A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
On error estimates of the penalty method for unsteady Navier-Stokes equations
SIAM Journal on Numerical Analysis
On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes
Mathematics of Computation
Staggered incremental unknowns for solving Stokes and generalized Stokes problems
Applied Numerical Mathematics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
SIAM Journal on Numerical Analysis
A finite element penalty-projection method for incompressible flows
Journal of Computational Physics
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
Improvements on open and traction boundary conditions for Navier-Stokes time-splitting methods
Journal of Computational Physics
A Dynamic Penalty or Projection Method for Incompressible Fluids
Journal of Scientific Computing
| Hi-index | 7.30 |
We deal with the time-dependent Navier-Stokes equations (NSE) with Dirichlet boundary conditions on the whole domain or, on a part of the domain and open boundary conditions on the other part. It is shown numerically that combining the penalty-projection method with spatial discretization by the Marker And Cell scheme (MAC) yields reasonably good results for solving the above-mentioned problem. The scheme which has been introduced combines the backward difference formula of second-order (BDF2, namely Gear's scheme) for the temporal approximation, the second-order Richardson extrapolation for the nonlinear term, and the penalty-projection to split the velocity and pressure unknowns. Similarly to the results obtained for other projection methods, we estimate the errors for the velocity and pressure in adequate norms via the energy method.