CLS-VoF lacks 3D support (integral.h surface tension + two-phase-clsvof.h)

## Summary

The CLS-VoF (Coupled Level-Set Volume-of-Fluid) implementation in Basilisk **does not support true 3D simulations**. While the code may compile with 3D grids (`grid/octree.h`), it contains hardcoded 2D implementations that produce incorrect results in 3D.

**Critical Issue**: The surface tension implementation (`integral.h`) lacks 3D formulations for curvature calculation and stress tensor computation, making CLS-VoF fundamentally incompatible with 3D flows.

## 🔴 Three Specific Bugs

### 1. integral.h: 2D-Only Curvature Calculation (Lines 98-107)

The `distance_curvature()` function only computes derivatives in x and y:

```c
static inline double distance_curvature (Point point, scalar d)
{
double dx = (d[1] - d[-1])/2.; // x derivative only
double dy = (d[0,1] - d[0,-1])/2.; // y derivative only
// Missing: dz, dzz, dxz, dyz for 3D
double dn = sqrt(sq(dx) + sq(dy)) + 1e-30; // 2D gradient only
return (sq(dx)*dyy - 2.*dx*dy*dxy + sq(dy)*dxx)/cube(dn)/Delta;
}
```

**Missing for 3D**: z-direction derivatives and 3D mean curvature formula.

### 2. integral.h: 2×2 Stress Tensor Instead of 3×3 (Lines 146-147)

```c
scalar Sxx[], Sxy[], Syy[], Syx[];
tensor S; S.x.x = Sxx, S.x.y = Sxy, S.y.y = Syy, S.y.x = Syx;
```

**Missing for 3D**: `Sxz`, `Syz`, `Szz` components needed for full 3D stress tensor.

### 3. two-phase-clsvof.h: 4-Vertex Averaging Instead of 8 (Line 37)

```c
event init (i = 0)
{
vertex scalar phi[];
foreach_vertex()
phi[] = (d[] + d[-1] + d[0,-1] + d[-1,-1])/4.; // Only 4 vertices (2D)
fractions (phi, f);
}
```

**Required for 3D**: Average over all 8 vertices of a cube.

## 📊 Evidence

### Test Cases Are 2D/Axisymmetric Only
- `test/rising.c` → 2D or axisymmetric
- `test/capwave.c` → 2D
- `test/marangoni.c` → Axisymmetric
- No 3D test cases exist for CLS-VoF

### User Evidence
File: `basilisk-wiki/sandbox/farsoiya/marangoni_surfactant/3D_rising_bubble.c`

```c
#include "grid/octree.h" // 3D grid
#include "two-phase.h" // Using standard VOF
// #include "two-phase-clsvof.h" // CLS-VoF commented out for 3D!
```

Users have encountered this limitation and switched to standard VOF for 3D.

## 💥 Impact

**Current Status**:
- ✅ Works perfectly in 2D Cartesian
- ✅ Works perfectly in axisymmetric
- ❌ Produces **incorrect results in 3D**:
- Wrong initial interface
- Incorrect surface tension forces
- Missing z-direction stress components

**Affected Use Cases**:
- 3D rising/falling bubbles and droplets
- 3D capillary-driven flows
- Any 3D surface tension-dominated flow
- Users trying to leverage CLS-VoF's superior curvature accuracy in 3D

## ✅ Current Workaround

For 3D two-phase flows, use standard VOF:

```c
#include "grid/octree.h"
#include "two-phase.h" // Standard VOF (not CLS-VoF)
#include "tension.h" // Height-function curvature
```

## 📋 Detailed Technical Report

A comprehensive analysis is available in: **CLS-VOF_3D-missing.md**

This report includes:
- Detailed code analysis with line numbers
- Required changes for 3D support
- Technical requirements for implementation
- Testing recommendations

## 🔧 Suggested Fix

The main blocker is `integral.h` (surface tension), not the CLS-VoF coupling itself. Required changes:

1. **Extend curvature to 3D**: Add z-derivatives and 3D mean curvature formula
2. **Extend stress tensor to 3×3**: Add Sxz, Syz, Szz components
3. **Extend stencils**: Update to handle 3D neighbors
4. **Fix initialization**: Use 8-vertex averaging for 3D

## 🎯 Priority

This is a **significant limitation** because:
- CLS-VoF is advertised as a superior method for surface tension
- Users expect it to work in 3D (code compiles without warnings)
- Silent failure produces incorrect results
- Many modern CFD applications require 3D simulations

## 🏷️ Labels

- `bug`: Current behavior is incorrect in 3D
- `enhancement`: Adding 3D support would be a valuable feature

---

**Reported by**: Comphy Lab team
**Repository**: comphy-lab/basilisk-C (fork of basilisk.fr)
**Basilisk Version**: Current main branch (synced with basilisk.fr)