Home
Radioss 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.
Fluid-Structure Interaction (TYPE 1 Interface)

Welcome
What's New
View new features for Radioss 2026.
Radioss Overview
Radioss is a leading explicit finite element solver for crash and impact simulation.
Tutorials
Discover Radioss functionality with interactive tutorials.
Radioss User Guide
This manual provides details on the features, functionality, and simulation methods available in Altair Radioss.
Radioss Reference Guide
This manual provides a detailed list of all the input keywords and options available in Radioss.
Radioss Example Guide
This manual presents examples solved using Radioss with regard to common problem types.
Radioss Verification Problems
This manual presents solved verification models.
Radioss Frequently Asked Questions
This section provides quick responses to typical and frequently asked questions regarding Radioss.
Radioss 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
Radioss User Subroutines
This manual describes the interface between Altair Radioss and user subroutines.

Fluid-Structure Interaction (TYPE 1 Interface)

TYPE1 interface is used to model fluid-structure interactions, as shown in Figure 1.

This interface allows Lagrangian elements (structure) to interact with ALE (Arbitrary Lagrangian Eulerian) elements, which model a viscous fluid. Full slip conditions are applied at the boundary between the two domains.

The acceleration of the Lagrange node is computed by:

{\vec{γ}}_{i} = \frac{{\vec{F}}_{i} + \vec{F} {}_{a}}{m {}_{i}+ m_{a}}

The acceleration of the ALE node is computed by:

{\vec{γ}}_{a} = \frac{\vec{F} {}_{a}}{m_{a}}

The grid velocity of the ALE node is equal to the material velocity of the Lagrange node:

{\vec{w}}_{a} = {\vec{v}}_{i}

The normal material velocities of Lagrange and ALE nodes are equal. Therefore:

{\vec{v}}_{a} \cdot \vec{n} = {\vec{v}}_{i} \cdot \vec{n}