Numerical Methods for Solving the Cahn-Hilliard Equation and Its Applicability to Related Energy-Based Models

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10318706" target="_blank" >RIV/00216208:11320/15:10318706 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s11831-014-9112-1" target="_blank" >http://dx.doi.org/10.1007/s11831-014-9112-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11831-014-9112-1" target="_blank" >10.1007/s11831-014-9112-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Numerical Methods for Solving the Cahn-Hilliard Equation and Its Applicability to Related Energy-Based Models

Popis výsledku v původním jazyce

In this paper, we review some numerical methods presented in the literature in the last years to approximate the Cahn-Hilliard equation. Our aim is to compare the main properties of each one of the approaches to try to determine which one we should choose depending on which are the crucial aspects when we approximate the equations. Among the properties that we consider desirable to control are the time accuracy order, energy-stability, unique solvability and the linearity or nonlinearity of the resulting systems. In particular, we concern about the iterative methods used to approximate the nonlinear schemes and the constraints that may arise on the physical and computational parameters. Furthermore, we present the connections of the Cahn-Hilliard equation with other physically motivated systems (not only phase field models) and we state how the ideas of efficient numerical schemes in one topic could be extended to other frameworks in a natural way.

Název v anglickém jazyce

Numerical Methods for Solving the Cahn-Hilliard Equation and Its Applicability to Related Energy-Based Models

Popis výsledku anglicky

In this paper, we review some numerical methods presented in the literature in the last years to approximate the Cahn-Hilliard equation. Our aim is to compare the main properties of each one of the approaches to try to determine which one we should choose depending on which are the crucial aspects when we approximate the equations. Among the properties that we consider desirable to control are the time accuracy order, energy-stability, unique solvability and the linearity or nonlinearity of the resulting systems. In particular, we concern about the iterative methods used to approximate the nonlinear schemes and the constraints that may arise on the physical and computational parameters. Furthermore, we present the connections of the Cahn-Hilliard equation with other physically motivated systems (not only phase field models) and we state how the ideas of efficient numerical schemes in one topic could be extended to other frameworks in a natural way.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/LL1202" target="_blank" >LL1202: Materiály s implicitními konstitutivními vztahy: Od teorie přes redukci modelů k efektivním numerickým metodám</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Archives of Computational Methods in Engineering

ISSN

1134-3060

e-ISSN

—

Svazek periodika

22

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

21

Strana od-do

269-289

Kód UT WoS článku

000351767800004

EID výsledku v databázi Scopus

2-s2.0-84926278140