A convergent and universally bounded interpolation scheme for the treatment of advection

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Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions (2003, background): “A new convection scheme especially designed for differential constitutive relations has been proposed in [16] and it is here adopted throughout.”
Viscous flow through microfabricated hyperbolic contractions (2007, methodology): “Central differences are used to discretize the diffusive terms, while the CUBISTA high-resolution scheme (Alves et al. 2003) is employed in the discretization of the advective terms.”
The log-conformation tensor approach in the finite-volume method framework (2009, positive): “The advective term in Eq. (9) is discretised with the CUBISTA high-resolution scheme [ 23 ], formally of third-order accuracy and especially designed to deal with differential constitutive relations.”
Numerical Methods for Viscoelastic Fluid Flows (2021, methodology): “Alves et al. (2003a) demonstrated that the CUBISTA scheme provides second-order accuracy (third order in the best scenario) while maintaining bounded values ( φ f will remain between φ P and φ F ) and improved iterative convergence properties.”