Mass conservation¶
The mass conservation is defined at each cell center and described as:
\[\pder{\rho}{t}
+
\frac{1}{J}
\dif{}{\gx}
\left(
\jhx
\rho
\ux
\right)
+
\frac{1}{J}
\dif{}{\gy}
\left(
\jhy
\rho
\uy
\right)
+
\frac{1}{J}
\dif{}{\gz}
\left(
\jhz
\rho
\uz
\right)
=
0.\]
Specifically the rescaled version
\[\pder{H}{t}
+
\frac{1}{J}
\dif{}{\gx}
\left(
\jhx
\ux
H
\right)
+
\frac{1}{J}
\dif{}{\gy}
\left(
\jhy
\uy
H
\right)
+
\frac{1}{J}
\dif{}{\gz}
\left(
\jhz
\uz
H
\right)
=
0\]
is considered.
src/interface/update/main.c¶
86const double hx_xm = HXXF(i );
87const double hx_xp = HXXF(i+1);
88const double jd_xm = JDXF(i );
89const double jd_x0 = JDXC(i );
90const double jd_xp = JDXF(i+1);
91const double flux_xm = FLUXX(i , j );
92const double flux_xp = FLUXX(i+1, j );
93const double flux_ym = FLUXY(i , j );
94const double flux_yp = FLUXY(i , j+1);
95SRC(i, j) = 1. / jd_x0 * (
96 + jd_xm / hx_xm * flux_xm
97 - jd_xp / hx_xp * flux_xp
98 + jd_x0 / hy * flux_ym
99 - jd_x0 / hy * flux_yp
100);
src/interface/update/main.c¶
108const double hx_xm = HXXF(i );
109const double hx_xp = HXXF(i+1);
110const double jd_xm = JDXF(i );
111const double jd_x0 = JDXC(i );
112const double jd_xp = JDXF(i+1);
113const double flux_xm = FLUXX(i , j , k );
114const double flux_xp = FLUXX(i+1, j , k );
115const double flux_ym = FLUXY(i , j , k );
116const double flux_yp = FLUXY(i , j+1, k );
117const double flux_zm = FLUXZ(i , j , k );
118const double flux_zp = FLUXZ(i , j , k+1);
119SRC(i, j, k) = 1. / jd_x0 * (
120 + jd_xm / hx_xm * flux_xm
121 - jd_xp / hx_xp * flux_xp
122 + jd_x0 / hy * flux_ym
123 - jd_x0 / hy * flux_yp
124 + jd_x0 / hz * flux_zm
125 - jd_x0 / hz * flux_zp
126);