Front propagation

Node.js example of frontPropagation, in examples/frontPropagation. Run the command below from that folder (see running an example). The results are from FEAScript-core 0.4.0.

Solidification front in 2D

A solidification front that starts on the bottom, left and right edges of a 4 m × 2 m domain and moves inward at unit speed. The solution $u$ of the eikonal equation $|\nabla u| = 1$ is the time at which the front reaches each point, which at unit speed is the distance to the nearest of those edges. The top edge has a zero gradient.

node solidificationFront2D/solidificationFront2D.js

Source: solidificationFront2D.js

Geometry

Mesh

Results

The contours follow the distance to the nearest initial front edge. The last point reached is the middle of the top edge, (2 m, 2 m), at $u = 1.9812$, against an exact distance of 2: the viscous term that stabilizes the eikonal equation smooths the solution slightly (see the verification page). The example prints the node coordinates and the solution vector.