## 6 Conclusions  
The previous sections have shown that large anisotropies in the diffusion problem are difficult to recover in a Cartesian mesh without extensive refinement of the mesh, which would typically involve large computational resources to solve the problem accurately. In the case of conducting fluids, the use of Magnetic Field Aligned Meshes (MFAMs) helps to solve this problem. These conclusions may be extrapolated to other fluid flows contained in mediums which impose anisotropicity in the problem, such as, for example, non-Newtonian fluids or porous mediums in microfluidic devices or tissues.  
For small anisotropicity levels, the relatively smaller numerical diffusion errors might be traded-off against the difficulties of using the non-Cartesian mesh. A first one is that gradient reconstruction in a curvilinear mesh, such as the MFAM, might cause large errors for certain types of solutions (if the implementation or the parameters of the method are incorrectly selected). Then there is the added difficulty of handling a non-Cartesian problem, purely from a coding perspective.  
Regarding the example problem shown in this paper, it could be argued that conducting flows, such as plasma discharges in electric propulsion devices happen under complex magnetic topologies (with distinct regions of confinement) and depend greatly on the operating parameters of these devices; this means that prior knowledge of the anisotropicity level in the different transport terms of the governing equations is difficult to attain. Consequently, large refinement of a structured mesh might be needed to deal with numerical diffusion if Cartesian meshes are used. Furthermore, issues in gradient reconstruction may also appear in Cartesian structured meshes if mesh resolution and the order of the method are not selected properly. In the case of MFAMs, various strategies have been presented in this work in order to provide additional confidence on the capability to deal with errors introduced by mesh irregularities.  
In light of the results derived above, it can be concluded that the use of curvilinear meshes aligned with the preferential directions of the fluid flow problem in highly anisotropic mediums provides a distinct advantage in bounding numerical errors in the solution, as long as specific challenges in these meshes are taken into account. In particular, the use of MFAMs for the simulation of magnetically confined conducting flows (or specific populations within them), modeled as highly anisotropic fluids, is recommended.  
The authors have restricted this work to the use of the WLSQR method as proposed by [PERSON] due to its proved robustness. The use of hybrid methods, as mentioned along the manuscript, may be considered in the future in order to further refine the quality of Gradient Reconstruction. Other, future work will be oriented toward: (1) adding \"attractor points\" in MFAM meshing strategies for additional control over mesh refinement, (2) mesh quality improvement methods in boundary elements for problems with non-trivial boundary conditions or (3) the effects over Mesh Quality and Gradient Reconstruction of local element clustering and the use of hanging nodes.  
This work has been supported by Spain's R&D National Plan, grant number ESP2013-41052-P.  
[PERSON] co-wrote the paper, provided the theoretical framework for the anisotropic diffusion problem and provided the meshing and Gradient Reconstruction results; [PERSON] provided the time-dependent and statistical results for the numerical diffusion benchmarks; [PERSON] co-wrote the paper and thoroughly expanded the literature review aspect; [PERSON] provided the theoretical background for the Plasma Thrusters aspects and was the general reviewer for the paper.  
The authors declare no conflict of interest.