src/viscosity.h

1
2
3
4
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
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
  
#include "poisson.h"

  struct Viscosity {
    vector u;
    face vector mu;
    scalar rho;
    double dt;
    int nrelax;
    scalar * res;
  };

  #if AXI
  # define lambda ((coord){1., 1. + dt/rho[]*(mu.x[] + mu.x[1] + \
  					    mu.y[] + mu.y[0,1])/2./sq(y)})
  #else // not AXI
  # if dimension == 1
  #   define lambda ((coord){1.})
  # elif dimension == 2
  #   define lambda ((coord){1.,1.})
  # elif dimension == 3
  #   define lambda ((coord){1.,1.,1.})
  #endif
  #endif

  static void relax_viscosity (scalar * a, scalar * b, int l, void * data)
  {
    struct Viscosity * p = (struct Viscosity *) data;
    (const) face vector mu = p->mu;
    (const) scalar rho = p->rho;
    double dt = p->dt;
    vector u = vector(a[0]), r = vector(b[0]);

  #if JACOBI
    vector w[];
  #else
    vector w = u;
  #endif

    foreach_level_or_leaf (l) {
      foreach_dimension()
        w.x[] = (dt/rho[]*(2.*mu.x[1]*u.x[1] + 2.*mu.x[]*u.x[-1]
                 #if dimension > 1
  			   + mu.y[0,1]*(u.x[0,1] +
  					(u.y[1,0] + u.y[1,1])/4. -
  					(u.y[-1,0] + u.y[-1,1])/4.)
  			   - mu.y[]*(- u.x[0,-1] +
  				     (u.y[1,-1] + u.y[1,0])/4. -
  				     (u.y[-1,-1] + u.y[-1,0])/4.)
                 #endif
  	       #if dimension > 2
  			   + mu.z[0,0,1]*(u.x[0,0,1] +
  					  (u.z[1,0,0] + u.z[1,0,1])/4. -
  					  (u.z[-1,0,0] + u.z[-1,0,1])/4.)
  			   - mu.z[]*(- u.x[0,0,-1] +
  				     (u.z[1,0,-1] + u.z[1,0,0])/4. -
  				     (u.z[-1,0,-1] + u.z[-1,0,0])/4.)
                 #endif
  			   ) + r.x[]*sq(Delta))/
      (sq(Delta)*lambda.x + dt/rho[]*(2.*mu.x[1] + 2.*mu.x[]
                                      #if dimension > 1
  				      + mu.y[0,1] + mu.y[]
                                      #endif
  			            #if dimension > 2
  				      + mu.z[0,0,1] + mu.z[]
  			            #endif
  			     ));
    }

  #if JACOBI
    foreach_level_or_leaf (l)
      foreach_dimension()
        u.x[] = (u.x[] + 2.*w.x[])/3.;
  #endif

  #if TRASH
    vector u1[];
    foreach_level_or_leaf (l)
      foreach_dimension()
        u1.x[] = u.x[];
    trash ({u});
    foreach_level_or_leaf (l)
      foreach_dimension()
        u.x[] = u1.x[];
  #endif
  }

  static double residual_viscosity (scalar * a, scalar * b, scalar * resl, 
  				  void * data)
  {
    struct Viscosity * p = (struct Viscosity *) data;
    (const) face vector mu = p->mu;
    (const) scalar rho = p->rho;
    double dt = p->dt;
    vector u = vector(a[0]), r = vector(b[0]), res = vector(resl[0]);
    double maxres = 0.;
  #if TREE
    /* conservative coarse/fine discretisation (2nd order) */
    foreach_dimension() {
      face vector taux[];
      foreach_face(x)
        taux.x[] = 2.*mu.x[]*(u.x[] - u.x[-1])/Delta;
      #if dimension > 1
        foreach_face(y)
  	taux.y[] = mu.y[]*(u.x[] - u.x[0,-1] + 
  			   (u.y[1,-1] + u.y[1,0])/4. -
  			   (u.y[-1,-1] + u.y[-1,0])/4.)/Delta;
      #endif
      #if dimension > 2
        foreach_face(z)
  	taux.z[] = mu.z[]*(u.x[] - u.x[0,0,-1] + 
  			   (u.z[1,0,-1] + u.z[1,0,0])/4. -
  			   (u.z[-1,0,-1] + u.z[-1,0,0])/4.)/Delta;
      #endif
      boundary_flux ({taux});
      foreach (reduction(max:maxres)) {
        double d = 0.;
        foreach_dimension()
  	d += taux.x[1] - taux.x[];
        res.x[] = r.x[] - lambda.x*u.x[] + dt/rho[]*d/Delta;
        if (fabs (res.x[]) > maxres)
  	maxres = fabs (res.x[]);
      }
    }
    boundary (resl);
  #else
    /* "naive" discretisation (only 1st order on trees) */
    foreach (reduction(max:maxres))
      foreach_dimension() {
        res.x[] = r.x[] - lambda.x*u.x[] +
          dt/rho[]*(2.*mu.x[1,0]*(u.x[1] - u.x[])
  		  - 2.*mu.x[]*(u.x[] - u.x[-1])
          #if dimension > 1
  		  + mu.y[0,1]*(u.x[0,1] - u.x[] +
  			       (u.y[1,0] + u.y[1,1])/4. -
  			       (u.y[-1,0] + u.y[-1,1])/4.)
  		  - mu.y[]*(u.x[] - u.x[0,-1] +
  			    (u.y[1,-1] + u.y[1,0])/4. -
  			    (u.y[-1,-1] + u.y[-1,0])/4.)
  	#endif
          #if dimension > 2
  		  + mu.z[0,0,1]*(u.x[0,0,1] - u.x[] +
  				 (u.z[1,0,0] + u.z[1,0,1])/4. -
  				 (u.z[-1,0,0] + u.z[-1,0,1])/4.)
  		  - mu.z[]*(u.x[] - u.x[0,0,-1] +
  			    (u.z[1,0,-1] + u.z[1,0,0])/4. -
  			    (u.z[-1,0,-1] + u.z[-1,0,0])/4.)
  	#endif
  		  )/sq(Delta);
        if (fabs (res.x[]) > maxres)
  	maxres = fabs (res.x[]);
      }
  #endif
    return maxres;
  }

  #undef lambda

  mgstats viscosity (struct Viscosity p)
  {
    vector u = p.u, r[];
    foreach()
      foreach_dimension()
        r.x[] = u.x[];

    face vector mu = p.mu;
    scalar rho = p.rho;
    restriction ({mu,rho});

    return mg_solve ((scalar *){u}, (scalar *){r},
  		   residual_viscosity, relax_viscosity, &p, p.nrelax, p.res);
  }

  mgstats viscosity_explicit (struct Viscosity p)
  {
    vector u = p.u, r[];
    mgstats mg = {0};
    mg.resb = residual_viscosity ((scalar *){u}, (scalar *){u}, (scalar *){r}, &p);
    foreach()
      foreach_dimension()
        u.x[] += r.x[];
    boundary ((scalar *){u});
    return mg;
  }