SFEMaNS  version 5.3
Reference documentation for SFEMaNS
my_mathjax.js
Go to the documentation of this file.
1 
2 //Enable Numbering
3  MathJax.Hub.Config({
4  TeX: { equationNumbers: { autoNumber: "AMS" } }
5  });
6 
7 
8 //Macros
9  MathJax.Hub.Config({
10  TeX: {
11  Macros: {
12  bold: ["{\\bf #1}",1],
13 
14  // Some Boldfonts
15  ba: '{{\\bf a}}',
16  bb: '{{\\bf b}}',
17  bc: '{{\\bf c}}',
18  bd: '{{\\bf d}}',
19  be: '{{\\bf e}}',
20  bef: '{{\\bf f}}',
21  bg: '{{\\bf g}}',
22  bh: '{{\\bf h}}',
23  bi: '{{\\bf i}}',
24  bj: '{{\\bf j}}',
25  bk: '{{\\bf k}}',
26  bl: '{{\\bf l}}',
27  bm: '{{\\bf m}}',
28  bn: '{{\\bf n}}',
29  bo: '{{\\bf o}}',
30  bp: '{{\\bf p}}',
31  bq: '{{\\bf q}}',
32  br: '{{\\bf r}}',
33  bs: '{{\\bf s}}',
34  bt: '{{\\bf t}}',
35  bu: '{{\\bf u}}',
36  bv: '{{\\bf v}}',
37  bw: '{{\\bf w}}',
38  bx: '{{\\bf x}}',
39  by: '{{\\bf y}}',
40  bz: '{{\\bf z}}',
41 
42  bA: '{{\\bf A}}',
43  bB: '{{\\bf B}}',
44  bC: '{{\\bf C}}',
45  bD: '{{\\bf D}}',
46  bE: '{{\\bf E}}',
47  bF: '{{\\bf F}}',
48  bG: '{{\\bf G}}',
49  bH: '{{\\bf H}}',
50  bI: '{{\\bf I}}',
51  bJ: '{{\\bf J}}',
52  bK: '{{\\bf K}}',
53  bL: '{{\\bf L}}',
54  bM: '{{\\bf M}}',
55  bN: '{{\\bf N}}',
56  bO: '{{\\bf O}}',
57  bP: '{{\\bf P}}',
58  bQ: '{{\\bf Q}}',
59  bR: '{{\\bf R}}',
60  bS: '{{\\bf S}}',
61  bT: '{{\\bf T}}',
62  bU: '{{\\bf U}}',
63  bV: '{{\\bf V}}',
64  bW: '{{\\bf W}}',
65  bX: '{{\\bf X}}',
66  bY: '{{\\bf Y}}',
67  bZ: '{{\\bf Z}}',
68 
69 
70  calA:'{{\\mathcal A}}',
71  calB:'{{\\mathcal B}}',
72  calC:'{{\\mathcal C}}',
73  calD:'{{\\mathcal D}}',
74  calE:'{{\\mathcal E}}',
75  calF:'{{\\mathcal F}}',
76  calG:'{{\\mathcal G}}',
77  calH:'{{\\mathcal H}}',
78  calI:'{{\\mathcal I}}',
79  calJ:'{{\\mathcal J}}',
80  calK:'{{\\mathcal K}}',
81  calL:'{{\\mathcal L}}',
82  calM:'{{\\mathcal M}}',
83  calN:'{{\\mathcal N}}',
84  calO:'{{\\mathcal O}}',
85  calP:'{{\\mathcal P}}',
86  calQ:'{{\\mathcal Q}}',
87  calR:'{{\\mathcal R}}',
88  calS:'{{\\mathcal S}}',
89  calT:'{{\\mathcal T}}',
90  calU:'{{\\mathcal U}}',
91  calV:'{{\\mathcal V}}',
92  calW:'{{\\mathcal W}}',
93  calX:'{{\\mathcal X}}',
94  calY:'{{\\mathcal Y}}',
95  calZ:'{{\\mathcal Z}}',
96 
97 
98 
99 
100  //Some Constants
101  Rm: '{R_{\\text{m}}}',
102  Re: '{R_{\\text{e}}}',
103  Rec: '{R_{\\text{ec}}}',
104  Rmc: '{R_{\\text{mc}}}',
105 
106 
107  //Some Operators
108  SCAL: '{{\\cdot}}', //scalar product
109  CROSS:'{\\times }',
110  DIV: '{\\nabla \\cdot }', //Divergence
111  ROT: '{\\nabla \\times }', //Curl
112  GRAD: '{\\nabla}' , //Gradient
113  LAP: '{{\\Delta}}', //Laplacian
114  LAPh: '{{\\Delta_h}}', //Laplacian
115 
116  //New characters
117  muc: '{\\mu^c}',
118  muv: '{\\mu^v}',
119  bnc: '{\\bn^c}',
120  bnv: '{\\bn^v}',
121  front: '{\\Gamma}',
122  frontc:'{{\Gamma_c}}',
123  frontf:'{{\Gamma_f}}',
124  frontv:'{{\Gamma_v}}',
125 
126  Omegac: '{{\\Omega_c}}',
127  Omegacf: '{{\\Omega_{cf}}}',
128  Omegacs: '{{\\Omega_{cs}}}',
129  Omegav: '{{\\Omega_v}}',
130  Omegacfmed: '{{\\Omega_{cf}^{2D}}}',
131  Omegacsmed:'{{\\Omega_{cs}^{2D}}}',
132  Omegacmed:'{{\\Omega_{c}^{2D}}}',
133  Omegavmed:'{{\\Omega_v^{2D}}}'
134 
135 
136 
137  //Some Spaces....
138 
139 
140  }
141  }
142 });
initialization::bn
real(kind=8), dimension(:,:,:), allocatable, target bn
Definition: initialization.f90:58
bu
section doc_intro_frame_work_num_app Numerical approximation subsection doc_intro_fram_work_num_app_Fourier_FEM Fourier Finite element representation The SFEMaNS code uses a hybrid Fourier Finite element formulation The Fourier decomposition allows to approximate the problem’s solutions for each Fourier mode modulo nonlinear terms that are made explicit The variables are then approximated on a meridian section of the domain with a finite element method The numerical approximation of a function f $f f is written in the following generic f with f $t f the time and f $M f the number of Fourier modes considered The unknown f f f f f f f f Omega_v f and f Omega f We also consider f a penalty method of the divergence of the velocity field is also implemented The method proceeds as the pressure and the pressure increments< li > For f $n geq0 f let f bu
Definition: doc_intro.h:324