$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\halfi}{{1/2}}
\newcommand{\xpoint}{\boldsymbol{x}}
\newcommand{\normalvec}{\boldsymbol{n}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
\newcommand{\Ix}{\mathcal{I}_x}
\newcommand{\Iy}{\mathcal{I}_y}
\newcommand{\It}{\mathcal{I}_t}
\newcommand{\setb}[1]{#1^0} % set begin
\newcommand{\sete}[1]{#1^{-1}} % set end
\newcommand{\setl}[1]{#1^-}
\newcommand{\setr}[1]{#1^+}
\newcommand{\seti}[1]{#1^i}
\newcommand{\Real}{\mathbb{R}}
$$
Mesh
- Mesh point: \( (x_i,y_j,z_k,t_n) \)
- \( x \) direction: \( x_0 < x_1 < \cdots < x_{N_x} \)
- \( y \) direction: \( y_0 < y_1 < \cdots < y_{N_y} \)
- \( z \) direction: \( z_0 < z_1 < \cdots < z_{N_z} \)
- \( u^{n}_{i,j,k} \approx \uex(x_i,y_j,z_k,t_n) \)
