Tri-quadratic skew upwind scheme for scalar advection in a control-volume-based finite element method

This paper develops a new tri-quadratic non-inverted skew upwind scheme (NISUS) for additional refinement of nodal integration points in numerical advection–diffusion of scalar transport. Using a control-volume-based finite element method, the performance of the eight-noded hexahedral formulation is compared with tri-quadratic hexahedral elements (27-noded hexahedral). As an extension of the NISUS formulation developed with eight-noded hexahedral elements, the new 27-noded hexahedral version uses isoparametric shape functions and integration point interpolation. The proposed method is applied to three cases of advection–diffusion of heat transfer and energy transport, including radial heat flow in a rotating hollow sphere, advection–diffusion in a cubical cavity, and combined advection/diffusion in an inlet/outlet tank. Performance improvement of the two versions of NISUS in terms of speed, accuracy, and stability are presented as a comparative assessment for the design of energy conversion systems.