cfdsolver/index2d.html at main · mehdiansari-cfd/cfdsolver · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>2D Euler Laboratory</title>

<link rel="stylesheet" href="lab.css">

<!-- React + Babel from CDN -->
<script crossorigin src="https://unpkg.com/react@18/umd/react.production.min.js"></script>
<script crossorigin src="https://unpkg.com/react-dom@18/umd/react-dom.production.min.js"></script>
<script src="https://unpkg.com/@babel/standalone/babel.min.js"></script>
<script>
  // Force the classic JSX runtime (React.createElement). Recent @babel/standalone
  // defaults preset-react to the *automatic* runtime, which emits an
  // `import ... "react/jsx-runtime"` that a non-module page with UMD React can't
  // resolve — leaving the page stuck on "Loading...". Registering a classic-runtime
  // preset keeps everything buildless and dependency-free.
  Babel.registerPreset('react-classic', {
    presets: [[Babel.availablePresets['react'], { runtime: 'classic' }]]
  });
</script>

<!-- 2D solver (math layer, no DOM). -->
<script src="solver2d.js"></script>
</head>
<body>
<div id="root">
  <div style="padding: 40px; font-family: ui-monospace, 'SF Mono', Menlo, Consolas, monospace; color: #98a0ab;">
    Loading...
  </div>
</div>

<script type="text/babel" data-presets="react-classic">
const { useState, useEffect, useMemo, useRef, useCallback } = React;

// ---------- Warm 4-stop perceptual colormap (cream → gold → rust → near-black) ----------
// Matches the existing 1D lab's palette. norm in [0, 1].
const STOPS = [
  [247, 242, 227],
  [218, 178,  98],
  [173,  88,  62],
  [ 50,  34,  30]
];
function colormap(norm, out, offset) {
  const t = Math.max(0, Math.min(1, norm));
  const seg = t * 3;
  const i = Math.min(2, Math.floor(seg));
  const f = seg - i;
  const a = STOPS[i], b = STOPS[i + 1];
  out[offset    ] = a[0] + (b[0] - a[0]) * f;
  out[offset + 1] = a[1] + (b[1] - a[1]) * f;
  out[offset + 2] = a[2] + (b[2] - a[2]) * f;
  out[offset + 3] = 255;
}

// ---------- 2D heatmap on a canvas ----------
function Heatmap({ result, mode, busy }) {
  const canvasRef = useRef(null);
  useEffect(() => {
    const cv = canvasRef.current;
    if (!cv || !result) return;
    const { Nx, Ny } = result;

    // Pick the field according to view mode.
    let field, label;
    if (mode === "pressure") { field = result.p;  label = "p"; }
    else if (mode === "Mach")     { field = result.M;  label = "M"; }
    else if (mode === "schlieren") {
      // sqrt(|∇rho|^2) on the interior with one-sided differences at the edges.
      const f = new Float64Array(Nx * Ny);
      for (let j = 0; j < Ny; j++) {
        for (let i = 0; i < Nx; i++) {
          const iL = Math.max(0, i - 1), iR = Math.min(Nx - 1, i + 1);
          const jB = Math.max(0, j - 1), jT = Math.min(Ny - 1, j + 1);
          const gx = result.rho[j * Nx + iR] - result.rho[j * Nx + iL];
          const gy = result.rho[jT * Nx + i] - result.rho[jB * Nx + i];
          f[j * Nx + i] = Math.sqrt(Math.sqrt(gx * gx + gy * gy));
        }
      }
      field = f; label = "|∇ρ|";
    } else { field = result.rho; label = "ρ"; }

    let minV = Infinity, maxV = -Infinity;
    for (let k = 0; k < field.length; k++) {
      if (field[k] < minV) minV = field[k];
      if (field[k] > maxV) maxV = field[k];
    }
    const range = Math.max(maxV - minV, 1e-12);

    // Render the heatmap as ImageData. Pixel-perfect mapping: 1 grid cell = 1 pixel.
    cv.width = Nx; cv.height = Ny;
    const ctx = cv.getContext("2d");
    const img = ctx.createImageData(Nx, Ny);
    const data = img.data;
    // Flip y so that increasing j goes upward in the displayed image.
    for (let j = 0; j < Ny; j++) {
      const srcRow = j * Nx;
      const dstRow = (Ny - 1 - j) * Nx;
      for (let i = 0; i < Nx; i++) {
        const norm = (field[srcRow + i] - minV) / range;
        colormap(norm, data, (dstRow + i) * 4);
      }
    }
    ctx.putImageData(img, 0, 0);

    // Stretch via CSS to the canvas display size; let imageSmoothing off look pixelated.
    cv.style.imageRendering = "pixelated";

    // Tiny min/max readout overlay (in the caption div, not on the canvas).
    cv.dataset.label = label;
    cv.dataset.min = minV.toExponential(2);
    cv.dataset.max = maxV.toExponential(2);
  }, [result, mode]);

  return (
    <div style={{ position: "relative", background: "#1c1a17", padding: 6 }}>
      <canvas ref={canvasRef}
        style={{ display: "block", width: "100%", height: "auto",
                 aspectRatio: result ? (result.Nx + "/" + result.Ny) : "1/1",
                 background: "#1c1a17", opacity: busy ? 0.55 : 1, transition: "opacity 120ms" }} />
    </div>
  );
}

// ---------- SVG line plot (1D slice through the 2D field) ----------
function LinePlot({ x, y, label, color }) {
  const W = 360, H = 200;
  const pad = { l: 48, r: 12, t: 24, b: 28 };
  const pw = W - pad.l - pad.r, ph = H - pad.t - pad.b;
  let yMin = Infinity, yMax = -Infinity;
  for (let i = 0; i < y.length; i++) {
    if (Number.isFinite(y[i])) {
      if (y[i] < yMin) yMin = y[i];
      if (y[i] > yMax) yMax = y[i];
    }
  }
  if (!Number.isFinite(yMin)) { yMin = 0; yMax = 1; }
  const yPad = Math.max((yMax - yMin) * 0.08, 1e-6);
  const yLo = yMin - yPad, yHi = yMax + yPad;
  const xMin = x[0], xMax = x[x.length - 1];
  const toX = v => pad.l + ((v - xMin) / (xMax - xMin)) * pw;
  const toY = v => pad.t + (1 - (v - yLo) / (yHi - yLo)) * ph;
  let path = "";
  for (let i = 0; i < x.length; i++) {
    path += (i === 0 ? "M" : "L") + toX(x[i]).toFixed(2) + " " + toY(y[i]).toFixed(2);
  }
  const fmt = v => {
    const a = Math.abs(v);
    if (a === 0) return "0";
    if (a < 0.01 || a >= 1000) return v.toExponential(1);
    return v.toFixed(a < 1 ? 3 : 2);
  };
  return (
    <svg viewBox={"0 0 " + W + " " + H} style={{ display: "block", width: "100%" }}>
      <rect x={pad.l} y={pad.t} width={pw} height={ph} fill="#f7f2e3" stroke="#1c1a17" strokeWidth="0.6" />
      {[0.25, 0.5, 0.75].map((f, i) => (
        <line key={"v" + i} x1={pad.l + f * pw} x2={pad.l + f * pw} y1={pad.t} y2={pad.t + ph}
              stroke="#c8c0aa" strokeWidth="0.4" strokeDasharray="2 3" />
      ))}
      {[0.25, 0.5, 0.75].map((f, i) => (
        <line key={"h" + i} x1={pad.l} x2={pad.l + pw} y1={pad.t + f * ph} y2={pad.t + f * ph}
              stroke="#c8c0aa" strokeWidth="0.4" strokeDasharray="2 3" />
      ))}
      <path d={path} fill="none" stroke={color} strokeWidth="1.6" strokeLinejoin="round" />
      <text x={pad.l} y={pad.t - 8} fontFamily="ui-serif, 'Iowan Old Style', Palatino, Georgia, serif" fontSize="13" fontStyle="italic" fill="#1c1a17">{label}</text>
      <text x={pad.l - 6} y={toY(yHi) + 4} fontFamily="ui-monospace, 'SF Mono', Menlo, Consolas, monospace" fontSize="9" fill="#5a5547" textAnchor="end">{fmt(yHi)}</text>
      <text x={pad.l - 6} y={toY(yLo) + 4} fontFamily="ui-monospace, 'SF Mono', Menlo, Consolas, monospace" fontSize="9" fill="#5a5547" textAnchor="end">{fmt(yLo)}</text>
      <text x={toX(xMin)} y={pad.t + ph + 14} fontFamily="ui-monospace, 'SF Mono', Menlo, Consolas, monospace" fontSize="9" fill="#5a5547" textAnchor="start">{xMin.toFixed(2)}</text>
      <text x={toX(xMax)} y={pad.t + ph + 14} fontFamily="ui-monospace, 'SF Mono', Menlo, Consolas, monospace" fontSize="9" fill="#5a5547" textAnchor="end">{xMax.toFixed(2)}</text>
    </svg>
  );
}

// ---------- Numeric input ----------
function NumField({ label, value, onChange, step }) {
  return (
    <label style={{ display: "flex", flexDirection: "column", gap: 3, fontFamily: "ui-monospace, 'SF Mono', Menlo, Consolas, monospace", fontSize: 11, color: "var(--ink)" }}>
      <span style={{ letterSpacing: "0.08em", textTransform: "uppercase", color: "var(--muted)", fontSize: 9 }}>{label}</span>
      <input type="number" value={value} step={step || 0.1}
        onChange={e => onChange(parseFloat(e.target.value))}
        style={{ fontFamily: "ui-monospace, 'SF Mono', Menlo, Consolas, monospace", fontSize: 13, padding: "5px 7px",
          background: "var(--field)", border: "1px solid var(--faint)", color: "var(--ink)",
          borderRadius: 0, outline: "none", width: "100%" }} />
    </label>
  );
}

// ---------- Main app ----------
function App() {
  // Default preset = Sod-radial
  const presetName0 = "Sod-radial";
  const p0 = PRESETS2D[presetName0];

  const [presetName, setPresetName] = useState(presetName0);
  const [Nx, setNx]           = useState(p0.N);
  const [Ny, setNy]           = useState(p0.N);
  const [Lx, setLx]           = useState(p0.Lx);
  const [Ly, setLy]           = useState(p0.Ly);
  const [gamma, setGamma]     = useState(p0.gamma);
  const [cfl, setCfl]         = useState(p0.cfl);
  const [tEnd, setTEnd]       = useState(p0.tEnd);
  const [flux, setFlux]       = useState("HLLC");
  const [viewMode, setViewMode] = useState("density");
  const [showSlices, setShowSlices] = useState(true);

  const [result, setResult] = useState(null);
  const [info, setInfo]     = useState({ t: 0, step: 0, ms: 0 });
  const [busy, setBusy]     = useState(false);
  const [err, setErr]       = useState(null);
  const [animating, setAnimating] = useState(false);
  const stateRef = useRef(null);
  const rafRef   = useRef(null);

  const params = useMemo(() => ({
    Nx, Ny, Lx, Ly, gamma, cfl, flux,
    initFn: PRESETS2D[presetName].init
  }), [Nx, Ny, Lx, Ly, gamma, cfl, flux, presetName]);

  const validate = () => {
    if (gamma <= 1)                       return "gamma must be > 1.";
    if (cfl <= 0 || cfl > 0.9)            return "CFL must be in (0, 0.9].";
    if (Nx < 20 || Nx > 400)              return "Nx must be in [20, 400].";
    if (Ny < 20 || Ny > 400)              return "Ny must be in [20, 400].";
    if (tEnd <= 0)                        return "t_end must be positive.";
    return null;
  };

  const stopAnim = () => {
    if (rafRef.current) cancelAnimationFrame(rafRef.current);
    rafRef.current = null;
    setAnimating(false);
  };

  const runFinal = useCallback(() => {
    stopAnim();
    const e = validate(); if (e) { setErr(e); return; }
    setErr(null); setBusy(true);
    // Yield to let "computing..." render before the synchronous solve.
    setTimeout(() => {
      const t0 = performance.now();
      let s = initState2D(params);
      s = stepUntil2D(s, tEnd);
      const ms = performance.now() - t0;
      setResult(extract2D(s));
      setInfo({ t: s.t, step: s.step, ms });
      setBusy(false);
    }, 10);
  }, [params, tEnd]);

  const animate = () => {
    stopAnim();
    const e = validate(); if (e) { setErr(e); return; }
    setErr(null);
    const wallStart = performance.now();
    let s = initState2D(params);
    stateRef.current = s;
    setResult(extract2D(s));
    setInfo({ t: 0, step: 0, ms: 0 });
    setAnimating(true);
    // Time-march in chunks of CFL-limited steps so each rAF tick stays responsive.
    // We aim for ~20 frames per simulation regardless of step count.
    const FRAMES = 40;
    let frame = 0;
    const tick = () => {
      frame++;
      const target = Math.min(tEnd, (frame / FRAMES) * tEnd);
      stateRef.current = stepUntil2D(stateRef.current, target);
      setResult(extract2D(stateRef.current));
      setInfo({ t: stateRef.current.t, step: stateRef.current.step,
                ms: performance.now() - wallStart });
      if (stateRef.current.t < tEnd) {
        rafRef.current = requestAnimationFrame(tick);
      } else {
        rafRef.current = null;
        setAnimating(false);
      }
    };
    rafRef.current = requestAnimationFrame(tick);
  };

  // Initial render on mount
  useEffect(() => { runFinal(); /* eslint-disable-next-line */ }, []);

  const loadPreset = name => {
    stopAnim();
    const p = PRESETS2D[name];
    setPresetName(name);
    setNx(p.N); setNy(p.N);
    setLx(p.Lx); setLy(p.Ly);
    setGamma(p.gamma); setCfl(p.cfl); setTEnd(p.tEnd);
  };

  // Slice plots: x-slice through the y-midline, y-slice through the x-midline.
  const slices = useMemo(() => {
    if (!result || !showSlices) return null;
    const jMid = Math.floor(result.Ny / 2);
    const iMid = Math.floor(result.Nx / 2);
    return {
      xs: result.xs, ys: result.ys,
      rhoX: slice2D(result.rho, result.Nx, result.Ny, "x", jMid),
      pX:   slice2D(result.p,   result.Nx, result.Ny, "x", jMid),
      rhoY: slice2D(result.rho, result.Nx, result.Ny, "y", iMid),
      pY:   slice2D(result.p,   result.Nx, result.Ny, "y", iMid),
      jMid, iMid
    };
  }, [result, showSlices]);

  const C = { rho: "#8b3a2f", p: "#4a5d23" };
  const fieldLabel = viewMode === "schlieren" ? "|∇ρ| (schlieren)" :
                     viewMode === "pressure"  ? "pressure" :
                     viewMode === "Mach"      ? "Mach"     : "density";

  return (
    <div className="grain" style={{ minHeight: "100vh", background: "var(--bg)", color: "var(--ink)",
      fontFamily: "ui-monospace, 'SF Mono', Menlo, Consolas, monospace" }}>
      <div style={{ display: "flex", alignItems: "center", gap: 0,
                     borderBottom: "1.5px solid var(--line)", background: "var(--surface)",
                     padding: "0 22px", position: "sticky", top: 0, zIndex: 10 }}>
        <span className="smallcaps" style={{ fontFamily: "ui-serif, 'Iowan Old Style', Palatino, Georgia, serif", fontStyle: "italic",
                     fontSize: 13, color: "var(--ink)", padding: "10px 14px 10px 0" }}>
          Euler Lab
        </span>
        <a href="index.html" className="tablink" style={{ fontSize: 11, letterSpacing: "0.08em",
                     textTransform: "uppercase", padding: "10px 18px 10px 0", borderBottom: "none" }}>
          ← 1D Shock Tube + Nozzle
        </a>
        <span style={{ fontSize: 11, letterSpacing: "0.08em", textTransform: "uppercase",
                     padding: "10px 0", marginLeft: "auto", color: "var(--accent)", fontWeight: 700,
                     borderBottom: "2.5px solid var(--accent)" }}>
          2D Cartesian
        </span>
      </div>
      <details style={{ padding: "8px 22px 0", fontSize: 11, color: "var(--muted)" }}>
        <summary style={{ cursor: "pointer", letterSpacing: "0.06em", textTransform: "uppercase", fontSize: 10 }}>
          what am I looking at?
        </summary>
        <p style={{ margin: "6px 0 0", maxWidth: 760, lineHeight: 1.5 }}>
          Full 2D compressible Euler on a Cartesian grid. Pick a <i>preset</i> initial condition
          (radial Sod, a four-quadrant 2D Riemann problem, the Sedov point blast, or a Kelvin–Helmholtz
          shear layer), choose a Riemann <i>flux</i>, then <i>run</i> or <i>animate</i>. The heatmap shows
          the chosen field over the whole grid; the line-outs cut through the x- and y-midlines so you can
          read wave structure quantitatively. The <b>← 1D</b> link switches to the shock-tube + nozzle lab.
        </p>
      </details>
      <div style={{ padding: "16px 22px 36px" }}>
      <header style={{ borderBottom: "1.5px solid var(--line)", paddingBottom: 10, marginBottom: 16 }}>
        <div style={{ display: "flex", justifyContent: "space-between", alignItems: "baseline", flexWrap: "wrap", gap: 8 }}>
          <h1 style={{ fontFamily: "ui-serif, 'Iowan Old Style', Palatino, Georgia, serif", fontWeight: 600, fontStyle: "italic", fontSize: 34, lineHeight: 1, margin: 0 }}>
            2D Euler <span style={{ fontStyle: "normal", fontWeight: 400 }}>{"· cartesian laboratory"}</span>
          </h1>
          <span className="smallcaps" style={{ fontSize: 10, color: "var(--muted)" }}>{flux + " · MUSCL · SSP-RK2"}</span>
        </div>
        <p style={{ margin: "6px 0 0", fontSize: 11, color: "var(--muted)", maxWidth: 760 }}>
          Pick a 2D initial condition, choose a Riemann flux, and time-march. The heatmap renders the
          chosen field across the whole grid; the line-out plots cut through the x- and y-midlines so
          you can read the wave structure quantitatively.
        </p>
      </header>

      <div style={{ display: "flex", flexWrap: "wrap", gap: 6, marginBottom: 14, alignItems: "center" }}>
        <span className="smallcaps" style={{ fontSize: 10, color: "var(--muted)", marginRight: 4 }}>{"presets ›"}</span>
        {Object.keys(PRESETS2D).map(name => (
          <button key={name} className="btn" onClick={() => loadPreset(name)}
                  style={presetName === name ? { background: "var(--accent)", color: "var(--accent-ink)" } : {}}>{name}</button>
        ))}
      </div>

      <div style={{ display: "grid", gridTemplateColumns: "1fr 1fr", gap: 14, marginBottom: 16 }}>
        <fieldset style={{ border: "1px solid var(--faint)", padding: "10px 12px 12px", margin: 0 }}>
          <legend className="smallcaps" style={{ fontFamily: "ui-serif, 'Iowan Old Style', Palatino, Georgia, serif", fontStyle: "italic", fontSize: 13, padding: "0 6px" }}>
            grid
          </legend>
          <div style={{ display: "grid", gridTemplateColumns: "1fr 1fr 1fr 1fr", gap: 8 }}>
            <NumField label="Nx" value={Nx}  onChange={v => setNx(Math.round(v))} step={20} />
            <NumField label="Ny" value={Ny}  onChange={v => setNy(Math.round(v))} step={20} />
            <NumField label="Lx" value={Lx}  onChange={setLx} step={0.1} />
            <NumField label="Ly" value={Ly}  onChange={setLy} step={0.1} />
          </div>
        </fieldset>

        <fieldset style={{ border: "1px solid var(--faint)", padding: "10px 12px 12px", margin: 0 }}>
          <legend className="smallcaps" style={{ fontFamily: "ui-serif, 'Iowan Old Style', Palatino, Georgia, serif", fontStyle: "italic", fontSize: 13, padding: "0 6px" }}>
            numerics
          </legend>
          <div style={{ display: "grid", gridTemplateColumns: "1fr 1fr 1fr", gap: 8 }}>
            <NumField label="gamma" value={gamma} onChange={setGamma} step={0.05} />
            <NumField label="CFL"   value={cfl}   onChange={setCfl}   step={0.05} />
            <NumField label="t end" value={tEnd}  onChange={setTEnd}  step={0.05} />
          </div>
        </fieldset>
      </div>

      <div style={{ display: "flex", flexWrap: "wrap", gap: 10, alignItems: "center", marginBottom: 14, padding: "10px 12px",
                     background: "var(--elevated)", color: "var(--ink)", borderRadius: 10 }}>
        <label style={{ display: "flex", alignItems: "center", gap: 6, fontSize: 10, letterSpacing: "0.08em", textTransform: "uppercase" }}>
          <span>flux</span>
          <select value={flux} onChange={e => setFlux(e.target.value)} style={{ background: "var(--field)", color: "var(--ink)" }}>
            <option value="HLLC">HLLC</option>
            <option value="HLL">HLL</option>
            <option value="Roe">Roe</option>
            <option value="Rusanov">Rusanov</option>
          </select>
        </label>
        <label style={{ display: "flex", alignItems: "center", gap: 6, fontSize: 10, letterSpacing: "0.08em", textTransform: "uppercase" }}>
          <span>view</span>
          <select value={viewMode} onChange={e => setViewMode(e.target.value)} style={{ background: "var(--field)", color: "var(--ink)" }}>
            <option value="density">density</option>
            <option value="schlieren">schlieren</option>
            <option value="pressure">pressure</option>
            <option value="Mach">Mach</option>
          </select>
        </label>
        <label style={{ display: "flex", alignItems: "center", gap: 6, fontSize: 10, letterSpacing: "0.08em", textTransform: "uppercase", cursor: "pointer" }}>
          <input type="checkbox" checked={showSlices} onChange={e => setShowSlices(e.target.checked)} style={{ accentColor: "var(--accent)" }} />
          <span>centerline slices</span>
        </label>
        <button className="btn btn-primary" onClick={runFinal} disabled={busy || animating}>
          {busy ? "computing..." : "run to t_end"}
        </button>
        <button className="btn" onClick={animate} disabled={busy || animating}
                style={{ background: animating ? "var(--accent-2)" : "var(--field)", color: animating ? "var(--accent-ink)" : "var(--ink)" }}>
          {animating ? "animating..." : "animate"}
        </button>
        {animating && <button className="btn" onClick={stopAnim} style={{ background: "var(--field)", color: "var(--ink)" }}>stop</button>}

        <div style={{ marginLeft: "auto", fontSize: 11, display: "flex", gap: 18, color: "var(--ink)" }}>
          <span><span style={{ color: "var(--muted)" }}>t = </span>{info.t.toFixed(4)}</span>
          <span><span style={{ color: "var(--muted)" }}>steps = </span>{info.step}</span>
          <span><span style={{ color: "var(--muted)" }}>wall = </span>{info.ms.toFixed(0)} ms</span>
        </div>
      </div>

      {err && (
        <div style={{ padding: "8px 12px", border: "1px solid var(--danger)", background: "var(--danger-bg)", color: "var(--accent)",
                        fontSize: 11, marginBottom: 12 }}>
          ! {err}
        </div>
      )}

      <div style={{ display: "grid", gridTemplateColumns: showSlices ? "1.6fr 1fr" : "1fr", gap: 14 }}>
        <div>
          <div className="smallcaps" style={{ fontFamily: "ui-serif, 'Iowan Old Style', Palatino, Georgia, serif", fontStyle: "italic", fontSize: 13, color: "var(--ink)", marginBottom: 4 }}>
            {fieldLabel} field {"· " + Nx + " × " + Ny}
          </div>
          {result && <Heatmap result={result} mode={viewMode} busy={busy} />}
        </div>

        {showSlices && slices && (
          <div style={{ display: "grid", gridTemplateRows: "1fr 1fr 1fr 1fr", gap: 10, background: "var(--elevated)", padding: 10, borderRadius: 12 }}>
            <div style={{ background: "#efe9d8", padding: "6px 8px 3px", borderRadius: 8 }}>
              <LinePlot x={slices.xs} y={slices.rhoX}
                        label={"density along y = " + (slices.ys[slices.jMid] || 0).toFixed(3)}
                        color={C.rho} />
            </div>
            <div style={{ background: "#efe9d8", padding: "6px 8px 3px", borderRadius: 8 }}>
              <LinePlot x={slices.xs} y={slices.pX}
                        label={"pressure along y = " + (slices.ys[slices.jMid] || 0).toFixed(3)}
                        color={C.p} />
            </div>
            <div style={{ background: "#efe9d8", padding: "6px 8px 3px", borderRadius: 8 }}>
              <LinePlot x={slices.ys} y={slices.rhoY}
                        label={"density along x = " + (slices.xs[slices.iMid] || 0).toFixed(3)}
                        color={C.rho} />
            </div>
            <div style={{ background: "#efe9d8", padding: "6px 8px 3px", borderRadius: 8 }}>
              <LinePlot x={slices.ys} y={slices.pY}
                        label={"pressure along x = " + (slices.xs[slices.iMid] || 0).toFixed(3)}
                        color={C.p} />
            </div>
          </div>
        )}
      </div>

      <footer style={{ marginTop: 16, paddingTop: 10, borderTop: "1px solid var(--line)", fontSize: 10, color: "var(--muted)",
                        display: "flex", justifyContent: "space-between", flexWrap: "wrap", gap: 8 }}>
        <span>dU/dt + dF/dx + dG/dy = 0  {"·"}  U = [rho, rho*u, rho*v, E]  {"·"}  ideal gas</span>
        <span className="smallcaps">finite volume {"·"} 2D cartesian {"·"} transmissive BCs</span>
      </footer>
      </div>
    </div>
  );
}

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