GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Stabilized finite element methods. II: The incompressible Navier-Stokes equations
Computer Methods in Applied Mechanics and Engineering
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Parallel Newton--Krylov--Schwarz Algorithms for the Transonic Full Potential Equation
SIAM Journal on Scientific Computing
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
Proceedings of the 2002 ACM/IEEE conference on Supercomputing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A numerical method for large-eddy simulation in complex geometries
Journal of Computational Physics
Journal of Computational Physics
Petascale Direct Numerical Simulation of Blood Flow on 200K Cores and Heterogeneous Architectures
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Benchmark computations of 3D laminar flow around a cylinder with CFX, OpenFOAM and FeatFlow
International Journal of Computational Science and Engineering
Hi-index | 0.00 |
Numerical simulation of three-dimensional incompressible flows at high Reynolds number using the unsteady Navier---Stokes equations is challenging. In order to obtain accurate simulations, very fine meshes are necessary, and such simulations are increasingly important for modern engineering practices, such as understanding the flow behavior around high speed trains, which is the target application of this research. To avoid the time step size constraint imposed by the CFL number and the fine spacial mesh size, we investigate some fully implicit methods, and focus on how to solve the large nonlinear system of equations at each time step on large scale parallel computers. In most of the existing implicit Navier---Stokes solvers, segregated velocity and pressure treatment is employed. In this paper, we focus on the Newton---Krylov---Schwarz method for solving the monolithic nonlinear system arising from the fully coupled finite element discretization of the Navier---Stokes equations on unstructured meshes. In the subdomain, LU or point-block ILU is used as the local solver. We test the algorithm for some three-dimensional complex unsteady flows, including flows passing a high speed train, on a supercomputer with thousands of processors. Numerical experiments show that the algorithm has superlinear scalability with over three thousand processors for problems with tens of millions of unknowns.