[Enhancement] Replace BCG scheme with conservative advection for log-conformation tensor

[VatsalSy]

Overview

Currently using Bell-Collela-Glaz (BCG) scheme for log-conformation tensor advection. Proposal to evaluate and potentially implement a conservative form using VoF color function transport method.

Related Issues

• [Enhancement] Bound conformation tensor fields inside one of the fluids #6 [Enhancement] Bound conformation tensor fields inside one of the fluids

This enhancement is closely related to issue #6, as both deal with the handling of conformation tensor fields. The conservative form implementation could potentially help with maintaining proper bounds on the tensor fields.

Proposed Changes

1. Implementation Investigation

• Study conservative form implementation in navier-stokes/conserving.h
• Analyze compatibility with log-conformation tensor transport
• Evaluate VoF color function transport method integration
• Document potential impacts on numerical stability

2. Performance Analysis

• Benchmark current BCG implementation
• Implement test cases for conservative form
• Compare performance metrics:
  • Computational cost
  • Memory usage
  • Numerical accuracy
  • Stability characteristics
  • Conservation properties

3. VoF Integration

• Design VoF color function transport integration
• Test boundary condition handling
• Evaluate impact on multi-phase simulations
• Document any limitations or constraints

Technical Considerations

• Impact on existing simulations
• Compatibility with 3D implementation
• Integration with current tensor field calculations
• Effect on numerical stability
• Conservation properties validation

Expected Benefits

• Improved conservation properties
• Potentially better stability
• More consistent behavior with VoF method
• Better handling of tensor field boundaries

Implementation Strategy

1. Create test implementation branch
2. Develop prototype using simple test cases
3. Compare results with current implementation
4. Document performance differences
5. Make recommendation for full implementation

Labels

• enhancement
• performance
• numerical-methods
• help wanted

References

• navier-stokes/conserving.h
• Current BCG implementation
• Related research papers (to be added)