[Latex] Riemann 问题中的激波，接触间断，膨胀波的 Tikz 绘图

1. 三种膨胀波

Latex 代码

\begin{figure}
    \centering
    \begin{subfigure}[b]{0.32\textwidth}
        \centering
        \resizebox{\linewidth}{!}{
            \begin{tikzpicture}
                \coordinate (o) at (0,0);
                \coordinate (S1) at (2.5,2.5);
                \draw[->] (0,0) -- (3,0) node[right] {$x$};
                \draw[->] (0,0) -- (0,3) node[above] {$t$};
                \draw[-] (o) -- (S1) node[right] {$S_1$};
                \draw[->] (0.5,2) -- (2,2.3) node[midway, above] {$\boldsymbol{U}_L$};
                \draw[->] (2,0.5) -- (2.3,2) node[midway, right] {$\boldsymbol{U}_R$};
                \node[below left] {$o$};
            \end{tikzpicture}
        }
        \caption{shock wave}
        \label{fig:shock_wave_1}
    \end{subfigure}
    \begin{subfigure}[b]{0.32\textwidth}
        \centering
        \resizebox{\linewidth}{!}{
            \begin{tikzpicture}
                \coordinate (o) at (0,0);
                \coordinate (S2) at (2.5,2.5);
                \draw[->] (0,0) -- (3,0) node[right] {$x$};
                \draw[->] (0,0) -- (0,3) node[above] {$t$};
                \draw[dashed] (o) -- (S2) node[right] {$S_2$};
                \draw[->] (0.7,1.5) -- (1.7,2.5) node[midway, left] {$\boldsymbol{U}_L$};
                \draw[->] (1.5,0.7) -- (2.5,1.7) node[midway, right] {$\boldsymbol{U}_R$};
                \node[below left] {$o$};
            \end{tikzpicture}
        }
        \caption{contact discontinuity}
        \label{fig:contact_discontinuity_1}
    \end{subfigure}
    \begin{subfigure}[b]{0.32\textwidth}
        \centering
        \resizebox{\linewidth}{!}{
            \begin{tikzpicture}
                \coordinate (o) at (0,0);
                \coordinate (S1) at (1.8,2.7);
                \coordinate (S2) at (2.2,2.7);
                \coordinate (S3) at (2.5,2.5);
                \coordinate (S4) at (2.7,2.2);
                \coordinate (S5) at (2.7,1.8);
                \draw[->] (0,0) -- (3,0) node[right] {$x$};
                \draw[->] (0,0) -- (0,3) node[above] {$t$};
                \draw[-] (o) -- (S1) node[right] {};
                \draw[-] (o) -- (S2) node[right] {};
                \draw[-] (o) -- (S3) node[right] {};
                \draw[-] (o) -- (S4) node[right] {};
                \draw[-] (o) -- (S5) node[right] {};
                \draw[->] (0.5,1.5) -- (1.4,2.85) node[midway, left] {$\boldsymbol{U}_L$};
                \draw[->] (1.5,0.5) -- (2.85,1.4) node[midway, right] {$\boldsymbol{U}_R$};
                \node[below left] {$o$};
            \end{tikzpicture}
        }
        \caption{rarefaction wave}
        \label{fig:rarefaction_wave_1}
    \end{subfigure}
    \caption{Wave of Riemann problem. $S_1, S_2$ is wave speed, $U_L,U_R$ are initial data states connected by a single wave.}
    \label{fig:wave_of_riemann}
\end{figure}

输出：

绘图参考：

《Riemann Solvers and Numerical Methods for Fluid Dynamics》P84

2. Riemann 问题的解

Latex 代码：

\begin{figure}
    \centering
    \begin{subfigure}[b]{0.4\textwidth}
        \centering
        \resizebox{\linewidth}{!}{
            \begin{tikzpicture}
                \coordinate (o) at (0,0);
                \coordinate (S1) at (2.5,2.5);
                \coordinate (S2) at (1.2,3);
                \coordinate (S3) at (-2.5,2.5);
                \draw[->] (-3,0) -- (3,0) node[right] {$x$};
                \draw[->] (0,0) -- (0,3) node[above] {$t$};
                \draw[-] (o) -- (S1) node[right] {};
                \draw[dashed] (o) -- (S2) node[right] {};
                \draw[-] (o) -- (S3) node[right] {};
                \node[below left] (o) {$o$};
            \end{tikzpicture}
        }
        \caption{shock, contact, shock}
        \label{fig:riemann_sol_1}
    \end{subfigure}
    \begin{subfigure}[b]{0.4\textwidth}
        \centering
        \resizebox{\linewidth}{!}{
            \begin{tikzpicture}
                \coordinate (o) at (0,0);
                \coordinate (S1) at (2.2,2.7);
                \coordinate (S2) at (2.5,2.5);
                \coordinate (S3) at (2.7,2.2);
                \coordinate (S4) at (1.2,3);
                \coordinate (S5) at (-2.2,2.7);
                \coordinate (S6) at (-2.5,2.5);
                \coordinate (S7) at (-2.7,2.2);
                \draw[->] (-3,0) -- (3,0) node[right] {$x$};
                \draw[->] (0,0) -- (0,3) node[above] {$t$};
                \draw[-] (o) -- (S1) node[right] {};
                \draw[-] (o) -- (S2) node[right] {};
                \draw[-] (o) -- (S3) node[right] {};
                \draw[dashed] (o) -- (S4) node[right] {};
                \draw[-] (o) -- (S5) node[right] {};
                \draw[-] (o) -- (S6) node[right] {};
                \draw[-] (o) -- (S7) node[right] {};
                \node[below left] (o) {$o$};
            \end{tikzpicture}
        }
        \caption{rarefaction, contact, rarefaction}
        \label{fig:riemann_sol_2}
    \end{subfigure}\\
    \begin{subfigure}[b]{0.4\textwidth}
        \centering
        \resizebox{\linewidth}{!}{
            \begin{tikzpicture}
                \coordinate (o) at (0,0);
                \coordinate (S1) at (2.5,2.5);
                \coordinate (S2) at (1.2,3);
                \coordinate (S3) at (-2.2,2.7);
                \coordinate (S4) at (-2.5,2.5);
                \coordinate (S5) at (-2.7,2.2);
                \draw[->] (-3,0) -- (3,0) node[right] {$x$};
                \draw[->] (0,0) -- (0,3) node[above] {$t$};
                \draw[-] (o) -- (S1) node[right] {};
                \draw[dashed] (o) -- (S2) node[right] {};
                \draw[-] (o) -- (S3) node[right] {};
                \draw[-] (o) -- (S4) node[right] {};
                \draw[-] (o) -- (S5) node[right] {};
                \node[below left] (o) {$o$};
            \end{tikzpicture}
        }
        \caption{rarefaction, contact, shock}
        \label{fig:riemann_sol_3}
    \end{subfigure}
    \begin{subfigure}[b]{0.4\textwidth}
        \centering
        \resizebox{\linewidth}{!}{
            \begin{tikzpicture}
                \coordinate (o) at (0,0);
                \coordinate (S1) at (2.2,2.7);
                \coordinate (S2) at (2.5,2.5);
                \coordinate (S3) at (2.7,2.2);
                \coordinate (S4) at (1.2,3);
                \coordinate (S5) at (-2.5,2.5);
                \draw[->] (-3,0) -- (3,0) node[right] {$x$};
                \draw[->] (0,0) -- (0,3) node[above] {$t$};
                \draw[-] (o) -- (S1) node[right] {};
                \draw[-] (o) -- (S2) node[right] {};
                \draw[-] (o) -- (S3) node[right] {};
                \draw[dashed] (o) -- (S4) node[right] {};
                \draw[-] (o) -- (S5) node[right] {};
                \node[below left] (o) {$o$};
            \end{tikzpicture}
        }
        \caption{shock, contact, rarefaction}
        \label{fig:riemann_sol_4}
    \end{subfigure}
    \caption{Four situations of Riemann problem.}
    \label{fig:riemann_four_solutions}
\end{figure}

输出：

绘图参考：

《Riemann Solvers and Numerical Methods for Fluid Dynamics》P118