A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
Deflation of conjugate gradients with applications to boundary value problems
SIAM Journal on Numerical Analysis
Compressible and incompressible flow; an algorithm for all seasons
Computer Methods in Applied Mechanics and Engineering
An analysis of the fractional step method
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Scheduling Algorithms
Stopping criteria for iterations in finite element methods
Numerische Mathematik
High Resolution Aerospace Applications Using the NASA Columbia Supercomputer
International Journal of High Performance Computing Applications
Journal of Computational Physics
A variational subgrid scale model for transient incompressible flows
International Journal of Computational Fluid Dynamics
Deflated preconditioned conjugate gradient solvers for the Pressure-Poisson equation
Journal of Computational Physics
Evaluation of message passing communication patterns in finite element solution of coupled problems
VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
Journal of Computational Physics
Journal of Computational Physics
| Hi-index | 31.46 |
This paper presents a parallel implementation of fractional solvers for the incompressible Navier-Stokes equations using an algebraic approach. Under this framework, predictor-corrector and incremental projection schemes are seen as sub-classes of the same class, making apparent its differences and similarities. An additional advantage of this approach is to set a common basis for a parallelization strategy, which can be extended to other split techniques or to compressible flows. The predictor-corrector scheme consists in solving the momentum equation and a modified ''continuity'' equation (namely a simple iteration for the pressure Schur complement) consecutively in order to converge to the monolithic solution, thus avoiding fractional errors. On the other hand, the incremental projection scheme solves only one iteration of the predictor-corrector per time step and adds a correction equation to fulfill the mass conservation. As shown in the paper, these two schemes are very well suited for massively parallel implementation. In fact, when compared with monolithic schemes, simpler solvers and preconditioners can be used to solve the non-symmetric momentum equations (GMRES, Bi-CGSTAB) and to solve the symmetric continuity equation (CG, Deflated CG). This gives good speedup properties of the algorithm. The implementation of the mesh partitioning technique is presented, as well as the parallel performances and speedups for thousands of processors.