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No ad hoc design of the mesh is needed, instead the mesh is optimized based on solution features, in particular no boundary layer mesh is needed.
However, to minimize the bending strain energy a fine mesh is needed.
It is also shown that a fine finite-difference mesh is needed to obtain accurate solutions for high viscosity ratios.
Compared to the CFEM, only a fraction of the mesh is needed to achieve comparable accuracy in each mode.
Because the wave thickness is small compared with the computational domain, a fine mesh is needed, limiting the practicality of the process to two-dimensional geometries.
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(4) No time consuming adaptive re-meshing is needed.
In practice, to establish an effective mesh, frequently, significant expertise in building meshes is needed, because great care must be taken in cleaning up the CAD geometry and preparing an effective mesh.
The motion of the interface is tracked by the solution of a scalar transport equation for a phase-indicator field that is discontinuous at the interface and uniform elsewhere; no explicit interface reconstruction, which is perceived to be difficult to implement on unstructured meshes, is needed.
For a correct evaluation of these fields in a numerical modelling, detailed FE models with dense meshes are needed.
These problems, characterized by data varying over a wide range of scales cannot be easily solved by classical numerical methods that need mesh resolution down to the finest scales and multiscale methods capable of capturing the large scale components of the solution on macroscopic meshes are needed.
For economical analysis of transient problems, not only the mesh refinement but also the mesh recovery is needed.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com