A simplified gradient evaluation on non-orthogonal meshes; application to a plasma torch simulation method

A numerical method is proposed to evaluate gradients on non-uniform, non-orthogonal, three-dimensional structured meshes of hexahedra, as commonly used by finite volume methods. The method uses isoparametric transforms on tetrahedra to evaluate the gradient on a regular mesh and transform it back to the general mesh. It provides second-order accuracy, even on highly non-orthogonal meshes. Results of stationary three-dimensional numerical simulations of a direct current plasma torch, making use of the proposed method, are presented.