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The ALE formulation is available in the ANSYS LS-DYNA program only for PLANE162 and SOLID164 elements. For both of these element types, KEYOPT(5) defines the element continuum treatment. The default KEYOPT(5) setting is zero, which defines the material continuum to be Lagrangian. Setting KEYOPT(5) = 1 defines the ALE formulation. The current implementation of ALE in ANSYS LS-DYNA does not allow mixing of materials within an element.

In general, the 2-D ALE formulation (PLANE162) is not as robust as the 3-D formulation. Therefore, it may be advantageous to model 2-D problems with SOLID164 elements and then apply nodal motion constraints in the depth direction.

As described earlier, the greatest advantage of the ALE method is that it allows smoothing of a distorted mesh without performing a complete remesh. The algorithms for moving the mesh relative to the material control the range of the problems that can be solved by an ALE formulation. In the ANSYS LS-DYNA program, smoothing may be applied via the EDALE command. Using this command, you must define at least one of four different weighting factor options:

AFAC - Simple average smoothing weight factor. For this method, the coordinates of a node are the simple average of the coordinates of its surrounding nodes.

BFAC - Volume-weighted smoothing weight factor. This method uses a volume-weighted average of the coordinates of the centroids of the elements surrounding a node.

DFAC - Equipotential smoothing weight factor. Equipotential zoning is a method of making a structured mesh for finite difference or finite element calculations by using the solutions of Laplace equations as the mesh lines. The same method can be used to smooth selected points in an unstructured 3-D mesh provided that it is at least locally structured.

EFAC - Equilibrium smoothing weight factor (available only for PLANE162). For this method, artificial springs are attached to each ALE element node. The springs are used to adjust the position of each node from the equilibrium solution. This approach can overcome possible calculation instabilities found in the other smoothing methods.

The EDALE command also allows you to define start and end times for ALE smoothing.

You can define two additional ALE options with the EDGCALE command:

ADV - Number of cycles between advection

METH - Advection method (donor cell or Van Leer)

In general, it is not worthwhile to advect an element unless at least twenty percent of its volume will be transported, because the gain in the time step size will not offset the cost of the advection calculations. It is best to begin an ALE analysis with a Van Leer advection technique (METH = 1).

If you are working in the GUI, all ALE related options are accessed by picking Main Menu> Solution> Analysis Options> ALE Options.

The remap step maps the solution from a distorted Lagrangian mesh onto the new mesh. The underlying assumptions of the remap step are 1) the topology of the mesh is fixed (that is, the element nodal connectivity remains unchanged), and 2) the mesh motion during a step is less than the characteristic lengths of the surrounding elements. The algorithms for performing the remap step are taken from the computational fluid dynamics community and are referred to as “advection” algorithms.

The donor cell algorithm is a first order Godunov method applied to the advection equation. Aside from its first order accuracy, it is a good advection algorithm; it is stable, monotonic and simple. The Van Leer algorithm is a higher order Godunov method that improves the estimates of the initial values of left and right states for the Riemann problem at the nodes. The donor cell algorithm assumes that the distribution of the initial value function is constant over an element. Van Leer replaces the piecewise constant distribution with a higher order interpolation function that is subject to an element level conservation constraint.