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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.
Stability
The Courant condition (neglecting viscosity effects) is used to determine the stability of an ALE process.

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新機能
Radioss 2025の新機能を確認できます。
概要
Radioss^®は、衝突と衝撃ソリューションのための優れた陽解法有限要素ソルバーです。
Tutorials
Discover Radioss functionality with interactive tutorials.
ユーザーガイド
This manual provides details on the features, functionality, and simulation methods available in Altair Radioss.
リファレンスガイド
本マニュアルは、Radiossで使用することのできるすべての入力キーワードとオプションを詳細なリストで提供しています。
例題集
このマニュアルは一般的な問題のタイプに関して、Radiossを用いて解かれた例題を示します。
検証問題
このマニュアルでは、解析済みの検証モデルを紹介します。
よくある質問
このセクションでは、Radiossに関するよくある質問へのクィックレスポンスを提供しています。
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
This manual describes the interface between Altair Radioss and user subroutines.

Stability

The Courant condition (neglecting viscosity effects) is used to determine the stability of an ALE process.

The maximum time step is calculated by:

図 1.

Δ t \leq k \frac{Δ l}{c + ν - w}

Where,

$k$: Coefficient
$Δ l$: Smallest characteristic length of an element
$c$: Material speed of sound
$ν$: Material velocity
$w$: Grid velocity

The speed of sound is determined by:

図 2.

c = \sqrt{\frac{1}{ρ} \frac{\partial p}{\partial ρ} + \frac{4}{3} \frac{μ}{ρ}}

Where,

$ρ$: Density
$μ$: Dynamic viscosity
$p$: Pressure

The relative velocity between the material and grid motion (

ν

w

) is computed by:

図 3.

ν - w = \sqrt{\frac{1}{N} {\sum_{i = 1}^{3} \sum_{I = 1}^{N} (ν_{i}^{I} - w_{i}^{I})}^{2}}

Where,

$N$: Number of nodes of the considered element (usually $N$ =8)