Mathematics of Computation
Cavity flow dynamics at higher reynolds number and higher aspect ratio
Journal of Computational Physics
Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Hopf bifurcation in the driven cavity
Journal of Computational Physics
Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions
Journal of Computational Physics
The stability of numerical boundary treatments for compact high-order finite-difference schemes
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
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
Multigrid Solution of Automatically Generated High-Order Discretizations for the Biharmonic Equation
SIAM Journal on Scientific Computing
Accurate projection methods for the incompressible Navier—Stokes equations
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
Numerical investigation on the stability of singular driven cavity flow
Journal of Computational Physics
High order accurate solution of the incompressible Navier-Stokes equations
Journal of Computational Physics
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
Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
Discontinuous Galerkin method based on non-polynomial approximation spaces
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A Fast Direct Solver for the Biharmonic Problem in a Rectangular Grid
SIAM Journal on Scientific Computing
A Compact Difference Scheme for the Biharmonic Equation in Planar Irregular Domains
SIAM Journal on Numerical Analysis
A compact scheme for the streamfunction formulation of Navier-Stokes equations
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
Recent Developments in the Pure Streamfunction Formulation of the Navier-Stokes System
Journal of Scientific Computing
A new family of (5,5)CC-4OC schemes applicable for unsteady Navier-Stokes equations
Journal of Computational Physics
Computers & Mathematics with Applications
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In this paper we continue the study, which was initiated in (Ben-Artzi et al. in Math. Model. Numer. Anal. 35(2):313---303, 2001; Fishelov et al. in Lecture Notes in Computer Science, vol. 2667, pp. 809---817, 2003; Ben-Artzi et al. in J. Comput. Phys. 205(2):640---664, 2005 and SIAM J. Numer. Anal. 44(5):1997---2024, 2006) of the numerical resolution of the pure streamfunction formulation of the time-dependent two-dimensional Navier-Stokes equation. Here we focus on enhancing our second-order scheme, introduced in the last three afore-mentioned articles, to fourth order accuracy. We construct fourth order approximations for the Laplacian, the biharmonic and the nonlinear convective operators. The scheme is compact (nine-point stencil) for the Laplacian and the biharmonic operators, which are both treated implicitly in the time-stepping scheme. The approximation of the convective term is compact in the no-leak boundary conditions case and is nearly compact (thirteen points stencil) in the case of general boundary conditions. However, we stress that in any case no unphysical boundary condition was applied to our scheme. Numerical results demonstrate that the fourth order accuracy is actually obtained for several test-cases.