GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Compact h4 finite-difference approximations to operators of Navier-Stokes type
Journal of Computational Physics
High accuracy solutions of incompressible Navier-Stokes equations
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A perturbational h4 exponential finite difference scheme for the convective diffusion equation
Journal of Computational Physics
Implicit-explicit methods for time-dependent partial differential equations
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
Finite Difference Solutions of Incompressible Flow Problems with Corner Singularities
Journal of Scientific Computing
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations
Journal of Computational Physics
High order schemes based on upwind schemes with modified coefficients
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
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 Scientific Computing
Journal of Scientific Computing
Computers & Mathematics with Applications
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In this paper, we extend a previous work on a compact scheme for the steady Navier–Stokes equations [Li, Tang, and Fornberg (1995), Int. J. Numer. Methods Fluids, 20, 1137–1151] to the unsteady case. By exploiting the coupling relation between the streamfunction and vorticity equations, the Navier–Stokes equations are discretized in space within a 3×3 stencil such that a fourth order accuracy is achieved. The time derivatives are discretized in such a way as to maintain the compactness of the stencil. We explore several known time-stepping approaches including second-order BDF method, fourth-order BDF method and the Crank–Nicolson method. Numerical solutions are obtained for the driven cavity problem and are compared with solutions available in the literature. For large values of the Reynolds number, it is found that high-order time discretizations outperform the low-order ones.