Compact h4 finite-difference approximations to operators of Navier-Stokes type
Journal of Computational Physics
Accurate solutions to the square thermally driven cavity at high Rayleigh number
Computers and Fluids
Projection method I: convergence and numerical boundary layers
SIAM Journal on Numerical Analysis
Vorticity boundary condition and related issues for finite difference schemes
Journal of Computational Physics
Essentially compact schemes for unsteady viscous incompressible flows
Journal of Computational Physics
Projection Method II: Godunov--Ryabenki Analysis
SIAM Journal on Numerical Analysis
Comparison of second- and fourth-order discretizations for multigrid Poisson solvers
Journal of Computational Physics
A conservative finite-volume second-order-accurate projection method on hybrid unstructured grids
Journal of Computational Physics
A Compact Fourth-Order Finite Difference Scheme for Unsteady Viscous Incompressible Flows
Journal of Scientific Computing
A Central-Difference Scheme for a Pure Stream Function Formulation of Incompressible Viscous Flow
SIAM Journal on Scientific Computing
Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows
Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows
SIAM Journal on Numerical Analysis
A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations
Journal of Computational Physics
A new paradigm for solving Navier-Stokes equations: streamfunction-velocity formulation
Journal of Computational Physics
High-order compact exponential finite difference methods for convection-diffusion type problems
Journal of Computational Physics
A stabilized finite element method based on two local Gauss integrations for the Stokes equations
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
A Compact Difference Scheme for the Biharmonic Equation in Planar Irregular Domains
SIAM Journal on Numerical Analysis
A High Order Compact Scheme for the Pure-Streamfunction Formulation of the Navier-Stokes Equations
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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In this paper, an effective compact finite difference approximation which carries streamfunction and its first derivatives (velocities) as the unknown variables for the streamfunction-velocity formulation of the steady two dimensional incompressible Navier-Stokes equation is developed on non-uniform orthogonal Cartesian grids. To solve the resulting system of equations, a multigrid iterative strategy on nonuniform grids is introduced by using the interpolation techniques. Numerical experiments, involving two test problems with analytical solutions and the lid-driven square cavity flow problem are carried out to display the superiority of the currently developed method on nonuniform grid. Numerical results show that the present method on nonuniform grids gets as similarly efficient convergence rate as on uniform grids, viz., second order accuracy and the resolution of the computed solutions for the problems with the sharp changes can be significantly improved when the nonuniform grid strategy is utilized. The backward-facing step flow is also calculated by the present method to exhibit the capability to simulate the distant field using fewer grid points. The solution for the natural convection problem reveals further the wide applications of the present method not only in the flow problems but also in the heat transfer problems. All of these numerical results demonstrate the accuracy and efficiency of the currently proposed schemes.