ALE (Arbitrary Lagrangian-Eulerian) CNF Parameters

The Arbitrary Lagrangian-Eulerian (ALE) method is a collection of technologies designed to simulate fluid flow with moving or deforming meshes, particularly useful for Fluid-Structure Interaction (FSI) problems. ALE involves key concepts such as:

Modified Navier-Stokes equations with mesh velocity.
Time integration methods that satisfy geometric conservation laws.
Stable coupling between fluid forces acting on solids and the solid's response to these forces.
Data exchange between fluid and solid meshes.
Deformation of the fluid mesh.

In this context, mesh movement is the focus. Specifically, given boundary motion, either prescribed by you or determined by fluid forces, how to move the internal mesh nodes to maintain a valid mesh, avoiding negative-volume elements, sometimes called "inside-out" elements.

AcuSolve provides two mesh motion technologies:

Equation based mesh motion: This solves displacement equations for mesh nodes using methods such as hyper-elastic models and Mesh Quality Metric (MQM).
Interpolated Mesh Motion (MMI): This approach skips solving equations, saving CPU time. Mesh node displacements are computed directly using simple algebraic interpolation.

In the input file (.INP), the command for mesh movement is:

EQUATION {

mesh = eulerian # arbitrary_lagrangian_eulerian, specified

}

Eulerian means a stationary mesh.
arbitrary_lagrangian_eulerian indicates equation-based mesh movement.
Specified denotes mesh motion defined by algebraic relations (MMI) or user inputs, without solving additional equations.

ALE CNF Parameters

For fine control of equation-based ALE methods, the following configuration (CNF) parameters can be specified.

Mesh Poisson Ratio

parameter: -alenu <real>

default: 0.0

Relevant for hyperelastic models only. MQM does not use this parameter, although both models fall under ALE. This ratio affects the compressibility of the mesh material in hyperelastic models.

Mesh Reference Push Factor

parameter: -alefct <real>

default= 0

This parameter applies only to the Ogden. Ogden solves for the displacement of mesh nodes, which can be measured relative to the reference mesh in two ways:

Relative to the initial mesh (when the parameter is set to 0).
Relative to the mesh from the previous time step (when the parameter is set to 1).

When using option 2, the displacement magnitude is typically smaller as the mesh deforms progressively away from the initial configuration. This makes the equations easier to solve and allows for greater mesh deformation. However, because the reference mesh changes with each time step, the mesh cannot return to its original shape. This behavior is not ideal for cyclic movements, for example, pistons or valves, where restoring the original mesh configuration is important. However, for one-way motion, for example, a falling object or water collapse due to gravity, setting this parameter to 1 can help push the mesh deformation further. By default, the value is 0, meaning no reference push is applied.

Mesh Volume Absorption Factor

parameter: -alevaf <real>

default = 0

Applicable only to the Ogden hyperelastic model, this parameter introduces stiffness by having larger elements absorb more deformation. Typically set between 0.1 to 0.5, it helps preserve the shape of smaller elements and mimics some MQM effects.

MQM Reference Push Factor

parameter: -mqmpush <real>

default = 0

This controls the reference push factor for MQM-based mesh movement, influencing mesh stability during deformation.

Applying Mesh Parameters

To use mesh_volume_absorption_factor, add it to the Acusim.cnf file.

mesh_volume_absorption_factor =0.5