## Solver: overRhoSimpleFoam Description

overRhoSimpleFoam is a pressure-based solver designed for steady-state simulations of compressible flow. It handles laminar and turbulent, single-phase flows with temperature and density variations (it solves the energy equation).

Based on rhoSimpleFoam, the solver enhances its predecessor’s capabilities by incorporating overset (Chimera) meshes. This advancement makes the solver particularly suitable for scenarios involving significant object motion, where traditional dynamic meshes prove inadequate.

The overset framework offers a universal approach to implementing overset meshes for both stationary and dynamic scenarios. It utilizes mappings from cell to cell across various, separate mesh regions to create a unified domain. This approach facilitates intricate mesh movements and interactions without the drawbacks typical of mesh deformation, accommodating both single-phase and multiphase flows.

The solver uses the **SIMPLE** (Semi-Implicit Method for Pressure-Linked Equations) algorithm for pressure-momentum coupling, augmented by under-relaxation techniques to enhance convergence. It supports Multiple Reference Frame (MRF), porosity modeling and allows easy integration of passive scalar transport equations and source terms.

The applications are very similar to rhoSimpleFoam; however, the use of overset meshes can save significant time that would otherwise be spent on remeshing. For instance, in simulating flow around an airfoil, the fluid mesh could be a simple box surrounding the airfoil’s overset mesh. To easily change the angle of attack, the overset mesh can simply be rotated. Another example is the steady-state flow through a valve, where the overset mesh represents the plug that can close off the flow.

## Solver: overRhoSimpleFoam Features

**Steady-State****Compressible****Single-Phase**

- High-Speed Aerodynamics
- Subsonic Flow
- Transonic Flow
- Pressure-Based Solver
- Overset (Chimera) Meshes

- Laminar and Turbulent (RANS, LES, DES)
- Equation of State Models
- Rotating Objects:
- Multiple Reference Frames (MRF)
- Rotating Mesh Motion

- Passive Scalar
- Porosity Modeling
- Heat Transfer
- Heat Source
- Source Term (explicit/implicit)
- SIMPLE Algorithm
- Solution Limiters:
- Velocity Damping
- Pressure Limit
- Temperature Limit

## Solver: overRhoSimpleFoam Application

**Aerospace**

- Aircraft Aerodynamics
- Wing Optimization and Motion
- High-Speed Aerodynamics
- Supersonic Flow

**Automotive**

- Airflow Ducts
- Intercooler Flows

**Energy**

- Steam Turbines

**Rotating Machinery**

- Centrifugal Pumps

## Solver: overRhoSimpleFoam Compressible Solvers Comparison

Compressible Solvers In this group, we have included single-phase, pressure and density-based solvers that can handle flows with significant variations in density, mostly applicable for and **high-speed aerodynamics** (**Ma > 0.3**)

**Subsonic / Transonic, Steady-State, Ma < 1**

- rhoSimpleFoam steady-state, pressure-based, small density changes
- overRhoSimpleFoam extension of rhoSimpleFoam with Overset

**Subsonic / Transonic, Transient, Ma < 1**

- rhoPimpleFoam transient, pressure-based, small density changes, DyM
- overRhoPimpleDyMFoam extension of rhoPimpleFoam with Overset, DyM

**Transonic / Supersonic, Pressure-Based, Ma > 1**

- sonicFoam transient, pressure-based, shock waves
- sonicDyMFoam extension of sonicFoam with DyM

**Transonic / Supersonic, Density-Based, Ma > 1**

- rhoCentralFoam transient, density-based, shock waves
- rhoCentralDyMFoam extension of rhoCentralFoam with DyM

- Ma - Mach Number
- DyM - Dynamic Mesh
- Overset - also known as Chimera Grid (Method)

## Solver: overRhoSimpleFoam Results Fields

This solver provides the following results fields:

**Primary Results Fields**- quantities produced by the solver as default outputs**Derivative Results**- quantities that can be computed based on primary results and supplementary models. They are not initially produced by the solver as default outputs.

**Primary Results Fields**

Velocity | \(U\) [\(\frac{m}{s}\)] |

Temperature | \(T\) [\(K\)] |

Pressure | \(p\) [\(Pa\)] |

**Derivative Results**

Density | \(\rho\) [\(\frac{kg}{m^{3}}\)] |

Vorticity | \(\omega\) [\(\frac{1}{s}\)] |

Mach Number | \(Ma\) [\(-\)] |

Peclet Number | \(Pe\) [\(-\)] |

Stream Function | \(\psi\) [\(\frac{m^2}{s}\)] |

Q Criterion | \(Q\) [\(-\)] |

Wall Functions (for RANS/LES turbulence) | \(y^+\) [\(-\)] |

Wall Shear Stress | \(WSS\) [\(Pa\)] |

Wall Heat Flux | \(\phi_q\) [\(W/m^2\)] |

Turbulent Fields (for RANS/LES turbulence) | \(k\) \(\epsilon\) \(\omega\) \(R\) \(L\) \(I\) \(\nu_t\) \(\alpha_t\) |

Volumetric Stream | \(\phi\) [\(\frac{m^{3}}{s}\)] |

Passive Scalar | \(scalar_i\) [\(-\)] |

Forces and Torque acting on the Boundary | \(F\) [\(N\)] \(M\) [\(-\)] |

Force Coefficients | \(C_l\) [\(-\)] \(C_d\) [\(-\)] \(C_m\) [\(-\)] |

Average, Minimum or Maximum in Volume from any Result Field | \(Avg\) \(Min\) \(Max\) |