KerM

Kernel Mixing Model for Turbulent Combustion and Transport PDF method.

This repo is for 0-D simple validation, for PaSR validation please refer to PaSR

1. Usage

• Fortran version:
  • src_fortran/mixing_test.f90: main program for testing.
  • src_fortran/mixing_model_kerm.f90: source code of KerM with differential diffusion supported.
  • src_fortran/mixing_model_iem.f90: source code of IEM, used for comparison.
  • src_fortran/mixing_model_mcurl.f90: source code of MC, used for comparison.
  • src_fortran/mixing_model_mcmg.f90: source code of MCMG adopted from ¹, which implements the mapping closure mixing model used for comparison.
  • src_fortran/emst.f and src_fortran/emst_subs.f: source code of EMST adopted from ², used for comparison.

  # build executable file (single precision float)
  make fortran
  # run simulation, faster than cpp version
  ./mix
  # show results
  python performance.py fortran

  • Comparison results of 10k particles for EMST and MCMG; 50k particles for other models, where the dash lines are for the DNS data from ³ (For KerM, sigma_k=0.25 is used)

  • Performance of mixing models

    

C++ version

• C++ Version:

  • src_cpp/MixingModels.hpp: implementation of mixing models
  • src_cpp/main.cpp: run simulation
  • performance.py: show results

  # build executable file
  make
  # run simulation, taking around 10 seconds for N=1000
  ./mix
  # show results
  python performance.py

  Comparison results of 4k particles for EMST and 100k particles for other models (KerM sigma_k=0.25), where the dash lines are for the DNS data from ³

  

  Performance of mixing models (EMST-1D do not account aging properties and no IEM assisted, for original EMST implementation, please refer to the Fortran version)

  

Python version

• Python Version:

  • src_python/models.py: implementation of mixing models
  • src_python/mixing_py.py: run simulation

  # run simulation, EMST taking around 6 seconds for N=400
  python src_python/mixing_py.py

  Comparison results of 400 particles for EMST and 50k particles for other models (only uniform weighted samples are used), where the dash lines are for the DNS data from ³

  

2. Implementations

Please refer to TheoryGuide.pdf

Footnotes

1. The original MCMG implementation comes from https://tnfworkshop.org/wp-content/uploads/2019/03/MM-INTAS.zip ↩

2. The original EMST implementation comes from https://tcg.mae.cornell.edu/emst/ ↩

3. A. Juneja, S.B. Pope, A DNS study of turbulent mixing of two passive scalars, Physiscs of Fluids 8 (1996) 2161. ↩ ↩² ↩³