TY - JOUR
T1 - Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method. Part II: Higher-Order Schemes
AU - Esmaeilzadeh , M.
AU - Barron , R.M.
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 819
EP - 850
PY - 2022
DA - 2022/07
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2021-0129
UR - https://global-sci.org/intro/article_detail/nmtma/20817.html
KW - Cartesian cut-stencil finite difference method, compact higher-order formulation,
irregular domain, Neumann boundary conditions, local truncation error.
AB - <p style="text-align: justify;">Compact higher-order (HO) schemes for a new finite difference method,
referred to as the Cartesian cut-stencil FD method, for the numerical solution of
the convection-diffusion equation in complex shaped domains have been addressed
in this paper. The Cartesian cut-stencil FD method, which employs 1-D quadratic
transformation functions to map a non-uniform (uncut or cut) physical stencil to
a uniform computational stencil, can be combined with compact HO Padé-Hermitian
formulations to produce HO cut-stencil schemes. The modified partial differential
equation technique is used to develop formulas for the local truncation error for the
cut-stencil HO formulations. The effect of various HO approximations for Neumann
boundary conditions on the solution accuracy and global order of convergence are
discussed. The numerical results for second-order and compact HO formulations of
the Cartesian cut-stencil FD method have been compared for test problems using the
method of manufactured solutions.</p>