A metamorphic positivity-preserving conservative formulation applied to the solution of general anisotropic diffusion problems in distorted 2-D grids.

Numerical schemes which employ linear operator to discretize elliptic equation in arbitrary meshes are not capable to guarantee the positivity of the solutions when tensors with higher anisotropic ratio are considered. In this paper, we propose an alternative framework strategy which preserves the positivity of the solutions. The so-called Metamorphic method initially employs a linear operator in the discretization procedure and since the positivity of the solution is not satisfied in some cell of the mesh, the method suffers metamorphosis and uses a non-linear operator to recompute the solution only in those "problematic" control volumes. This strategy reduces the number of iterations when compared to conventional non-linear formulations. Besides, for some cases where the positivity is satisfied throughout the domain, the iterative procedure becomes unnecessary. The performance of our proposition is evaluated by solving a steady-state diffusion benchmark problem with distorted mesh where we observe the gain in accuracy of the solution. [ABSTRACT FROM AUTHOR]