date2026-07-28tags:openfoam: :wiki:read5 minlinks2 out · 0 in
Overview
This note catalogs all OpenFOAM solvers organized by physics domain. Each solver is an executable (.Foam) that solves a specific combination of governing equations: continuity, momentum (Navier-Stokes), energy, species transport, turbulence, radiation, and multiphase interface capture. Solvers are chosen based on flow regime (compressible vs. incompressible), phase behavior (single, two, multiphase, granular), and thermal state ($T = const$ vs. $T = T(x_i, t)$).
Black-Scholes PDE is the heat equation with a moving boundary
See: G. Winkler (2024) "A Note on CFD Methods Applied to Finance"
ANSYS Equivalent Solver Mapping
The following table identifies which ANSYS Fluent setting corresponds to each OpenFOAM solver. This is useful for engineers migrating between platforms or cross-referencing literature.
OpenFOAM Solver
ANSYS Fluent Equivalent
Discretization
----------------
------------------------
----------------
icoFoam
Pressure-based, steady, laminar
Segregated, SIMPLE
simpleFoam
Pressure-based, steady, RANS
Segregated, SIMPLE; default = second order upwind
pisoFoam
Pressure-based, trans, laminar
Segregated, PISO
pimpleFoam
Pressure-based, trans, RANS/LES
Segregated, PISO with under-relaxation
rhoSimpleFoam
Density-based, steady
Coupled or segregated, density-based solver
rhoPimpleFoam
Density-based, trans
Coupled density-based, adaptive time step
rhoCentralFoam
Density-based, steady, shock-capturing
Roe/HLLC flux; upwind schemes for convection
interFoam
VOF model, single-phase free surface
Implicit VOF (Geometric Reconstruction)
buoyantSimpleFoam
Pressure-based, gravity + energy
Segregated, coupled gravity
chtMultiRegionFoam
Fluent conjugate heat transfer
Segregated pressure-based, multi-region
fireFoam
Fluent FDS-compat mode
Segregated, combustion model (EDC/PDF)
mhdFoam
MHD module (if licensed)
Segregated, MHD model enabled
solidDisplacementFoam
Mechanical (ANSYS Structural)
Linear elastic solver
blackSholesFoam
N/A (no CFD equivalent)
Financial engineering
Foundation v14 Module Mapping (Solvers)
The v14 Foundation release introduced a modular solver architecture. The following table maps solvers to their physics modules:
Module
Solver / Function
--------
------------------
liquidPhase
liquidRegion (incompressible liquid)
compressibleFlow
compressibleRegion (variable density)
multiphaseVOF
multiRegionTwoPhase (VOF-based multiphase)
multiphaseEulerian
multiRegionEulerian (Euler-Euler multiphase)
heatTransfer
heatRegion (solid or fluid conduction)
conjugateHeatTransfer
conjugateRegion (fluid + solid coupling)
combustion
combustionRegion (reacting flow)
multiphaseGranular
granularRegion (kinetic theory granular)
electromagneticsRegion (MHD, EHD)
solidMechanics
solidRegion (structural mechanics)
lagrangian
particleCloud (Lagrangian particles)
meshMotion
dynamicRegion (moving/deforming mesh)
porousRegion (porous media)
The foamRun executable configures solver modules via caseRunDict, while foamMultiRun uses a multi-region configuration file specifying per-region physics and coupling.
Dry Notes on Solver Usage
1. simpleFoam is to OpenFOAM what #include <iostream> is to C++. It is the simplest useful solver. If you cannot set up simpleFoam for flow over a backward-facing step within an hour, you are not yet at the level where OpenFOAM will feel natural.
2. rhoCentralFoam for shock tubes works out of the box. rhoCentralFoam for wing-body interference at $M=5$ does not. There is a reason.
3. For the record, blackSholesFoam was written by someone with a keen sense of humor and a deep understanding of the irony that the most widely-used CFD framework in the world is being used to price American options. This is not an endorsement of OpenFOAM in finance, but a note that the code exists and it does work.
Cross-Links
References
Weller, H. G. et al. (1998). "A tensorial approach to computational hydrodynamics." Computers in Physics, 12(6), 620-631.