, 0.3395157711048486, 0.34903674409706004, 0.3586240758166367, 0.37696773772135544, 0.39551279452548904, 0.405368583523584, 0.41526993881252094, 0.4341514046736241, 0.45315842473407264, 0.46322714244758334, 0.47332007049363567, 0.49250583178995627, 0.5117397538472421, 0.5218968796801184, 0.5320565604762159, 0.5513093454418482, 0.5705323021222791, 0.5806522221285496, 0.5907530101312969, 0.6098347181135295, 0.6288089776530621, 0.6387665380140359, 0.6486835160116822, 0.6673581620798409, 0.6858490683708452, 0.695521123181887, 0.7051316471549629, 0.7231682805439557, 0.7409471551451067, 0.750214089370382, 0.7593993052395966, 0.776574865535551, 0.7934218357554671, 0.8021690445161704, 0.8108153580198282, 0.826917433765158, 0.842624151844659, 0.8507434577462454, 0.8587439392691016, 0.8735733948711226, 0.8879456146357794, 0.8953366056060118, 0.9025923125859393, 0.9159657510418547, 0.92882573015917, 0.9353970012518376, 0.9418182018099995, 0.9535702327915516, 0.9647589309238735, 0.9704292147306974, 0.9759364973925042, 0.9859217826407147, 0.9953008283091606], "y": [0.20623788824087325, -0.03241491009809324, -0.29507939060679766, 0.23623873269609302, -0.027585577456040712, 0.004313350059350864, 0.01476254058280817, -0.01721157470778843, 0.03434736236038124, 0.038724237939790275, 0.03181925481371039, 0.013067925859025236, 0.03486885890448915, 0.042481202128671645, 0.03501851015943105, 0.015909036645920815, 0.0382264257866124, 0.050603750253615895, 0.04074909200291018, 0.01668754734087274, 0.042578580309952416, 0.05688762348049166, 0.044929392184443924, 0.017952164471102032, 0.04651400838872089, 0.06223727169917289, 0.04886839703086001, 0.019200555295533436, 0.05029605474054757, 0.06726655622791733, 0.0527075304662895, 0.020459660657211044, 0.054096140505818006, 0.07232465832431548, 0.05665952663298194, 0.02174055342154122, 0.058211509232885185, 0.07729487853803824, 0.061532468955055784, 0.025560504727668312, 0.06348010066832105, 0.08406222179310655, 0.06612958730259766, 0.024559489802046218, 0.06818572278911528, 0.09170850885968963, 0.07232989187858518, 0.027256524618529572, 0.07469726623380099, 0.1009167636288525, 0.07983559505046622, 0.03002341284094004, 0.08279484063213181, 0.11236762405982625, 0.08926913248187733, 0.03359181585921587, 0.09307738153536377, 0.12704294504259758, 0.1014576432752425, 0.038292139685072606, 0.10648397467734837, 0.14636331891603216, 0.1176369873992688, 0.04462684318585172, 0.12445682501428437, 0.17256666480063043, 0.1397932644684586, 0.05341523426772068, 0.1493685467989573, 0.20943759629740424, 0.17135323066704725, 0.06610456824678135, 0.1854260458462798, 0.2639342325447021, 0.21877644691182546, 0.085501801168363, 0.24083154224177644, 0.3503440578763191, 0.295775140818178, 0.11777543293556274, 0.3336951766646977, 0.5029962333803876, 0.4369358737458022, 0.18249610438640246, 0.5046748026036173, 0.8342032220504721, 0.7741108696579317, 0.10962640823014302, 1.405963099843668, 1.3306140442815082, 0.6095690419298044, 4.579678421167686, 1.0118241885754142, 16.132545343820134, 15.240015604972607]}], "note": "One adjoint solve yields the sensitivity to every surface node."}], "tables": [{"id": "outputs", "title": "Outputs, adjoint derivatives and estimated discretization error", "columns": ["output", "value", "d/d\u03b1 [1/rad]", "d/dMach", "estimated error"], "rows": [["cl", 0.28268689801822905, 8.12012890264927, 0.2292193639874452, -0.002202668322225154], ["cd", 0.00019844886647335871, 0.005343024299988014, 0.00017935196500717138, 3.396142388952954e-05], ["cm", -0.0026602666502337727, -0.06736489774563614, 0.001975561309742916, null]]}, {"id": "meta", "title": "Case", "columns": ["elements", "p", "DOF", "Newton steps", "field sample"], "rows": [[576, 3, 36864, 16, "example_airfoil/field.json"]]}], "provenance": {"version": "0.4.0", "commit": "39979fcf902ad6116eb550b881b4278d4599c8e2", "dirty": false, "describe": "39979fcf90", "device": {"platform": "gpu", "device": "cuda:0", "device_kind": "NVIDIA GeForce RTX 3060 Ti", "jax": "0.11.2", "x64": true}, "timestamp": "2026-11-12T11:35:15-0500"}, "wall_time": 104.52, "level": "quick"}