In [15], our DT–MRI visualization algorithm based on anisotropic texture diffusion is introduced. The diffusion is modeled mathematically by the problem for the Allen–Cahn equation with a space–dependent anisotropic diffusion operator. To preserve its anisotropic properties in the discretized version of the problem, an appropriate numerical treatment is necessary, reducing the isotropic numerical diffusion. The first part of this contribution is concerned with the design and investigation of the finite volume scheme with multipoint flux approximation. Its desirable properties are investigated by means of our technique based on total variation measurement. The second part presents the recent achievements in applying the same scheme to the phase field model of dendritic crystal growth.