SIAM Journal on Scientific and Statistical Computing
An analysis of the fractional step method
Journal of Computational Physics
Effects of the computational time step on numerical solutions of turbulent flow
Journal of Computational Physics
A fourth-order accurate method for the incompressible Navier-Stokes equations on overlapping grids
Journal of Computational Physics
An analysis of numerical errors in large-eddy simulations of turbulence
Journal of Computational Physics
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
The Accuracy of the Fractional Step Method
SIAM Journal on Numerical Analysis
Spatial Finite Difference Approximations for Wave-Type Equations
SIAM Journal on Numerical Analysis
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
Boundary Conditions and Estimates for the Steady Stokes Equations on Staggered Grids
Journal of Scientific Computing
Robust multigrid algorithms for the Navier-Strokes equations
Journal of Computational Physics
Stability of pressure boundary conditions for Stokes and Navier-Stokes equations
Journal of Computational Physics
Algebraic splitting for incompressible Navier-Stokes equations
Journal of Computational Physics
A Multigrid-Preconditioned Newton--Krylov Method for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
A Compact Higher Order Finite Difference Method for the Incompressible Navier–Stokes Equations
Journal of Scientific Computing
Analysis of an exact fractional step method
Journal of Computational Physics
Preconditioners for saddle point problems arising in computational fluid dynamics
Applied Numerical Mathematics
A parallel block multi-level preconditioner for the 3D incompressible Navier--Stokes equations
Journal of Computational Physics
High Order Accurate Solution of Flow Past a Circular Cylinder
Journal of Scientific Computing
Journal of Computational Physics
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
A collocated method for the incompressible Navier-Stokes equations inspired by the Box scheme
Journal of Computational Physics
Hi-index | 31.48 |
High order methods are of great interest in the study of turbulent flows in complex geometries by means of direct simulation. With this goal in mind, the incompressible Navier-Stokes equations are discretized in space by a compact fourth order finite difference method on a staggered grid. The equations are integrated in time by a second order semi-implicit method. Stable boundary conditions are implemented and the grid is allowed to be curvilinear in two space dimensions. The method is extended to three dimensions by a Fourier expansion. In every time step, a system of linear equations is solved for the velocity and the pressure by an outer and an inner iteration with preconditioning. The convergence properties of the iterative method are analyzed. The order of accuracy of the method is demonstrated in numerical experiments. The method is used to compute the flow in a channel, the driven cavity and a constricted channel.