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Theory Manual
This manual provides detailed information about the theory used in the Altair Radioss Solver.
ALE, CFD and SPH Theory Manual
ALE Formulation
ALE or Arbitrary Lagrangian Eulerian formulation is used to model the interaction between fluids and solids; in particular, the fluid loading on structures. It can also be used to model fluid-like behavior, as seen in plastic deformation of materials.
ALE Kinematic Conditions

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Theory Manual
This manual provides detailed information about the theory used in the Altair Radioss Solver.
- Large Displacement Finite Element Analysis Theory Manual
- ALE, CFD and SPH Theory Manual
  - ALE Formulation
    ALE or Arbitrary Lagrangian Eulerian formulation is used to model the interaction between fluids and solids; in particular, the fluid loading on structures. It can also be used to model fluid-like behavior, as seen in plastic deformation of materials.
    - Referential Domain
    - Conservation of Momentum
    - Conservation of Mass
    - Conservation of Internal Energy
      Conservation of internal energy is used to model temperature dependent material behavior. It also allows an energy balance evaluation.
    - Rezoned Quantities
    - ALE Materials
    - Numerical Integration
    - Improved Integration Method
    - Momentum Transport Force
    - Stability
      The Courant condition (neglecting viscosity effects) is used to determine the stability of an ALE process.
    - ALE Kinematic Conditions
    - Automatic Grid Computation
    - Fluid-Structure Interaction (TYPE 1 Interface)
    - Example: High Velocity Impacts
      A typical application of the ALE method is using high velocity impacts.
  - Computational Aero-Acoustic
  - Smooth Particle Hydrodynamics
    Smooth Particle Hydrodynamics (SPH) is a meshless numerical method based on interpolation theory. It allows any function to be expressed in terms of its values at a set of disordered point's so-called particles.
- Appendix A: Basic Relations of Elasticity
User Subroutines
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ALE Kinematic Conditions

Boundary Conditions

Boundaries with Lagrangian materials are declared automatically Lagrangian.

Nodes can be declared Lagrangian.

Constraints can be applied separately or simultaneously on:

Material velocity
Grid velocity

These constraints can be applied in one or several directions of a skew reference frame.

When the flag is set to 1, boundary condition is activated with global reference frame or skew reference frame.

Figure 1.

i = DOF with respect to global reference frame or skew reference frame

VELOCITY: Vi = 0

ACCELERATION: π i = 0

The boundary conditions can be changed during Engine runs with /BCS or /BCSR Engine options.

ALE Links

An ALE link is identical to a rigid link. The secondary node sets' grid velocity can be controlled by two main nodes, M1 and M2.

There are three options to choose from:

Option 0: Velocity is linearly interpolated with respect to order of input.
$W_{N I} = W {}_{M 1} + (W_{M 2} - W_{M}_{12}) \frac{I}{N + 1}$
Option 1: Velocity is set to maximum absolute velocity of main nodes.
$W_{N I} = W_{M 1} if | W_{M 1} | < | W_{M 2} |$
Option 2: Velocity is set to minimum absolute velocity of main nodes.
$W_{N I} = W_{M 1} if | W_{M 1} | < | W_{M 2} |$; The input data is specified at each restart run.