Spatial resolution in mixing processes is an acute problem. We propose a
line method, akin to the contour dynamics technique, which is an
extension of the particle method but with the particles redistributed on
the line with time. We have used up to 10(5) particles per line and ten
lines to investigate the dynamical and structural properties of mixing
for both Newtonian and non-Newtonian temperature-dependent viscosity
convection in 2D geometry. The spatial structures and the time history
of the lines formed in Newtonian convection are different from those
produced in non-Newtonian convection, which has the tendency for
producing long-living horizontal structures. Efficient mixing in the
upper mantle would be inhibited by non-Newtonian rheology.