Block-implicit multigrid solution of Navier-Stokes equations in primitive variables
Journal of Computational Physics
An efficient scheme for solving steady incompressible Navier-Stokes equations
Journal of Computational Physics
High accuracy solutions of incompressible Navier-Stokes equations
Journal of Computational Physics
SIAM Journal on Scientific and Statistical Computing
Simulation of cavity flow by the lattice Boltzmann method
Journal of Computational Physics
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
A numerical method for solving incompressible viscous flow problems
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
A conservative finite-volume second-order-accurate projection method on hybrid unstructured grids
Journal of Computational Physics
An efficient high-order Taylor weak statement formulation for the Navier-Strokes equation
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
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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
SIAM Journal on Numerical Analysis
A Compact Difference Scheme for the Biharmonic Equation in Planar Irregular Domains
SIAM Journal on Numerical Analysis
Computers & Mathematics with Applications
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Recently, a new paradigm for solving the steady Navier-Stokes equations using a streamfunction-velocity formulation was proposed by Gupta and Kalita [M.M. Gupta, J.C. Kalita, A new paradigm for solving Navier-Stokes equations: streamfunction-velocity formulation, J. Comput. Phys. 207 (2005) 52-68], which avoids difficulties inherent in the conventional streamfunction-vorticity and primitive variable formulations. It is discovered that this formulation can reached second-order accurate and obtained accuracy solutions with little additional cost for a couple of fluid flow problems. In this paper, an efficient compact finite difference approximation, named as five point constant coefficient second-order compact (5PCC-SOC) scheme, is proposed for the streamfunction formulation of the steady incompressible Navier-Stokes equations, in which the grid values of the streamfunction and the values of its first derivatives (velocities) are carried as the unknown variables. The derivation approach is simple and can be easily used to derive compact difference schemes for other similar high order elliptic differential equations. Numerical examples, including the lid driven cavity flow problem and a problem of flow in a rectangular cavity with the hight-width ratio of 2, are solved numerically to demonstrate the accuracy and efficiency of the newly proposed scheme. The results obtained are compared with ones by different available numerical methods in the literature. The present scheme not only shows second-order accurate, but also proves more effective than the existing second-order compact scheme of the streamfunction formulation in the aspect of computational cost.