104 * @brief Transport with dispersion implemented using discontinuous Galerkin method.
105 *
106 * TransportDG implements the discontinuous Galerkin method for the transport and diffusion of substances.
107 * The concentration @f$ c_i ~[kg/m^3]@f$ of the i-th substance is governed by the advection-diffusion equation
108 * @f[
109 * \partial_t c_i + \mathbf v\cdot\nabla c_i - \mathrm{div}(D\nabla c_i) = F \mbox{ in }\Omega^d,
110 * @f]
111 * where @f$\mathbf v@f$ is the fluid velocity and @f$\Omega^d@f$ the @f$d@f$-dimensional domain, respectively.
112 * The hydrodynamic dispersivity tensor @f$\mathbf D ~[m^2/s]@f$ is given by:
113 * @f[
114 * \mathbf D = D_m\mathbf I + |\mathbf v|\left(\alpha_T\mathbf I + (\alpha_L-\alpha_T)\frac{\mathbf v\otimes\mathbf v}{|\mathbf v|^2}\right).
115 * @f]
116 * The molecular dispersivity @f$D_m~[m^2/s]@f$, as well as the longitudal and transversal dispersivity @f$\alpha_L,~\alpha_T~[m]@f$ are input parameters of the model.
117 *
118 * For lower dimensions @f$d=1,2@f$ the advection-diffusion equation is multiplied by the fracture cross-cut @f$\delta^d~[m^{3-d}]@f$.
119 *
120 * The boundary @f$\partial\Omega^d@f$ is divided into three disjoint parts @f$\Gamma^d_D\cup\Gamma^d_N\cup\Gamma^d_F@f$.
121 * We prescribe the following boundary conditions:
122 * @f{eqnarray*}{
123 * c_i^d &= c_{iD}^d &\mbox{ on }\Gamma^d_D \mbox{ (Dirichlet)},\\
124 * \mathbf D^d\nabla c_i^d\cdot\mathbf n &= 0 &\mbox{ on }\Gamma^d_N \mbox{ (Neumann)},
125 * @f}
126 * The transfer of mass through fractures is described by the transmission conditions on @f$\Gamma^d_F@f$:
127 * @f[
128 * -\mathbf D^d\nabla c_i^d\cdot\mathbf n = \sigma(c_i^d-c_i^{d-1}) + \left\{\begin{array}{cl}0 &\mbox{ if }\mathbf v^d\cdot\mathbf n\ge 0\\\mathbf v^d\cdot\mathbf n(c_i^{d-1}-c_i^d) & \mbox{ if }\mathbf v^d\cdot\mathbf n<0\end{array}\right.,\qquad
