We recently proposed (J. Comput. Phys. 2005; 207 (1): 52–68) a new paradigm for solving
the steady-state two-dimensional (2D) Navier–Stokes (N–S) equations using a …

In this paper, we extend the Sun and Zhang's [24] work on high order finite difference
method, which is based on the Richardson extrapolation technique and an operator …

In this paper, we develop a rational high order compact alternating direction implicit (RHOC
ADI) method for solving the three dimensional (3D) unsteady convection diffusion equation …

In this work, a higher-order compact discretization is developed on the nonuniform polar
grid. The discretization carries theoretically optimal third-order convergence in space and …

In the last few decades, the Higher Order Compact (HOC) finite difference schemes are
gaining momentum in the fluid dynamics community because of their high accuracy and …

A fourth order compact numerical scheme for variable coefficient parabolic problems with
mixed derivatives is outlined. The finite difference scheme, presented here shows good …

We present a new finite-difference numerical method to solve the incompressible Navier–
Stokes equations using a collocated discretization in space on a logically Cartesian grid …

In this paper, we propose a high order compact scheme for the unsteady two-dimensional
reaction diffusion equations which is second order accurate in time and fourth order …

We investigate a special technique called 'pressure separation algorithm'(PSepA)(see
Applied Mathematics and Computation 2005; 165: 275–290 for an introduction) that is able …

We have recently analyzed the global two-dimensional (2D) stability of the staggered lid-
driven cavity (LDC) flow with a higher order compact (HOC) approach. In the analysis …