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\begin{document}
\begin{tabular}{|l|l|l|l|l|l||ll||l||l||l||l||l|}
\hline 
\multicolumn{7}{|l}{Initialization} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{cyan}{\footnotesize{}${\tt CompressibleFlowSolver}$}}\tabularnewline
\hline 
\multicolumn{7}{|l}{Time step loop $n$} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{brown}{\footnotesize{}${\tt UnsteadySystem}$}}\tabularnewline
\cline{2-13} \cline{3-13} \cline{4-13} \cline{5-13} \cline{6-13} \cline{7-13} \cline{8-13} \cline{9-13} \cline{10-13} \cline{11-13} \cline{12-13} \cline{13-13} 
\multirow{12}{*}{} & \multicolumn{6}{l}{Runge-Kutta loop $m=1,\cdots,M$} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{brown}{\footnotesize{}${\tt TimeIntegrationScheme}$}}\tabularnewline
\cline{3-13} \cline{4-13} \cline{5-13} \cline{6-13} \cline{7-13} \cline{8-13} \cline{9-13} \cline{10-13} \cline{11-13} \cline{12-13} \cline{13-13} 
 & \multirow{10}{*}{} & \multicolumn{5}{l}{Calculate source term $\mathbf{S}_{m}$} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{brown}{\footnotesize{}${\tt TimeIntegrationScheme}$}}\tabularnewline
\cline{3-13} \cline{4-13} \cline{5-13} \cline{6-13} \cline{7-13} \cline{8-13} \cline{9-13} \cline{10-13} \cline{11-13} \cline{12-13} \cline{13-13} 
 &  & \multicolumn{5}{l}{Netwon iteration $l$} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{brown}{\footnotesize{}${\tt NewtonSolver}$}}\tabularnewline
\cline{4-13} \cline{5-13} \cline{6-13} \cline{7-13} \cline{8-13} \cline{9-13} \cline{10-13} \cline{11-13} \cline{12-13} \cline{13-13} 
 &  & \multirow{8}{*}{} & \multicolumn{4}{l}{Calculate residual $\mathbf{N}\left(\bar{\mathbf{u}}^{l}\right)$} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{cyan}{\footnotesize{}${\tt CFSImplicit}$}}\tabularnewline
\cline{4-13} \cline{5-13} \cline{6-13} \cline{7-13} \cline{8-13} \cline{9-13} \cline{10-13} \cline{11-13} \cline{12-13} \cline{13-13} 
 &  &  & \multicolumn{4}{l}{GMRES iteration $k$} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{brown}{\footnotesize{}${\tt NekLinSysIterGMRES}$}}\tabularnewline
\cline{5-13} \cline{6-13} \cline{7-13} \cline{8-13} \cline{9-13} \cline{10-13} \cline{11-13} \cline{12-13} \cline{13-13} 
 &  &  & \multirow{5}{*}{} & \multicolumn{3}{l}{Calculate search vector $\mathbf{q}_{k}$} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{brown}{\footnotesize{}${\tt NekLinSysIterGMRES}$}}\tabularnewline
\cline{5-13} \cline{6-13} \cline{7-13} \cline{8-13} \cline{9-13} \cline{10-13} \cline{11-13} \cline{12-13} \cline{13-13} 
 &  &  &  & \multicolumn{3}{l}{BRJ iteration $j=1,\cdots,J$ } & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{brown}{\footnotesize{}${\tt PrecondBRJ}$}}\tabularnewline
\cline{6-13} \cline{7-13} \cline{8-13} \cline{9-13} \cline{10-13} \cline{11-13} \cline{12-13} \cline{13-13} 
 &  &  &  &  & \multicolumn{2}{l}{Calculate {\small{}$\hat{\mathbf{q}}^{j}=\hat{\mathbf{D}}^{-1}\left(\mathbf{q}_{k}-\left(\mathbf{\hat{L}}+\hat{\mathbf{U}}\right)\hat{\mathbf{q}}^{j-1}\right)$}} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{cyan}{\footnotesize{}${\tt CFSImplicit}$}}\tabularnewline
\cline{5-13} \cline{6-13} \cline{7-13} \cline{8-13} \cline{9-13} \cline{10-13} \cline{11-13} \cline{12-13} \cline{13-13} 
 &  &  &  & \multicolumn{3}{l}{Calculate $\partial\mathbf{N}/\partial\mathbf{u}\cdot\hat{\mathbf{q}}^{J}$} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{cyan}{\footnotesize{}${\tt CFSImplicit}$}}\tabularnewline
\cline{5-13} \cline{6-13} \cline{7-13} \cline{8-13} \cline{9-13} \cline{10-13} \cline{11-13} \cline{12-13} \cline{13-13} 
 &  &  &  & \multicolumn{3}{l}{Calculate linear system residual} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{brown}{\footnotesize{}${\tt NekLinSysIterGMRES}$}}\tabularnewline
\cline{4-13} \cline{5-13} \cline{6-13} \cline{7-13} \cline{8-13} \cline{9-13} \cline{10-13} \cline{11-13} \cline{12-13} \cline{13-13} 
 &  &  & \multicolumn{4}{l}{Calculate $\bar{\mathbf{u}}^{l+1}$ by linear combination of $\mathbf{q}_{k}$} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{brown}{\footnotesize{}${\tt NekLinSysIterGMRES}$}}\tabularnewline
\cline{2-13} \cline{3-13} \cline{4-13} \cline{5-13} \cline{6-13} \cline{7-13} \cline{8-13} \cline{9-13} \cline{10-13} \cline{11-13} \cline{12-13} \cline{13-13} 
 & \multicolumn{6}{l}{Calculate $\mathbf{u}^{n+1}$} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{brown}{\footnotesize{}${\tt TimeIntegrationScheme}$}}\tabularnewline
\hline 
\multicolumn{7}{|l}{Output and finalization} & \multicolumn{6}{l|}{{\footnotesize{}in }\textcolor{cyan}{\footnotesize{}${\tt CompressibleFlowSolver}$}}\tabularnewline
\hline 
\end{tabular}
\end{document}
