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.
Conservation of momentum, expressed in terms of a finite element formulation, is given
by:(1)
Where,
Weight functions
Material density
Velocity
Stress matrix
Body acceleration vector
Volume
This can be rewritten in a form similar to the explicit Lagrangian formulation with the addition
of a new nodal force , accounting for transport of momentum:(2)
Where,
Transport of momentum forces
Momentum Transport Force
By default, since version 2018.0 a streamline upwind technique is used to computed
transportation forces (SUPG). This formulation enables to get rid of false diffusion (numerical
issue with classical upwind technique). Nevertheless, SUPG method can be disabled in order to
retrieve numerical solution obtained with classical upwind technique from versions prior to
2017. For this purpose, Engine keyword must be define: /ALE/SUPG/OFF. Using
this keyword, momentum transport forces are computed using the classical upwind technique which
was the default method up to version 2017.(3)
The classical upwinding technique is introduced to add numerical diffusion to the scheme,
which otherwise is generally under diffuse and thus unstable.(4)
Upwind coefficient, given in input.
Full upwind (default value) is generally used and can be tuned with parameter from /UPWIND keyword (now obsolete
with SUPG formulation). 図 1.