TITLE:
High-Order Cartesian Cut-Stencil Finite Difference Solutions for Streamfunction-Vorticity Formulation of 2-D Navier-Stokes Equations
AUTHORS:
Mohammadali Esmaeilzadeh, Ronald M. Barron
KEYWORDS:
Computational Fluid Dynamics, Cut-Stencil Finite Difference, High-Order Discretization, Streamfunction-Vorticity Formulation
JOURNAL NAME:
Applied Mathematics,
Vol.17 No.3,
March
18,
2026
ABSTRACT: The formulation and implementation of a high-order Cartesian cut-stencil finite difference method (CCST-FDM) to 2-D steady incompressible fluid flow in regular and irregular domains is considered in this paper. The CCST-FDM is capable of simulating flows in complex geometries by employing 1-D quadratic transformation functions to map any (uniform or non-uniform) physical stencil to a uniform computational stencil. In this work, the CCST-FDM is combined with compact high-order (HO) Padé-Hermitian approximations to produce HO CCST-FD schemes. Two different high-order (globally 4th-order) accurate schemes are formulated for the CCST-FDM. Using the streamfunction-vorticity formulation of the Navier-Stokes equations, low and high-order solutions are computed for lid-driven flows in four different geometries, namely a square cavity and three irregular regions, namely L-shape, skewed quadrilateral and triangular cavities. Results from these geometries are compared to earlier studies for various Reynolds numbers. It is shown that the high-order CCST-FDMs can achieved higher accuracy on coarser grid than other high-order methods.