2D version of MHIT36

Version of MHIT36 simpliefied to work in 2D (single GPU version) Numerical scheme: Finite difference-based (FD2). Time integration:

• Temperature: SSP-RK3 + CN for Temperature along y (flag)
• Navier-Stokes: RK3
• Phase-field: RK3 (to be implemented)
• NS: Fractional method, Poisson solver based on FFT (along x - periodic) + TDMA (y, walls).

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If you use this code, please cite the following works:

  @article{roccon2025,
  title   = {MHIT36: A Phase-Field Code for Gpu Simulations of Multiphase Homogeneous Isotropic Turbulence},
  author  = {Roccon, A. and Enzenberger, L. and Zaza, D. and Soldati, A.},
  journal = {Computer Physics Communications},
  year    = {2025},
  volume  = {314},
  issue   = {109804},
  doi     = {https://doi.org/10.1016/j.cpc.2025.109804}
}

  @article{roccon2026,
  title   = {MHIT36: Extension to wall-bounded turbulence and scalar transport equation},
  author  = {Roccon, A.},
  journal = {Computer Physics Communications},
  year    = {2026},
  volume  = {---},
  issue   = {109956},
  doi     = {https://doi.org/10.1016/j.cpc.2025.109956}
}

Check list of features implemented (or to be implemented)

• Poisson solver (Matlab) ✅
• Poisson solver validation (Matlab) ✅
• Poisson solver convergence (Matlab) ✅
• Poisson solver (Fortran: FFT forth and back) ✅
• Poisson solver (Fortran) ✅
• Added support for stretched nodes along z (Matlab only, easy to move in Fortan) ✅
• Introduced phi ✅
• Introduced temperature ✅
• Introduced temporal loop ✅
• Navier-Stokes solution ✅
• Validation (phi) ✅
• Validation (temp) ✅
• Validation (NS): Channel flow (pressure-driven + wall-driven) ✅
• RB setup ✅
• GPU offloading of entire code ✅
• TDMA optimization (x 10 speed-up) ✅

Validation

• Aspect ratio: 2
• Ra from 1e3 to 1e9 + Pr=1
• Grid: 512 x 256

Example of single-phase RBC (Ra=1e9 + Pr=1)

Example of multiphase RBC (Ra=1e7 + Pr=1)

Performance and resolution tested

• 512 x 256 - 2.5 ms/iter - RTX5000 16GB (NS + Temp exp. + phase-field)
• 512 x 256 - 0.7 ms/iter - A100 64GB (NS + Temp exp. + phase-field)
• 2048 x 1024 - 19 ms/iter - RTX5000 16GB (NS + Temp exp. + phase-field)
• 2048 x 1024 - 5.5 ms/iter - A100 64GB (NS + Temp exp. + phase-field)
• 4096 x 2048 - 70 ms/iter - RTX5000 16GB (NS + Temp exp. + phase-field)

Grid points (staggered)