An analysis of the fractional step method
Journal of Computational Physics
Matrix computations (3rd ed.)
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
A modified nodal scheme for the time-dependent, incompressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
High order accurate solution of the incompressible Navier-Stokes equations
Journal of Computational Physics
Modeling Low Mach Number Reacting Flow with Detailed Chemistry and Transport
Journal of Scientific Computing
Preconditioning Strategies for Models of Incompressible Flow
Journal of Scientific Computing
Journal of Computational Physics
A high-order discontinuous Galerkin method for the unsteady incompressible Navier-Stokes equations
Journal of Computational Physics
ALADINS: An ALgebraic splitting time ADaptive solver for the Incompressible Navier-Stokes equations
Journal of Computational Physics
Hi-index | 31.48 |
Fully discretized incompressible Navier-Stokes equations are solved by splitting the algebraic system with an approximate factorization. This splitting affects the temporal convergence order of velocity and pressure. The splitting error is proportional to the pressure variable, and a simple analysis shows that the original convergence order of the time-integration scheme can be retained by solving for incremental pressure. The combination of splitting and incremental pressure is shown to be equivalent to an error-correcting method using the full pressure. In numerical experiments employing a third-order time-integration scheme and various orders for the pressure increment, the splitting error is shown to control the convergence order, and the full order of the scheme is recaptured for both velocity and pressure. The difference between perturbing the momentum or the continuity equation is also explored.