# ALE/CFD Materials

- Newtonian or turbulent viscous fluid with a $k\text{}-\text{}\epsilon $ model (activate LAW6 with /MAT/K-EPS)
- Viscous fluid for computational domain of Large Eddy Simulations (LES) (activate LAW46 with /MAT/LAW46 (LES_FLUID))
- Elementary boundary conditions (activate LAW11 with /MAT/LAW11 (BOUND))
- Elementary boundary conditions for turbulent flow (activate LAW11 with /MAT/B-K-EPS)
- Purely thermal materials (activate LAW18 with /MAT/LAW18 (THERM))
- Bimaterial (activate LAW20 with /MAT/LAW20 (BIMAT))
- Hydrodynamic bi-material liquid-gas (activate LAW37 with /MAT/LAW37 (BIPHAS))
- Multi-material solid, liquid, and gas (activate LAW51 with /MAT/LAW51 (MULTIMAT))
- Multi-fluid solid, liquid, and gas (activate LAW151 with /MAT/LAW151 (MULTIFLUID))

Many parameters are already defined by default and provide accurate results. You do not need to redefine these parameters, but you can adjust physical properties relevant to the material and units you are using.

## Turbulence with $k\text{}-\text{}\epsilon $ Model

The basic idea of turbulence (Reynolds equations) is to split the actual fluid velocity into its average component and its fluctuations; velocity fluctuations are assumed small with respect to average velocity. The isotropic turbulence theory then demonstrates the equivalence of these assumptions and the introduction of an additional viscous term to turbulent viscosity (Boussinesq approximation).

## L.E.S. Material

Turbulent models based on the Reynolds equations separate the average quantities from the fluctuations and by design, force a steady state solution.

Whenever a flow contains large structures, fluctuations cannot be neglected when compared to average quantities. Then the Reynolds equations cannot handle accurately such situations.

The Large Eddy Simulation (LES) is different. No steady state or average flow is searched. The grid mesh is assumed to partly resolve the turbulence. At least the macro structures, whereas the smaller scales are replaced by a viscous term (sub-grid scale), supposed to model the mainly dissipative effects of the micro turbulence.

Material LAW46 is designed for Large Eddy Simulations. Radioss can be
used with Smagorinsky's Sub-Grid-Scale model:
(`I`_{sgs}=1 or
2) or without:
(`I`_{sgs}=0)
(MILES approach). The equation of state is linear compressible (constant
compressibility), well suited for subsonic cases.

All elements connected to a node, either fixed or Lagrangian, will automatically be considered as wall elements and their viscosity will be set consistently with a logarithmic velocity profile.

Density, speed of sound, molecular kinematic viscosity, sub-grid scale model type (TYPE2 is recommended), and sub-grid scale constant (default is 0.1) must be provided.

Multi-Material Laws | LAW20 | LAW51 | LAW151 | |||
---|---|---|---|---|---|---|

Mach Number | Low (M<<1) | √ | √ | |||

High (M>>1) | √ | √ | √ | |||

Solid Material Involved | Deviatoric stresses | (Sand, steel,…) | √ | √ | ||

Analysis | 2D | Quad | √ | √ | ||

Tria | √ | √ | ||||

3D | Tetra | √ | ||||

Hexa | √ | √ | ||||

Numerical Scheme | Staggered | Staggered | Collocated | |||

Resolution Method | Hybrid FEM/FVM | Hybrid FEM/FVM | Full FVM | |||

Total Energy Conservation | √ | |||||

Phases Discretization | Phases Interface Tracking | Second Order (MUSCL algorithm) | Second Order (MUSCL algorithm) |

√ : yes;

blank: no