Solution of the implicitly discretised fluid flow equations by operator-splitting
Journal of Computational Physics
Analysis and convergence of the MAC scheme. I: The linear problem
SIAM Journal on Numerical Analysis
Parallel computational fluid dynamics: implementations and results
Parallel computational fluid dynamics: implementations and results
An analysis of the fractional step method
Journal of Computational Physics
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
Approximate Inverse Techniques for Block-Partitioned Matrices
SIAM Journal on Scientific Computing
Efficient parallel computation of unstructured finite element reacting flow solutions
Parallel Computing - Special issue on applications: parallel computing methods in applied fluid mechanics
Convergence Analysis of Pseudo-Transient Continuation
SIAM Journal on Numerical Analysis
The Accuracy of the Fractional Step Method
SIAM Journal on Numerical Analysis
Two-grid Method for Linear Elasticity on Unstructured Meshes
SIAM Journal on Scientific Computing
A multigrid tutorial: second edition
A multigrid tutorial: second edition
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
Parallel smoothed aggregation multigrid: aggregation strategies on massively parallel machines
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
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
A review of algebraic multigrid
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Multigrid
High-performacne parallel implicit CFD
Parallel Computing - Special issue on parallel computing in aerospace
Parallel Computational Fluid Dynamics: Towards Teraflops, Optimization, and Novel Formulations: Proceedings of the Parallel CFD '99 Conference
A Multigrid-Preconditioned Newton--Krylov Method for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
A Preconditioner for the Steady-State Navier--Stokes Equations
SIAM Journal on Scientific Computing
On balanced approximations for time integration of multiple time scale systems
Journal of Computational Physics
An Aggregation Multigrid Solver for convection-diffusion problems onunstructured meshes.
An Aggregation Multigrid Solver for convection-diffusion problems onunstructured meshes.
Pseudotransient Continuation and Differential-Algebraic Equations
SIAM Journal on Scientific Computing
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
High order accurate solution of the incompressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Acceleration of the generalized global basis (GGB) method for nonlinear problems
Journal of Computational Physics
Preconditioning Strategies for Models of Incompressible Flow
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Adaptive Time-Stepping for Incompressible Flow Part II: Navier-Stokes Equations
SIAM Journal on Scientific Computing
Shared-memory, distributed-memory, and mixed-mode parallelisation of a CFD simulation code
Computer Science - Research and Development
Stabilization and scalable block preconditioning for the Navier-Stokes equations
Journal of Computational Physics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Hi-index | 31.48 |
The development of robust and efficient algorithms for both steady-state simulations and fully implicit time integration of the Navier-Stokes equations is an active research topic. To be effective, the linear subproblems generated by these methods require solution techniques that exhibit robust and rapid convergence. In particular, they should be insensitive to parameters in the problem such as mesh size, time step, and Reynolds number. In this context, we explore a parallel preconditioner based on a block factorization of the coefficient matrix generated in an Oseen nonlinear iteration for the primitive variable formulation of the system. The key to this preconditioner is the approximation of a certain Schur complement operator by a technique first proposed by Kay, Loghin, and Wathen [SIAM J. Sci. Comput., 2002] and Silvester, Elman, Kay, and Wathen [J. Comput. Appl. Math. 128 (2001) 261]. The resulting operator entails subsidiary computations (solutions of pressure Poisson and convection-diffusion subproblems) that are similar to those required for decoupled solution methods; however, in this case these solutions are applied as preconditioners to the coupled Oseen system. One important aspect of this approach is that the convection-diffusion and Poisson subproblems are significantly easier to solve than the entire coupled system, and a solver can be built using tools developed for the subproblems. In this paper, we apply smoothed aggregation algebraic multigrid to both subproblems. Previous work has focused on demonstrating the optimality of these preconditioners with respect to mesh size on serial, two-dimensional, steady-state computations employing geometric multi-grid methods; we focus on extending these methods to large-scale, parallel, three-dimensional, transient and steady-state simulations employing algebraic multigrid (AMG) methods. Our results display nearly optimal convergence rates for steady-state solutions as well as for transient solutions over a wide range of CFL numbers on the two-dimensional and three-dimensional lid-driven cavity problem.