Improved iteration scheme for partial equilibrium flow
type: Item
instance of: scholarly article
title: Improved iteration scheme for partial equilibrium flow
zbMATH Open document ID: 0605.76117
DOI: 10.1016/0021-9991(85)90124-X
published in: Journal of Computational Physics
publication date: 1985-01-01T00:00:00Z
review text: A numerical method for partial equilibrium flow was recently described [the first author and \textit{L. D. Cloutman}, ibid. 39, 405-417 (1981; Zbl 0469.76068)]. The heart of the method is a quadratic iteration scheme in which the progress increment for equilibrium reaction s is obtained from the equilibrium constraint for reaction s alone. The scheme therefore converges best when the equilibrium reactions are weakly coupled, which can frequently be achieved by a judicious choice of the independent equilibrium reactions. The new iteration scheme consists of the following ingredients: (a) preconditioning of the equilibrium constraints conditions to make them more nearly linear in the progress variables, (b) application of a one-step Gauss-Seidel-Newton iteration to the preconditioned system, followed by (c) switching to a full Newton-Raphson iteration if the simpler Gauss-Seidel-Newton iteration fails to converge in a specified number of steps. If the equilibrium reactions are weakly coupled, convergence usually occurs before the full Newton-Raphson iteration is called into play. However, if the reactions are not weakly coupled the interaction between them is properly accounted for by the matrix inversion in the Newton-Raphson procedure.
Mathematics Subject Classification ID: 76T99
zbMATH DE Number: 3978709
zbMATH Keywords: weakly coupled equilibrium
zbMATH Keywords: partial equilibrium flow
zbMATH Keywords: quadratic iteration scheme
zbMATH Keywords: equilibrium reaction
zbMATH Keywords: equilibrium constraint
zbMATH Keywords: preconditioning of the equilibrium constraints conditions
zbMATH Keywords: one-step Gauss-Seidel-Newton iteration
zbMATH Keywords: preconditioned system
zbMATH Keywords: full Newton-Raphson iteration
zbMATH Keywords: convergence
zbMATH Keywords: matrix inversion
author: J. D. Ramshaw
author: Anthony A. Amsden
MaRDI profile type: Publication
cites work: Partial chemical equilibrium in fluid dynamics
cites work: Numerical method for partial equilibrium flow
cites work: Q5652137
Recommended article: A locally implicit improvement of the equilibrium Eulerian method
Recommended article: Improved balanced flow computation using parametric flow
Recommended article: Iterative methods for convection dominated flow
Recommended article: An improved finite element iterative method for three-dimensional fluid flow problems
Recommended article: Adaptive iteration to steady state of flow problems
Recommended article: Q4792237
Recommended article: Partitioned iterative solution methods for fluid-structure interaction
Recommended article: On iterative solvers for non‐Newtonian flow equations
Recommended article: Iterative adaptive implicit-explicit methods for flow problems
Recommended article: Méthodes itératives pour les fluides incompressibles
description: scientific article; zbMATH DE number 3978709