Jacobian-free Newton–Krylov (JFNK) methods are synergistic combinations of Newton-type
methods for superlinearly convergent solution of nonlinear equations and Krylov subspace …

Nonlinear, time-linearized and adjoint Reynolds-averaged Navier-Stokes (RANS)
computational fluid dynamics (CFD) solvers are widely used to assess and improve the …

This paper explores the development of a scalable, nonlinear, fully-implicit stabilized
unstructured finite element (FE) capability for 2D incompressible (reduced) resistive MHD …

The computational solution of the governing balance equations for mass, momentum, heat
transfer and magnetic induction for resistive magnetohydrodynamics (MHD) systems can be …

A nonlinear additive Schwarz preconditioned inexact Newton method (ASPIN) was
introduced recently for solving large sparse highly nonlinear systems of equations obtained …

A Newton–Krylov method is an implementation of Newton's method in which a Krylov
subspace method is used to solve approximately the linear subproblems that determine …

We present a numerical study of the structure and stability of laminar isothermal flows
formed by two counterflowing jets of an incompressible Newtonian fluid. We demonstrate …

We consider numerical simulation of two-phase flows in porous media using implicit
methods. Because of the complex features involving heterogeneous permeability and …

Nonlinearly preconditioned inexact Newton methods have been applied successfully for
some difficult nonlinear systems of algebraic equations arising from the discretization of …

Inexact Newton method is one of the effective tools for solving systems of nonlinear
equations. In each iteration step of the method, a forcing term, which is used to control the …