Contents

1. Available solvers with hybrid approximation
2. Meeting points for users and developers
3. Available OpenFOAM versions
4. Derived projects
5. Research studies where the library was useful
6. For citations

Available solvers with hybrid approximation

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United collection of hybrid Central solvers based on central-upwind schemes of Kurganov and Tadmor and LTS support for steady-state calculations: one-phase, two-phase and multicomponent versions.

Only OpenFOAM+ version of the OpenFOAM technology is supported since 2018. The framework contains next solvers:

1. Compressible single phase flow solvers:
   • pimpleCentralFoam - Pressure-based semi implicit solver for compressible flow of perfect gas;
   • rhoPimpleCentralFoam - Pressure-based semi implicit solver for compressible flow of real gas;
   • pimpleCentralDyMFoam - Pressure-based semi implicit solver for compressible flow of perfect gas with mesh motion and AMR;
   • chtMultiRegionCentralFoam - Pressure-based semi implicit solver for conjugate simulation of compressible perfect gas flow (Mach number is ranging from 0 to 6) and solid body heat transfer.
2. Multi-component solvers:
   • reactingPimpleCentralFoam - Pressure-based semi implicit solver for compressible flow with combustion and chemical reactions;
   • reactingPimpleCentralDyMFoam - Pressure-based semi implicit solver for compressible flow with combustion, chemical reactions and dynamic mesh (incl. AMI or AMR);
   • reactingLagrangianPimpleCentralFoam - Pressure-based semi implicit solver for compressible flow with combustion, particles motion, phase change and chemical reactions.
3. Multi-phase solvers:
   • vofTwoPhaseCentralFoam - an improved version (since OpenFOAM+ 2312) of interTwoPhaseCentralFoam solver that uses volumetric fluxes for transport (increased robustness).
   • interTwoPhaseCentralFoam - pressure-based solver for compressible (0-4 Mach numbers) flow of two-phase media with account to viscosity and gravity. The solver utilizes VoF method for resolution of phase interface and ACID technique ( https://doi.org/10.1016/j.jcp.2018.04.028) to calculate properties in the region where both phases are present.
   • twoPhaseMixingCentralFoam - Transient Eulerian two-phase solver. Liquid and gas are considered as compressible fluids. Mass transfer at the interface is not accounted.
   • twoPhaseMixingCentralDyMFoam - Transient Eulerian two-phase solver with dynamic meshes. Liquid and gas are considered as compressible fluids. Mass transfer at the interface is not accounted.

Meeting points for users and developers

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You can discuss questions of hybridCentralSolvers usage at Telegram Group: https://t.me/hybridCentralSolvers

There is a ResearchGate project dedicated to the development of hybridCentralSolvers library

Available OpenFOAM versions

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The library is available for next versions of OpenFOAM:

• OpenFOAM 3.1 - master branch
• OpenFOAM 4.1 - dev-of4.1 branch
• OpenFOAM 6 - dev-of6 branch
• OpenFOAM+ 1812 - digitef-dev-1812
• OpenFOAM+ 1912 - digitef-dev-1912
• OpenFOAM+ 2012 - digitef-dev-2012
• OpenFOAM+ 2112 - digitef-dev-2112
• OpenFOAM+ 2212 - digitef-dev-2212
• OpenFOAM+ 2312 - digitef-dev-2312
• OpenFOAM+ 2412 - digitef-dev-2412
• OpenFOAM+ 2512 - digitef-dev-2512

Latest changes and bug fixes are applied only in branches corresponding to latest version of OpenFOAM.

Derived projects

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The library or approach were used in next projects:

• multiRegionRectingPimpleCentralFoam - the solver for coupled simulation of gas dynamics and heat transfer using hybrid KT/PIMPLE approximation of convective fluxes
• adjointReactingRhoPimpleCentralFoam - the solver for adjoint shape optimization of region with gas flow modelled using hybrid KT/PIMPLE approximation of convective fluxes
• HLLCFoam - the solver for perfect gas dynamics using hybrid HLLC/PIMPLE approach (an extension of the hybrid KNP/PIMPLE scheme for HLLC approximate Riemann solver).

Research studies where the library was useful

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If you want to see your research in this list, please write to Issues.

<p align="center"> >>>>> 2026 <<<<< </p>

| Title | Description | |------|-------------| |Modeling of ammonia under-expanded jets for application in advanced propulsion systems: Article| | |Role of reaction rate uncertainties on the dynamics of two-dimensional detonation: Article| --- | |A pressure-based hybrid framework for sub-and supersonic compressible two-phase flow with non-equilibrium phase change: Article| |

<p align="center"> >>>>> 2025 <<<<< </p>

| Title | Description | |------|-------------| |Numerical Investigation of Cylindrical Water Droplets Subjected to Air Shock Loading at a High Weber Number|| |CFD Prediction of Tandem Water Columns Aerobreakup Using Open-Source Codes: Article| --- | |Performance evaluation of RANS turbulence model coupled with pressure-based solver for supersonic flow| --- | |Visual and Quantitative Assessment of OpenFOAM Solver Accuracy for Simulating Oblique Shock Train: Article|| |Application of Singular Value Decomposition and Autoencoder for Supersonic Flow over Backward Facing Step: Article|| |Assessment of Multi-Fidelity Tools for the Aeropropulsion Analysis of a Small-Scale Supersonic Unmanned Aerial Vehicle: MSc thesis|| |Assessment of Turbulence Modelling for Compressibility Effects in Ejector Ramjet Applications MSc thesis|| |Supersonic Combustion of Ethylene in a Pylon-Cavity Configuration with Curved Pylons: Article| --- | |Assessment of modern shock capturing schemes for all-speed flows in the OpenFOAM framework: Article| --- | |Ejector Recirculation and Entrainment: Article| --- | |Numerical investigation of supersonic two-component jet flow: Article|---| |Experimental–Numerical Comparison of H2–Air Detonations: Influence of N2 Chemistry and Diffusion Effects: Article|| |Zamana bağlı akış alanının açık kaynak programlar ile aerodinamik incelemesi: **