A computational model of the cochlea using the immersed boundary method
Journal of Computational Physics
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
A second-order projection method for the incompressible Navier-Stokes equations in arbitrary domains
Journal of Computational Physics
SIAM Journal on Scientific Computing
A projection method for locally refined grids
Journal of Computational Physics
An Adaptive Mesh Projection Method for Viscous Incompressible Flow
SIAM Journal on Scientific Computing
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
A Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries
SIAM Journal on Scientific Computing
Journal of Computational Physics
SIAM Journal on Scientific Computing
An adaptive version of the immersed boundary method
Journal of Computational Physics
Semicoarsening Multigrid on Distributed Memory Machines
SIAM Journal on Scientific Computing
A cell-centered adaptive projection method for the incompressible Euler equations
Journal of Computational Physics
On Newton-Krylov multigrid methods for the imcompressible Navier-Stokes equations
Journal of Computational Physics
A Note on Preconditioning for Indefinite Linear Systems
SIAM Journal on Scientific Computing
Efficient preconditioning of the linearized Navier—Stokes equations for incompressible flow
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
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
Divergence-free adaptive mesh refinement for Magnetohydrodynamics
Journal of Computational Physics
A Multigrid-Preconditioned Newton--Krylov Method for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
Approximate Projection Methods: Part I. Inviscid Analysis
SIAM Journal on Scientific Computing
A Preconditioner for the Steady-State Navier--Stokes Equations
SIAM Journal on Scientific Computing
Flexible Inner-Outer Krylov Subspace Methods
SIAM Journal on Numerical Analysis
Divergence- and curl-preserving prolongation and restriction formulas
Journal of Computational Physics
hypre: A Library of High Performance Preconditioners
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
A parallel block multi-level preconditioner for the 3D incompressible Navier--Stokes equations
Journal of Computational Physics
Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
Journal of Computational Physics
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
Stability of approximate projection methods on cell-centered grids
Journal of Computational Physics
Journal of Computational Physics
Block Preconditioners Based on Approximate Commutators
SIAM Journal on Scientific Computing
A second-order boundary-fitted projection method for free-surface flow computations
Journal of Computational Physics
Journal of Computational Physics
Runge-Kutta-Chebyshev projection method
Journal of Computational Physics
An adaptive, formally second order accurate version of the immersed boundary method
Journal of Computational Physics
Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations
Journal of Computational Physics
Journal of Computational Physics
A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A Dynamic Penalty or Projection Method for Incompressible Fluids
Journal of Scientific Computing
Journal of Computational Physics
Hi-index | 31.46 |
The projection method is a widely used fractional-step algorithm for solving the incompressible Navier-Stokes equations. Despite numerous improvements to the methodology, however, imposing physical boundary conditions with projection-based fluid solvers remains difficult, and obtaining high-order accuracy may not be possible for some choices of boundary conditions. In this work, we present an unsplit, linearly-implicit discretization of the incompressible Navier-Stokes equations on a staggered grid along with an efficient solution method for the resulting system of linear equations. Since our scheme is not a fractional-step algorithm, it is straightforward to specify general physical boundary conditions accurately; however, this capability comes at the price of having to solve the time-dependent incompressible Stokes equations at each timestep. To solve this linear system efficiently, we employ a Krylov subspace method preconditioned by the projection method. In our implementation, the subdomain solvers required by the projection preconditioner employ the conjugate gradient method with geometric multigrid preconditioning. The accuracy of the scheme is demonstrated for several problems, including forced and unforced analytic test cases and lid-driven cavity flows. These tests consider a variety of physical boundary conditions with Reynolds numbers ranging from 1 to 30000. The effectiveness of the projection preconditioner is compared to an alternative preconditioning strategy based on an approximation to the Schur complement for the time-dependent incompressible Stokes operator. The projection method is found to be a more efficient preconditioner in most cases considered in the present work.