Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
Journal of Computational Physics
An Analysis of Approximate Nonlinear Elimination
SIAM Journal on Scientific Computing
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Convergence Analysis of Pseudo-Transient Continuation
SIAM Journal on Numerical Analysis
Parallel Newton--Krylov--Schwarz Algorithms for the Transonic Full Potential Equation
SIAM Journal on Scientific Computing
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Nonlinearly Preconditioned Inexact Newton Algorithms
SIAM Journal on Scientific Computing
Journal of Computational Physics
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Journal of Computational Physics
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There are two major types of approaches for solving the incompressible Navier-Stokes equations. One of them is the so-called projection method, in which the velocity field and the pressure field are solved separately. This method is very efficient, but is difficult to be extended to another multi-physics problem when an appropriate splitting is not available. The other approach is the fully coupled method in which the velocity and pressure fields stay together throughout the computation. The coupled approach can be easily extended to other multi-physics problems, but it requires the solution of some rather difficult linear and nonlinear algebraic systems of equations. The paper focuses on a fully coupled domain decomposition based parallel inexact Newton's method with subspace correction for incompressible Navier-Stokes equations at high Reynolds numbers. The discussion is restricted to the velocity-vorticity formulation of the Navier-Stokes equations, but the idea can be generalized to other multi-physics problems.