Abstract In reducing the grid orientation effect for the numerical solution of partial
differential equations, interpolation functions play an important role when the advective
transport of the governing equations is considered. This is due to the fact that,
in general, the unknowns are evaluated in the vertices of the elements and such properties
must be extrapolated to inner parts of the elements. First-order schemes, such as
upwind, are the easiest methods to use for performing the extrapolation of the properties.
However, such methods introduce a large amount of numerical diffusion in the solution.
A few higher-order interpolation schemes, on the other hand, are capable of providing
solutions free of numerical diffusion, increasing the accuracy of the method and reducing
the computational efforts required. In this work, we investigate the TVD interpolation
scheme for three-dimensional unstructured grids in conjunction with Element-based
Finite Volume Method (EbFVM) using four types of elements: hexahedron, tetrahedron,
prism and pyramid.