18: P4est mesh from gmsh
Trixi.jl supports numerical approximations from structured and unstructured quadrilateral meshes with the P4estMesh mesh type.
The purpose of this tutorial is to demonstrate how to use the P4estMesh functionality of Trixi.jl for existing meshes with straight-sided (bilinear) elements/cells. This begins by running and visualizing an available unstructured quadrilateral mesh example. Then, the tutorial will cover how to use existing meshes generated by gmsh or any other meshing software that can export to the Abaqus input .inp format.
Running the simulation of a near-field flow around an airfoil
Trixi.jl supports solving hyperbolic-parabolic problems on several mesh types. A somewhat complex example that employs the P4estMesh is the near-field simulation of a Mach 2 flow around the NACA6412 airfoil.
using Trixi
trixi_include(joinpath(examples_dir(), "p4est_2d_dgsem",
"elixir_euler_NACA6412airfoil_mach2.jl"), tspan = (0.0, 0.5))[ Info: You just called `trixi_include`. Julia may now compile the code, please be patient.Conveniently, we use the Plots package to have a first look at the results:
using Plots
pd = PlotData2D(sol)
plot(pd["rho"])
plot!(getmesh(pd))Creating a mesh using gmsh
The creation of an unstructured quadrilateral mesh using gmsh is driven by a geometry file. There are plenty of possibilities for the user, see the documentation and tutorials.
To begin, we provide a complete geometry file for the NACA6412 airfoil bounded by a rectangular box. After this we give a breakdown of the most important parts required for successful mesh generation that can later be used by the p4est library and Trixi.jl. We emphasize that this near-field mesh should only be used for instructive purposes and not for actual production runs.
The associated NACA6412.geo file is given below:
// GMSH geometry script for a NACA 6412 airfoil with 11 degree angle of attack
// in a box (near-field mesh).
// see https://github.com/cfsengineering/GMSH-Airfoil-2D
// for software to generate gmsh `.geo` geometry files for NACA airfoils.
// outer bounding box
Point(1) = {-1.25, -0.5, 0, 1.0};
Point(2) = {1.25, -0.5, 0, 1.0};
Point(3) = {1.25, 0.5, 0, 1.0};
Point(4) = {-1.25, 0.5, 0, 1.0};
// lines of the bounding box
Line(1) = {1, 2};
Line(2) = {2, 3};
Line(3) = {3, 4};
Line(4) = {4, 1};
// outer box
Line Loop(8) = {1, 2, 3, 4};
// Settings
// This value gives the global element size factor (lower -> finer mesh)
Mesh.CharacteristicLengthFactor = 1.0 * 2^(-3);
// Insist on quads instead of default triangles
Mesh.RecombineAll = 1;
// Violet instead of green base color for better visibility
Mesh.ColorCarousel = 0;
// points of the airfoil contour
// Format: {x, y, z, DesiredCellSize}. See the documentation: https://gmsh.info/doc/texinfo/gmsh.html#Points
// These concrete points are generated using the tool from https://github.com/cfsengineering/GMSH-Airfoil-2D
Point(5) = {-0.4900332889206208, 0.09933466539753061, 0, 0.125};
Point(6) = {-0.4900274857651495, 0.1021542752054094, 0, 0.125};
Point(7) = {-0.4894921489729144, 0.1049830248247787, 0, 0.125};
Point(8) = {-0.4884253336670712, 0.1078191282319664, 0, 0.125};
Point(9) = {-0.4868257975566199, 0.1106599068424483, 0, 0.125};
Point(10) = {-0.4846930063965668, 0.1135018003016681, 0, 0.125};
Point(11) = {-0.4820271400142729, 0.1163403835785654, 0, 0.125};
Point(12) = {-0.4788290988083472, 0.1191703902233889, 0, 0.125};
Point(13) = {-0.4751005105908123, 0.1219857416089041, 0, 0.125};
Point(14) = {-0.4708437376101668, 0.1247795819332056, 0, 0.125};
Point(15) = {-0.4660618835629463, 0.1275443187232316, 0, 0.125};
Point(16) = {-0.4607588003749649, 0.1302716685409717, 0, 0.125};
Point(17) = {-0.4549390945110529, 0.132952707559475, 0, 0.125};
Point(18) = {-0.448608132554204, 0.1355779266432996, 0, 0.125};
Point(19) = {-0.4417720457819508, 0.138137290538182, 0, 0.125};
Point(20) = {-0.4344377334597768, 0.140620300747629, 0, 0.125};
Point(21) = {-0.4266128645686593, 0.1430160616500159, 0, 0.125};
Point(22) = {-0.4183058776865576, 0.1453133493887722, 0, 0.125};
Point(23) = {-0.4095259787518715, 0.147500683050503, 0, 0.125};
Point(24) = {-0.4002831364505879, 0.1495663976315875, 0, 0.125};
Point(25) = {-0.3905880749878933, 0.1514987182830453, 0, 0.125};
Point(26) = {-0.3804522640292948, 0.1532858353164163, 0, 0.125};
Point(27) = {-0.3698879056254708, 0.1549159794501833, 0, 0.125};
Point(28) = {-0.3589079179688306, 0.1563774967770029, 0, 0.125};
Point(29) = {-0.3475259158676376, 0.1576589229368209, 0, 0.125};
Point(30) = {-0.3357561878650377, 0.158749055989923, 0, 0.125};
Point(31) = {-0.3236136699747923, 0.1596370274972017, 0, 0.125};
Point(32) = {-0.3111139160522804, 0.1603123713324616, 0, 0.125};
Point(33) = {-0.298273064867608, 0.160765089773461, 0, 0.125};
Point(34) = {-0.2851078039966239, 0.1609857164445887, 0, 0.125};
Point(35) = {-0.2716353306943914, 0.160965375714529, 0, 0.125};
Point(36) = {-0.2578733099632437, 0.1606958381868515, 0, 0.125};
Point(37) = {-0.2438398300730194, 0.1601695719599709, 0, 0.125};
Point(38) = {-0.2295533558334121, 0.1593797893750759, 0, 0.125};
Point(39) = {-0.2150326799566391, 0.1583204890160489, 0, 0.125};
Point(40) = {-0.2002968728818922, 0.1569864927736143, 0, 0.125};
Point(41) = {-0.18536523146042, 0.1553734778363979, 0, 0.125};
Point(42) = {-0.1702572269208345, 0.1534780035235666, 0, 0.125};
Point(43) = {-0.1549924525477129, 0.1512975329264932, 0, 0.125};
Point(44) = {-0.1395905715122586, 0.1488304493795921, 0, 0.125};
Point(45) = {-0.1240712652914332, 0.1460760678321895, 0, 0.125};
Point(46) = {-0.1084541831014299, 0.1430346412430583, 0, 0.125};
Point(47) = {-0.09275889275279087, 0.1397073621660917, 0, 0.125};
Point(48) = {-0.07700483330818747, 0.1360963597385416, 0, 0.125};
Point(49) = {-0.06151286635366404, 0.1323050298149023, 0, 0.125};
Point(50) = {-0.04602933219022032, 0.1283521764905442, 0, 0.125};
Point(51) = {-0.03051345534800332, 0.1242331665904082, 0, 0.125};
Point(52) = {-0.01498163190522334, 0.1199540932779839, 0, 0.125};
Point(53) = {0.0005498526140696458, 0.1155214539466913, 0, 0.125};
Point(54) = {0.01606484191716884, 0.1109421303284033, 0, 0.125};
Point(55) = {0.03154732664394777, 0.106223368423828, 0, 0.125};
Point(56) = {0.0469814611314705, 0.1013727584299359, 0, 0.125};
Point(57) = {0.06235157928986135, 0.09639821481480275, 0, 0.125};
Point(58) = {0.07764220964363855, 0.09130795666388933, 0, 0.125};
Point(59) = {0.09283808959671735, 0.08611048839446452, 0, 0.125};
Point(60) = {0.1079241789809607, 0.08081458090718853, 0, 0.125};
Point(61) = {0.1228856729475325, 0.07542925321638272, 0, 0.125};
Point(62) = {0.1377080142575372, 0.06996375457378261, 0, 0.125};
Point(63) = {0.1523769050236616, 0.06442754707512513, 0, 0.125};
Point(64) = {0.1668783179480157, 0.05883028871526293, 0, 0.125};
Point(65) = {0.1811985070933818, 0.05318181683604975, 0, 0.125};
Point(66) = {0.1953240182159306, 0.04749213189240609, 0, 0.125};
Point(67) = {0.2092416986775084, 0.04177138144606024, 0, 0.125};
Point(68) = {0.2229387069452062, 0.03602984428372727, 0, 0.125};
Point(69) = {0.2364025216754475, 0.03027791454712048, 0, 0.125};
Point(70) = {0.2496209503696738, 0.02452608575629232, 0, 0.125};
Point(71) = {0.2625821375791982, 0.01878493460541621, 0, 0.125};
Point(72) = {0.2752745726282818, 0.01306510441121807, 0, 0.125};
Point(73) = {0.28768709681727, 0.007377288098728577, 0, 0.125};
Point(74) = {0.2998089100619555, 0.001732210616722449, 0, 0.125};
Point(75) = {0.3116295769214332, -0.003859389314124759, 0, 0.125};
Point(76) = {0.3231390319647309, -0.009386778203927332, 0, 0.125};
Point(77) = {0.3343275844265582, -0.01483924761490708, 0, 0.125};
Point(78) = {0.3451859221046181, -0.02020613485126957, 0, 0.125};
Point(79) = {0.3557051144551212, -0.02547684454806881, 0, 0.125};
Point(80) = {0.3658766148492779, -0.03064087116872238, 0, 0.125};
Point(81) = {0.3756922619615632, -0.0356878223992288, 0, 0.125};
Point(82) = {0.3851442802702071, -0.0406074434050937, 0, 0.125};
Point(83) = {0.394225279661484, -0.04538964189492445, 0, 0.125};
Point(84) = {0.4029282541416501, -0.05002451391298904, 0, 0.125};
Point(85) = {0.4112465796735204, -0.05450237026215737, 0, 0.125};
Point(86) = {0.4191740111683733, -0.05881376343890812, 0, 0.125};
Point(87) = {0.4267046786777481, -0.06294951494382847, 0, 0.125};
Point(88) = {0.4338330828434404, -0.06690074281456823, 0, 0.125};
Point(89) = {0.4405540896772232, -0.07065888921378868, 0, 0.125};
Point(90) = {0.4468629247542237, -0.07421574789251445, 0, 0.125};
Point(91) = {0.4527551669150955, -0.0775634913396257, 0, 0.125};
Point(92) = {0.4582267415819197, -0.08069469742118066, 0, 0.125};
Point(93) = {0.4632739138007936, -0.08360237530891265, 0, 0.125};
Point(94) = {0.4678932811302005, -0.08627999049569551, 0, 0.125};
Point(95) = {0.4720817664982195, -0.08872148869699745, 0, 0.125};
Point(96) = {0.4758366111533843, -0.09092131844134463, 0, 0.125};
Point(97) = {0.4791553678333992, -0.09287445215953141, 0, 0.125};
Point(98) = {0.4820358942729613, -0.09457640559161551, 0, 0.125};
Point(99) = {0.4844763471666588, -0.09602325534252773, 0, 0.125};
Point(100) = {0.4864751766953637, -0.09721165443119822, 0, 0.125};
Point(101) = {0.4880311217148797, -0.09813884569428721, 0, 0.125};
Point(102) = {0.4891432056939881, -0.09880267292366274, 0, 0.125};
Point(103) = {0.4898107334756874, -0.09920158963645126, 0, 0.125};
Point(104) = {0.4900332889206208, -0.09933466539753058, 0, 0.125};
Point(105) = {0.4897824225031319, -0.09926905587549506, 0, 0.125};
Point(106) = {0.4890301110661922, -0.09907236506934192, 0, 0.125};
Point(107) = {0.4877772173496635, -0.09874500608402761, 0, 0.125};
Point(108) = {0.48602517690576, -0.09828766683852558, 0, 0.125};
Point(109) = {0.4837759946062035, -0.09770130916007558, 0, 0.125};
Point(110) = {0.4810322398085871, -0.09698716747297723, 0, 0.125};
Point(111) = {0.4777970402368822, -0.09614674703990023, 0, 0.125};
Point(112) = {0.4740740746447117, -0.09518182170326678, 0, 0.125};
Point(113) = {0.4698675643422793, -0.09409443106501386, 0, 0.125};
Point(114) = {0.4651822636784212, -0.09288687703518478, 0, 0.125};
Point(115) = {0.460023449577924, -0.09156171967354482, 0, 0.125};
Point(116) = {0.4543969102408585, -0.09012177224394632, 0, 0.125};
Point(117) = {0.4483089331151018, -0.08857009539864649, 0, 0.125};
Point(118) = {0.4417662922553667, -0.08690999040934186, 0, 0.125};
Point(119) = {0.4347762351819332, -0.0851449913634191, 0, 0.125};
Point(120) = {0.4273464693498908, -0.08327885624791403, 0, 0.125};
Point(121) = {0.419485148335155, -0.08131555684993674, 0, 0.125};
Point(122) = {0.411200857836944, -0.07925926741086739, 0, 0.125};
Point(123) = {0.4025026015879757, -0.07711435198240155, 0, 0.125};
Point(124) = {0.3933997872536054, -0.07488535044544484, 0, 0.125};
Point(125) = {0.3839022123897198, -0.07257696316779733, 0, 0.125};
Point(126) = {0.3740200505167618, -0.07019403429336624, 0, 0.125};
Point(127) = {0.3637638373540689, -0.06774153367408606, 0, 0.125};
Point(128) = {0.3531444572451353, -0.06522453747557577, 0, 0.125};
Point(129) = {0.3421731297908021, -0.06264820750853495, 0, 0.125};
Point(130) = {0.3308613966940724, -0.06001776935966011, 0, 0.125};
Point(131) = {0.3192211088076166, -0.05733848941811218, 0, 0.125};
Point(132) = {0.3072644133633567, -0.05461565091590426, 0, 0.125};
Point(133) = {0.2950037413531683, -0.05185452912263369, 0, 0.125};
Point(134) = {0.2824517950208982, -0.04906036585632723, 0, 0.125};
Point(135) = {0.2696215354188702, -0.04623834349241404, 0, 0.125};
Point(136) = {0.2565261699769623, -0.04339355867155523, 0, 0.125};
Point(137) = {0.2431791400293651, -0.04053099592384862, 0, 0.125};
Point(138) = {0.2295941082432855, -0.03765550144139543, 0, 0.125};
Point(139) = {0.2157849458952252, -0.03477175724299444, 0, 0.125};
Point(140) = {0.2017657199439165, -0.03188425598348005, 0, 0.125};
Point(141) = {0.187550679854507, -0.02899727666564914, 0, 0.125};
Point(142) = {0.1731542441359161, -0.02611486151457043, 0, 0.125};
Point(143) = {0.1585909865622793, -0.02324079427214604, 0, 0.125};
Point(144) = {0.1438756220597465, -0.02037858016395433, 0, 0.125};
Point(145) = {0.129022992251319, -0.0175314277805827, 0, 0.125};
Point(146) = {0.1140480506645569, -0.01470223310184333, 0, 0.125};
Point(147) = {0.09896584761949168, -0.01189356587453844, 0, 0.125};
Point(148) = {0.08379151482656089, -0.009107658532933174, 0, 0.125};
Point(149) = {0.06854024973648176, -0.006346397826038436, 0, 0.125};
Point(150) = {0.05322729969528361, -0.003611319287478529, 0, 0.125};
Point(151) = {0.03786794596792287, -0.00090360465249055, 0, 0.125};
Point(152) = {0.0224774877026287, 0.00177591770710904, 0, 0.125};
Point(153) = {0.007071225915134205, 0.004426769294862437, 0, 0.125};
Point(154) = {-0.00833555242305456, 0.007048814950562587, 0, 0.125};
Point(155) = {-0.02372759010533726, 0.009642253300220296, 0, 0.125};
Point(156) = {-0.03908967513210498, 0.01220760427359278, 0, 0.125};
Point(157) = {-0.05440665578848514, 0.01474569380579989, 0, 0.125};
Point(158) = {-0.06966345527617318, 0.01725763587663899, 0, 0.125};
Point(159) = {-0.08484508582421563, 0.01974481207672138, 0, 0.125};
Point(160) = {-0.09987987792382108, 0.02219618763023203, 0, 0.125};
Point(161) = {-0.1145078729404739, 0.02450371976411331, 0, 0.125};
Point(162) = {-0.1290321771824579, 0.0267015185742735, 0, 0.125};
Point(163) = {-0.143440065923266, 0.02879471001709845, 0, 0.125};
Point(164) = {-0.1577189448447794, 0.03078883518202784, 0, 0.125};
Point(165) = {-0.1718563428491159, 0.03268980457290044, 0, 0.125};
Point(166) = {-0.1858399037768357, 0.03450385196323842, 0, 0.125};
Point(167) = {-0.1996573773370766, 0.03623748825421298, 0, 0.125};
Point(168) = {-0.2132966095779342, 0.03789745574015834, 0, 0.125};
Point(169) = {-0.2267455332406906, 0.0394906831577609, 0, 0.125};
Point(170) = {-0.2399921583489679, 0.04102424186233269, 0, 0.125};
Point(171) = {-0.2530245633834605, 0.04250530343879837, 0, 0.125};
Point(172) = {-0.2658308873846617, 0.04394109901707172, 0, 0.125};
Point(173) = {-0.2783993233102972, 0.04533888052223981, 0, 0.125};
Point(174) = {-0.2907181129514687, 0.04670588405019788, 0, 0.125};
Point(175) = {-0.3027755436824813, 0.0480492955198111, 0, 0.125};
Point(176) = {-0.3145599472847223, 0.04937621871394801, 0, 0.125};
Point(177) = {-0.3260597010456697, 0.05069364578437131, 0, 0.125};
Point(178) = {-0.337263231291058, 0.05200843025992359, 0, 0.125};
Point(179) = {-0.3481590194623916, 0.05332726256406103, 0, 0.125};
Point(180) = {-0.3587356108043638, 0.05465664801682354, 0, 0.125};
Point(181) = {-0.3689816256782782, 0.0560028872679817, 0, 0.125};
Point(182) = {-0.3788857734692287, 0.05737205908247899, 0, 0.125};
Point(183) = {-0.3884368690074614, 0.05877000537646382, 0, 0.125};
Point(184) = {-0.3976238513788748, 0.06020231838219783, 0, 0.125};
Point(185) = {-0.40643580495675, 0.06167432980291591, 0, 0.125};
Point(186) = {-0.4148619824472646, 0.06319110180426264, 0, 0.125};
Point(187) = {-0.4228918297057104, 0.06475741967717524, 0, 0.125};
Point(188) = {-0.43051501204915, 0.06637778599795482, 0, 0.125};
Point(189) = {-0.4377214417649294, 0.06805641610468524, 0, 0.125};
Point(190) = {-0.4445013064933708, 0.06979723470503821, 0, 0.125};
Point(191) = {-0.4508450981473512, 0.07160387342876083, 0, 0.125};
Point(192) = {-0.4567436420215075, 0.073479669138689, 0, 0.125};
Point(193) = {-0.4621881257395756, 0.07542766281688272, 0, 0.125};
Point(194) = {-0.4671701276898881, 0.07745059884734995, 0, 0.125};
Point(195) = {-0.471681644606229, 0.07955092452372269, 0, 0.125};
Point(196) = {-0.4757151179639407, 0.0817307896190848, 0, 0.125};
Point(197) = {-0.4792634588791559, 0.0839920458658267, 0, 0.125};
Point(198) = {-0.4823200712220043, 0.08633624620581726, 0, 0.125};
Point(199) = {-0.4848788726822436, 0.08876464368523246, 0, 0.125};
Point(200) = {-0.4869343135575803, 0.09127818988394577, 0, 0.125};
Point(201) = {-0.4884813930704814, 0.09387753278635144, 0, 0.125};
Point(202) = {-0.4895156730580155, 0.09656301401871749, 0, 0.125};
// splines of the airfoil
Spline(5) = {5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104};
Spline(6) = {104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,5};
// airfoil
Line Loop(9) = {5, 6};
// complete domain
Plane Surface(1) = {8, 9};
// labeling of the boundary parts
Physical Line(1) = {4}; // inflow
Physical Line(2) = {2}; // outflow
Physical Line(3) = {1, 3}; // airfoil
Physical Line(4) = {5, 6}; // upper/lower wall
Physical Surface(1) = {10};From which we can construct a mesh like this:
The first four points define the bounding box = (near-field) domain:
// outer bounding box
Point(1) = {-1.25, -0.5, 0, 1.0};
Point(2) = {1.25, -0.5, 0, 1.0};
Point(3) = {1.25, 0.5, 0, 1.0};
Point(4) = {-1.25, 0.5, 0, 1.0};which is constructed from connecting the points in lines:
// outer box
Line(1) = {1, 2};
Line(2) = {2, 3};
Line(3) = {3, 4};
Line(4) = {4, 1};
// outer box
Line Loop(8) = {1, 2, 3, 4};This is followed by a couple (in principle optional) settings where the most important one is
// Insist on quads instead of default triangles
Mesh.RecombineAll = 1;which forces gmsh to generate quadrilateral elements instead of the default triangles. This is strictly required to be able to use the mesh later with p4est, which supports only straight-sided quads, i.e., C2D4, CPS4, S4 in 2D and C3D in 3D. See for more details the (short) documentation on the interaction of p4est with .inp files. In principle, it should also be possible to use the recombine function of gmsh to convert the triangles to quads, but this is observed to be less robust than enforcing quads from the beginning.
Then the airfoil is defined by a set of points:
// points of the airfoil contour
Point(5) = {-0.4900332889206208, 0.09933466539753061, 0, 0.125};
Point(6) = {-0.4900274857651495, 0.1021542752054094, 0, 0.125};
...which are connected by splines for the upper and lower part of the airfoil:
// splines of the airfoil
Spline(5) = {5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
...
96,97,98,99,100,101,102,103,104};
Spline(6) = {104,105,106,107,108,109,110,111,112,113,114,115,
...
200,201,202,5};which are then connected to form a single line loop for easy physical group assignment:
// airfoil
Line Loop(9) = {5, 6};At the end of the file the physical groups are defined:
// labeling of the boundary parts
Physical Line(1) = {4}; // Inflow. Label in Abaqus .inp file: PhysicalLine1
Physical Line(2) = {2}; // Outflow. Label in Abaqus .inp file: PhysicalLine2
Physical Line(3) = {1, 3}; // Upper and lower wall/farfield/... Label in Abaqus .inp file: PhysicalLine3
Physical Line(4) = {5, 6}; // Airfoil. Label in Abaqus .inp file: PhysicalLine4which are crucial for the correct assignment of boundary conditions in Trixi.jl. In particular, it is the responsibility of a user to keep track on the physical boundary names between the mesh generation and assignment of boundary condition functions in an elixir.
After opening this file in gmsh, meshing the geometry and exporting to Abaqus .inp format, we can have a look at the input file:
*Heading
<something depending on gmsh>
*NODE
1, -1.25, -0.5, 0
2, 1.25, -0.5, 0
3, 1.25, 0.5, 0
4, -1.25, 0.5, 0
...
******* E L E M E N T S *************
*ELEMENT, type=T3D2, ELSET=Line1
1, 1, 7
...
*ELEMENT, type=CPS4, ELSET=Surface1
191, 272, 46, 263, 807
...
*NSET,NSET=PhysicalLine1
1, 4, 52, 53, 54, 55, 56, 57, 58,
*NSET,NSET=PhysicalLine2
2, 3, 26, 27, 28, 29, 30, 31, 32,
*NSET,NSET=PhysicalLine3
1, 2, 3, 4, 7, 8, 9, 10, 11, 12,
13, 14, 15, 16, 17, 18, 19, 20, 21, 22,
23, 24, 25, 33, 34, 35, 36, 37, 38, 39,
40, 41, 42, 43, 44, 45, 46, 47, 48, 49,
50, 51,
*NSET,NSET=PhysicalLine4
5, 6, 59, 60, 61, 62, 63, 64, 65, 66,
67, 68, 69, 70, 71, 72, 73, 74, 75, 76,
77, 78, 79, 80, 81, 82, 83, 84, 85, 86,
87, 88, 89, 90, 91, 92, 93, 94, 95, 96,
97, 98, 99, 100, 101, 102, 103, 104, 105, 106,
107, 108, 109, 110, 111, 112, 113, 114, 115, 116,
117, 118, 119, 120, 121, 122, 123, 124, 125, 126,
127, 128, 129, 130, 131, 132, 133, 134, 135, 136,
137, 138, 139, 140, 141, 142, 143, 144, 145, 146,
147, 148, 149, 150, 151, 152, 153, 154, 155, 156,
157, 158, 159, 160, 161, 162, 163, 164, 165, 166,
167, 168, 169, 170, 171, 172, 173, 174, 175, 176,
177, 178, 179, 180, 181, 182, 183, 184, 185, 186,
187, 188, 189, 190,First, the coordinates of the nodes are listed, followed by the elements. Note that gmsh exports also line elements of type T3D2 which are ignored by p4est. The relevant elements in 2D which form the gridcells are of type CPS4 which are defined by their four corner nodes. This is followed by the nodesets encoded via *NSET which are used to assign boundary conditions in Trixi.jl. Trixi.jl parses the .inp file and assigns the edges (in 2D, surfaces in 3D) of elements to the corresponding boundary condition based on the supplied boundary_symbols that have to be supplied to the P4estMesh constructor:
# boundary symbols
boundary_symbols = [:PhysicalLine1, :PhysicalLine2, :PhysicalLine3, :PhysicalLine4]
mesh = P4estMesh{2}(mesh_file, polydeg = polydeg, boundary_symbols = boundary_symbols)The same boundary symbols have then also be supplied to the semidiscretization alongside the corresponding physical boundary conditions:
# Supersonic inflow boundary condition.
# Calculate the boundary flux entirely from the external solution state, i.e., set
# external solution state values for everything entering the domain.
@inline function boundary_condition_supersonic_inflow(u_inner,
normal_direction::AbstractVector,
x, t, surface_flux_function,
equations::CompressibleEulerEquations2D)
u_boundary = initial_condition_mach2_flow(x, t, equations)
flux = Trixi.flux(u_boundary, normal_direction, equations)
return flux
end
# Supersonic outflow boundary condition.
# Calculate the boundary flux entirely from the internal solution state. Analogous to supersonic inflow
# except all the solution state values are set from the internal solution as everything leaves the domain
@inline function boundary_condition_supersonic_outflow(u_inner,
normal_direction::AbstractVector, x,
t,
surface_flux_function,
equations::CompressibleEulerEquations2D)
flux = Trixi.flux(u_inner, normal_direction, equations)
boundary_conditions = Dict(:PhysicalLine1 => boundary_condition_supersonic_inflow, # Left boundary
:PhysicalLine2 => boundary_condition_supersonic_outflow, # Right boundary
:PhysicalLine3 => boundary_condition_supersonic_outflow, # Top and bottom boundary
:PhysicalLine4 => boundary_condition_slip_wall) # Airfoil
semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver,
boundary_conditions = boundary_conditions)Note that you have to supply the boundary_symbols keyword to the P4estMesh constructor to select the boundaries from the available nodesets in the .inp file. If the boundary_symbols keyword is not supplied, all boundaries will be assigned to the default set :all.
Package versions
These results were obtained using the following versions.
using InteractiveUtils
versioninfo()
using Pkg
Pkg.status(["Trixi", "OrdinaryDiffEq", "Plots", "Download"],
mode = PKGMODE_MANIFEST)Julia Version 1.10.7
Commit 4976d05258e (2024-11-26 15:57 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 4 × AMD EPYC 7763 64-Core Processor
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-15.0.7 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
Status `~/work/Trixi.jl/Trixi.jl/docs/Manifest.toml`
⌃ [1dea7af3] OrdinaryDiffEq v6.66.0
[91a5bcdd] Plots v1.40.9
[a7f1ee26] Trixi v0.9.8 `~/work/Trixi.jl/Trixi.jl`
Info Packages marked with ⌃ have new versions available and may be upgradable.This page was generated using Literate.jl.