Advection¶
Wall-normal relation¶
\[-
\dmomadv{1}{1}\]
src/fluid/predict/ux.c¶
93static int advection_x (
94 const domain_t * domain,
95 const double * restrict ux,
96 double * restrict src
97) {
98 const int isize = domain->mysizes[0];
99 const int jsize = domain->mysizes[1];
100#if NDIMS == 3
101 const int ksize = domain->mysizes[2];
102#endif
103 const double * restrict hxxf = domain->hxxf;
104 const double * restrict jdxf = domain->jdxf;
105 BEGIN
106 const double hx_xm = HXXF(i-1);
107 const double hx_x0 = HXXF(i );
108 const double hx_xp = HXXF(i+1);
109 const double jd_xm = JDXF(i-1);
110 const double jd_x0 = JDXF(i );
111 const double jd_xp = JDXF(i+1);
112#if NDIMS == 2
113 const double ux_xm = + 0.5 * jd_xm / hx_xm * UX(i-1, j )
114 + 0.5 * jd_x0 / hx_x0 * UX(i , j );
115 const double ux_xp = + 0.5 * jd_x0 / hx_x0 * UX(i , j )
116 + 0.5 * jd_xp / hx_xp * UX(i+1, j );
117#else
118 const double ux_xm = + 0.5 * jd_xm / hx_xm * UX(i-1, j , k )
119 + 0.5 * jd_x0 / hx_x0 * UX(i , j , k );
120 const double ux_xp = + 0.5 * jd_x0 / hx_x0 * UX(i , j , k )
121 + 0.5 * jd_xp / hx_xp * UX(i+1, j , k );
122#endif
123 const double l = - 0.5 * ux_xm;
124 const double u = + 0.5 * ux_xp;
125 const double c = - l - u;
126 src[cnt] -= 1. / jd_x0 * (
127#if NDIMS == 2
128 + l * UX(i-1, j )
129 + c * UX(i , j )
130 + u * UX(i+1, j )
131#else
132 + l * UX(i-1, j , k )
133 + c * UX(i , j , k )
134 + u * UX(i+1, j , k )
135#endif
136 );
137 END
138 return 0;
139}
\[-
\dmomadv{2}{1}\]
src/fluid/predict/ux.c¶
142static int advection_y (
143 const domain_t * domain,
144 const double * restrict ux,
145 const double * restrict uy,
146 double * restrict src
147) {
148 const int isize = domain->mysizes[0];
149 const int jsize = domain->mysizes[1];
150#if NDIMS == 3
151 const int ksize = domain->mysizes[2];
152#endif
153 const double hy = domain->hy;
154 const double * restrict jdxf = domain->jdxf;
155 const double * restrict jdxc = domain->jdxc;
156 BEGIN
157 const double jd_xm = JDXC(i-1);
158 const double jd_x0 = JDXF(i );
159 const double jd_xp = JDXC(i );
160#if NDIMS == 2
161 const double uy_ym = + 0.5 * jd_xm / hy * UY(i-1, j )
162 + 0.5 * jd_xp / hy * UY(i , j );
163 const double uy_yp = + 0.5 * jd_xm / hy * UY(i-1, j+1)
164 + 0.5 * jd_xp / hy * UY(i , j+1);
165#else
166 const double uy_ym = + 0.5 * jd_xm / hy * UY(i-1, j , k )
167 + 0.5 * jd_xp / hy * UY(i , j , k );
168 const double uy_yp = + 0.5 * jd_xm / hy * UY(i-1, j+1, k )
169 + 0.5 * jd_xp / hy * UY(i , j+1, k );
170#endif
171 const double l = - 0.5 * uy_ym;
172 const double u = + 0.5 * uy_yp;
173 const double c = - l - u;
174 src[cnt] -= 1. / jd_x0 * (
175#if NDIMS == 2
176 + l * UX(i , j-1)
177 + c * UX(i , j )
178 + u * UX(i , j+1)
179#else
180 + l * UX(i , j-1, k )
181 + c * UX(i , j , k )
182 + u * UX(i , j+1, k )
183#endif
184 );
185 END
186 return 0;
187}
\[-
\dmomadv{3}{1}\]
src/fluid/predict/ux.c¶
191static int advection_z (
192 const domain_t * domain,
193 const double * restrict ux,
194 const double * restrict uz,
195 double * restrict src
196) {
197 const int isize = domain->mysizes[0];
198 const int jsize = domain->mysizes[1];
199 const int ksize = domain->mysizes[2];
200 const double hz = domain->hz;
201 const double * restrict jdxf = domain->jdxf;
202 const double * restrict jdxc = domain->jdxc;
203 BEGIN
204 const double jd_xm = JDXC(i-1);
205 const double jd_x0 = JDXF(i );
206 const double jd_xp = JDXC(i );
207 const double uz_zm = + 0.5 * jd_xm / hz * UZ(i-1, j , k )
208 + 0.5 * jd_xp / hz * UZ(i , j , k );
209 const double uz_zp = + 0.5 * jd_xm / hz * UZ(i-1, j , k+1)
210 + 0.5 * jd_xp / hz * UZ(i , j , k+1);
211 const double l = - 0.5 * uz_zm;
212 const double u = + 0.5 * uz_zp;
213 const double c = - l - u;
214 src[cnt] -= 1. / jd_x0 * (
215 + l * UX(i , j , k-1)
216 + c * UX(i , j , k )
217 + u * UX(i , j , k+1)
218 );
219 END
220 return 0;
221}
Stream-wise relation¶
\[-
\dmomadv{1}{2}\]
src/fluid/predict/uy.c¶
92static int advection_x (
93 const domain_t * domain,
94 const double * restrict uy,
95 const double * restrict ux,
96 double * restrict src
97) {
98 const int isize = domain->mysizes[0];
99 const int jsize = domain->mysizes[1];
100#if NDIMS == 3
101 const int ksize = domain->mysizes[2];
102#endif
103 const double * restrict hxxf = domain->hxxf;
104 const double * restrict jdxf = domain->jdxf;
105 const double * restrict jdxc = domain->jdxc;
106 BEGIN
107 const double hx_xm = HXXF(i );
108 const double hx_xp = HXXF(i+1);
109 const double jd_xm = JDXF(i );
110 const double jd_x0 = JDXC(i );
111 const double jd_xp = JDXF(i+1);
112#if NDIMS == 2
113 const double ux_xm = + 0.5 * jd_xm / hx_xm * UX(i , j-1)
114 + 0.5 * jd_xm / hx_xm * UX(i , j );
115 const double ux_xp = + 0.5 * jd_xp / hx_xp * UX(i+1, j-1)
116 + 0.5 * jd_xp / hx_xp * UX(i+1, j );
117#else
118 const double ux_xm = + 0.5 * jd_xm / hx_xm * UX(i , j-1, k )
119 + 0.5 * jd_xm / hx_xm * UX(i , j , k );
120 const double ux_xp = + 0.5 * jd_xp / hx_xp * UX(i+1, j-1, k )
121 + 0.5 * jd_xp / hx_xp * UX(i+1, j , k );
122#endif
123 const double l = - 0.5 * ux_xm;
124 const double u = + 0.5 * ux_xp;
125 const double c = - l - u;
126 src[cnt] -= 1. / jd_x0 * (
127#if NDIMS == 2
128 + l * UY(i-1, j )
129 + c * UY(i , j )
130 + u * UY(i+1, j )
131#else
132 + l * UY(i-1, j , k )
133 + c * UY(i , j , k )
134 + u * UY(i+1, j , k )
135#endif
136 );
137 END
138 return 0;
139}
\[-
\dmomadv{2}{2}\]
src/fluid/predict/uy.c¶
142static int advection_y (
143 const domain_t * domain,
144 const double * restrict uy,
145 double * restrict src
146) {
147 const int isize = domain->mysizes[0];
148 const int jsize = domain->mysizes[1];
149#if NDIMS == 3
150 const int ksize = domain->mysizes[2];
151#endif
152 const double hy = domain->hy;
153 const double * restrict jdxc = domain->jdxc;
154 BEGIN
155 const double jd = JDXC(i );
156#if NDIMS == 2
157 const double uy_ym = + 0.5 * jd / hy * UY(i , j-1)
158 + 0.5 * jd / hy * UY(i , j );
159 const double uy_yp = + 0.5 * jd / hy * UY(i , j )
160 + 0.5 * jd / hy * UY(i , j+1);
161#else
162 const double uy_ym = + 0.5 * jd / hy * UY(i , j-1, k )
163 + 0.5 * jd / hy * UY(i , j , k );
164 const double uy_yp = + 0.5 * jd / hy * UY(i , j , k )
165 + 0.5 * jd / hy * UY(i , j+1, k );
166#endif
167 const double l = - 0.5 * uy_ym;
168 const double u = + 0.5 * uy_yp;
169 const double c = - l - u;
170 src[cnt] -= 1. / jd * (
171#if NDIMS == 2
172 + l * UY(i , j-1)
173 + c * UY(i , j )
174 + u * UY(i , j+1)
175#else
176 + l * UY(i , j-1, k )
177 + c * UY(i , j , k )
178 + u * UY(i , j+1, k )
179#endif
180 );
181 END
182 return 0;
183}
\[-
\dmomadv{3}{2}\]
src/fluid/predict/uy.c¶
187static int advection_z (
188 const domain_t * domain,
189 const double * restrict uy,
190 const double * restrict uz,
191 double * restrict src
192) {
193 const int isize = domain->mysizes[0];
194 const int jsize = domain->mysizes[1];
195 const int ksize = domain->mysizes[2];
196 const double hz = domain->hz;
197 const double * restrict jdxc = domain->jdxc;
198 BEGIN
199 const double jd = JDXC(i );
200 const double uz_zm = + 0.5 * jd / hz * UZ(i , j-1, k )
201 + 0.5 * jd / hz * UZ(i , j , k );
202 const double uz_zp = + 0.5 * jd / hz * UZ(i , j-1, k+1)
203 + 0.5 * jd / hz * UZ(i , j , k+1);
204 const double l = - 0.5 * uz_zm;
205 const double u = + 0.5 * uz_zp;
206 const double c = - l - u;
207 src[cnt] -= 1. / jd * (
208 + l * UY(i , j , k-1)
209 + c * UY(i , j , k )
210 + u * UY(i , j , k+1)
211 );
212 END
213 return 0;
214}
Span-wise relation¶
\[-
\dmomadv{1}{3}\]
src/fluid/predict/uz.c¶
79static int advection_x (
80 const domain_t * domain,
81 const double * restrict uz,
82 const double * restrict ux,
83 double * restrict src
84) {
85 const int isize = domain->mysizes[0];
86 const int jsize = domain->mysizes[1];
87 const int ksize = domain->mysizes[2];
88 const double * restrict hxxf = domain->hxxf;
89 const double * restrict jdxf = domain->jdxf;
90 const double * restrict jdxc = domain->jdxc;
91 BEGIN
92 const double hx_xm = HXXF(i );
93 const double hx_xp = HXXF(i+1);
94 const double jd_xm = JDXF(i );
95 const double jd_x0 = JDXC(i );
96 const double jd_xp = JDXF(i+1);
97 const double ux_xm = + 0.5 * jd_xm / hx_xm * UX(i , j , k-1)
98 + 0.5 * jd_xm / hx_xm * UX(i , j , k );
99 const double ux_xp = + 0.5 * jd_xp / hx_xp * UX(i+1, j , k-1)
100 + 0.5 * jd_xp / hx_xp * UX(i+1, j , k );
101 const double l = - 0.5 * ux_xm;
102 const double u = + 0.5 * ux_xp;
103 const double c = - l - u;
104 src[cnt] -= 1. / jd_x0 * (
105 + l * UZ(i-1, j , k )
106 + c * UZ(i , j , k )
107 + u * UZ(i+1, j , k )
108 );
109 END
110 return 0;
111}
\[-
\dmomadv{2}{3}\]
src/fluid/predict/uz.c¶
114static int advection_y (
115 const domain_t * domain,
116 const double * restrict uz,
117 const double * restrict uy,
118 double * restrict src
119) {
120 const int isize = domain->mysizes[0];
121 const int jsize = domain->mysizes[1];
122 const int ksize = domain->mysizes[2];
123 const double hy = domain->hy;
124 const double * restrict jdxc = domain->jdxc;
125 BEGIN
126 const double jd = JDXC(i );
127 const double uy_ym = + 0.5 * jd / hy * UY(i , j , k-1)
128 + 0.5 * jd / hy * UY(i , j , k );
129 const double uy_yp = + 0.5 * jd / hy * UY(i , j+1, k-1)
130 + 0.5 * jd / hy * UY(i , j+1, k );
131 const double l = - 0.5 * uy_ym;
132 const double u = + 0.5 * uy_yp;
133 const double c = - l - u;
134 src[cnt] -= 1. / jd * (
135 + l * UZ(i , j-1, k )
136 + c * UZ(i , j , k )
137 + u * UZ(i , j+1, k )
138 );
139 END
140 return 0;
141}
\[-
\dmomadv{3}{3}\]
src/fluid/predict/uz.c¶
144static int advection_z (
145 const domain_t * domain,
146 const double * restrict uz,
147 double * restrict src
148) {
149 const int isize = domain->mysizes[0];
150 const int jsize = domain->mysizes[1];
151 const int ksize = domain->mysizes[2];
152 const double hz = domain->hz;
153 const double * restrict jdxc = domain->jdxc;
154 BEGIN
155 const double jd = JDXC(i );
156 const double uz_zm = + 0.5 * jd / hz * UZ(i , j , k-1)
157 + 0.5 * jd / hz * UZ(i , j , k );
158 const double uz_zp = + 0.5 * jd / hz * UZ(i , j , k )
159 + 0.5 * jd / hz * UZ(i , j , k+1);
160 const double l = - 0.5 * uz_zm;
161 const double u = + 0.5 * uz_zp;
162 const double c = - l - u;
163 src[cnt] -= 1. / jd * (
164 + l * UZ(i , j , k-1)
165 + c * UZ(i , j , k )
166 + u * UZ(i , j , k+1)
167 );
168 END
169 return 0;
170}