A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
Boundary conditions for incompressible flows
Journal of Scientific Computing
Multidimensional upwind methods for hyperbolic conservation laws
Journal of Computational Physics
On error estimates of projection methods for Navier-Stokes equations: first-order schemes
SIAM Journal on Numerical Analysis
An analysis of the fractional step method
Journal of Computational Physics
The second-order projection method for the backward-facing step flow
Journal of Computational Physics
Projection method I: convergence and numerical boundary layers
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Projection Method II: Godunov--Ryabenki Analysis
SIAM Journal on Numerical Analysis
On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes
Mathematics of Computation
A projection method for locally refined grids
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Wave propagation algorithms for multidimensional hyperbolic systems
Journal of Computational Physics
An Adaptive Mesh Projection Method for Viscous Incompressible Flow
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Journal of Computational Physics
The Accuracy of the Fractional Step Method
SIAM Journal on Numerical Analysis
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
The immersed interface method for the Navier-Stokes equations with singular forces
Journal of Computational Physics
Approximate Projection Methods: Part I. Inviscid Analysis
SIAM Journal on Scientific Computing
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
Runge-Kutta-Chebyshev projection method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
Projection methods are a popular class of methods for solving the incompressible Navier-Stokes equations. If a cell-centered grid is chosen, in order to use high-resolution methods for the advection terms, performing the projection exactly is problematic. An attractive alternative is to use an approximate projection, in which the velocity is required to be only approximately discretely divergence-free. The stability of the cell-centered, approximate projection is highly sensitive to the method used to update the pressure and compute the pressure gradient. This is demonstrated by analyzing a model problem and conducting numerical simulations of the Navier-Stokes equations.