# Translating grid with extrusion speed

I am putting into MATLAB code the equations that describe a plastic extrusion process. From a paper, I found I should use a spatial grid that translates with the extrusion speed, being the reference coordinate system the centerline of the extrudate.

In particular, $$s = 0$$ is the extruder die and the length of the domain is time dependent as the extrudate gets longer and longer. In the paper, new grid points are continually added to the solution domain at $$s = 0$$ (the extruder die) to account for the extrusion of fresh fluid. How would I do this?