We construct new first-and second-order pressure correctionschemes using the scalar
auxiliary variable approach for the Navier-Stokes equations. These schemes are linear …

We propose, analyze, and test Anderson-accelerated Picard iterations for solving the
incompressible Navier--Stokes equations (NSE). Anderson acceleration has recently gained …

Despite their well-established efficiency and accuracy, fractional-step schemes are not
commonly used in finite volume methods. This article presents first-, second-, and third-order …

A fractional-step method is proposed and analyzed for solving the incompressible thermal
Navier–Stokes equations coupled to the convection–conduction equation for heat transfer …

We analyze and test a simple-to-implement two-step iteration for the incompressible Navier-
Stokes equations that consists of first applying the Picard iteration and then applying the …

The incremental Picard Yosida (IPY) method has recently been developed as an iteration for
nonlinear saddle point problems that is as effective as Picard but more efficient. By …

We consider two modifications of the Arrow–Hurwicz (AH) iteration for solving the
incompressible steady Navier–Stokes equations for the purpose of accelerating the …

The Newton's method for solving stationary Navier-Stokes equations (NSE) is known to
convergent fast, however, may fail due to a bad initial guess. This work presents a simple-to …

This thesis studies nonlinear iterative solvers for the simulation of Newtonian and non-
Newtonian fluid models with two different approaches: Anderson acceleration (AA), an …

We propose a new, efficient, nonlinear iteration for solving the steady incompressible MHD
equations. The method consists of a careful combination of an incremental Picard iteration …