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The interface mesh is moved in a Lagrangian fashion.
In the second step, mesh is moved in ALE mode and the associated convection of the variables due to relative motion of the mesh is performed using a Godunov type scheme.
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This results in counter axial forces on a cyclic basis because the mesh is moving in opposite directions at each side of the coupling.
A moving mesh source term derived directly from the geometric conservation law is incorporated into the discrete equations to ensure the recovery of uniform flow while the mesh is moving.
We only consider the indirect ALE approach which consists of three key stages: a Lagrangian stage, in which the solution and the computational mesh are updated; a rezoning stage, in which the nodes of the computational mesh are moved to improve grid quality; and a remapping stage, in which the Lagrangian solution is transferred to the rezoned mesh.
When we add one run of Laplacian smoothing to the generated surface, each mesh vertex is moved to the centroid of the surrounding mesh vertices which are topologically connected.
Mesh points are moved towards locations where they are needed the most.
The left is moving mesh (x xi,t)), the right (u xi,t)).
Mesh routers have fixed locations whereas mesh clients are moving and changing their places arbitrarily.
In this framework, only the nodes of the computational mesh of the interface region are moved on the basis of the predicted fracture variables, reducing mesh distortions by using continuous rezoning procedures.
The method uses a finite difference mesh with vertices that may be moved with the fluid (Lagrangian), be held fixed (Eulerian), or be moved in any other prescribed manner, as in the Arbitrary Lagrangian Eulerian (ALE) technique.
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