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
Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
On error estimates of projection methods for Navier-Stokes equations: first-order schemes
SIAM Journal on Numerical Analysis
Modeling a no-slip flow boundary with an external force field
Journal of Computational Physics
An analysis of the fractional step method
Journal of Computational Physics
A fourth-order accurate method for the incompressible Navier-Stokes equations on overlapping grids
Journal of Computational Physics
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
Stability of pressure boundary conditions for Stokes and Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Finite difference schemes for incompressible flow based on local pressure boundary conditions
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations
Journal of Computational Physics
The immersed boundary method: A projection approach
Journal of Computational Physics
Stable and accurate pressure approximation for unsteady incompressible viscous flow
Journal of Computational Physics
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
Journal of Computational Physics
Hi-index | 31.45 |
Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries (which destroy uniform convergence to the solution). In this paper we recast the incompressible (constant density) Navier-Stokes equations (with the velocity prescribed at the boundary) as an equivalent system, for the primary variables velocity and pressure. equation for the pressure. The key difference from the usual approaches occurs at the boundaries, where we use boundary conditions that unequivocally allow the pressure to be recovered from knowledge of the velocity at any fixed time. This avoids the common difficulty of an, apparently, over-determined Poisson problem. Since in this alternative formulation the pressure can be accurately and efficiently recovered from the velocity, the recast equations are ideal for numerical marching methods. The new system can be discretized using a variety of methods, including semi-implicit treatments of viscosity, and in principle to any desired order of accuracy. In this work we illustrate the approach with a 2-D second order finite difference scheme on a Cartesian grid, and devise an algorithm to solve the equations on domains with curved (non-conforming) boundaries, including a case with a non-trivial topology (a circular obstruction inside the domain). This algorithm achieves second order accuracy in the L^~ norm, for both the velocity and the pressure. The scheme has a natural extension to 3-D.