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.
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.
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.
There are three different grid velocity formulations that can be used in an ALE simulation. New keywords define the type of method used. The different formulations are:
0 - J. Donea Grid Formulation: use keyword /DONEA
(NWALE =0 for version < 4.1)
1 - Average Displacement Formulation: use keyword /DISP
(NWALE =1 for version < 4.1)
2 - Nonlinear Spring Formulation: use keyword /SPRING
(NWALE =2 for version < 4.1)
J. Donea Grid Formulation
(/DONEA)
This formulation 12 computes grid velocity
using:(1)
Where,
Number of nodes connected to node I
Distance between node I and node J
α,
adimensional factors given in input
Therefore, the grid displacement is given by:(2)
Average Displacement Formulation (/DISP)
The average displacement formulation calculates average velocity to determine average
displacement.(3)
Nonlinear Spring Formulation (/SPRING)
Each grid node is connected to
neighboring grid nodes through a nonlinear viscous spring, similar to that shown in
Figure 1.
The input parameters required are:
Typical time step (Must be greater than the time step of the current
run.)
Nonlinearity factor
Damping coefficient
V
Shear factor (stiffness ratio between diagonal springs and springs along
connectivities)
This formulation is the best of the three, but it is the most
computationally expensive.
1Donea J., “An Arbitary Lagrangian-Eulerian finite element method for
transient dynamic fluid-structure interactions”, Computer methods in
applied mechanics, 1982.
2Brooks A.N. and Hughes T.J.R., “Streamline Upwind /Petrov-Galerkin
Formulations for Convection Dominated Flows with
particular Emphasis on the Incompressible
Navier-Stokes Equations”, Computer Methods in
Applied Mechanics and Engineering, Vol. 32,
1982.