Numerical Simulations For Non Conservative Hyperbolic System. Application to Transient Two-Phase Flow with Cavitation Phenomenon

被引：3

作者：

Achchab, Boujemaa ^{[1
]}

Agouzal, Abdellatif ^{[2
]}

Qadi El Idrissi, Abdelmjid ^{[1
]}

机构：

[1] Univ Hassan 1, Natl Sch Appl Sci, Berrechid 218, Morocco

[2] Univ Claude Bernard, Inst Camille Jordan, CNRS, Lyon, France

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2019年 / 24卷 / 02期

关键词：

non conservative system; MacCormack scheme; hyperbolic system; two phase flow; cavitation; SCHEME;

D O I：

10.3846/mma.2019.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A numerical method for simulating transient flows of gas-liquid mixtures is proposed. The mathematical model, established for a suspension of gas bubbles in liquid, includes an equation taking into account the relative velocity between the gas and liquid. A numerical technique based on the MacCormack scheme combined with the method of characteristics for the boundary conditions is presented. Theoretical results for transients initiated by a rapid closing valves are compared with measurements. A good agreement is found particularly for large values of initial dissolved gas concentration.

引用

页码：218 / 235

页数：18

共 18 条

[1] A comment on the computation of non-conservative products [J].

Abgrall, Remi ;

Karni, Smadar .

JOURNAL OF COMPUTATIONAL PHYSICS, 2010, 229 (08) :2759-2763

[2] Modelling of an Homogeneous Equilibrium Mixture Model (HEM) [J].

Bernard-Champmartin, A. ;

Poujade, O. ;

Mathiaud, J. ;

Ghidaglia, J. -M. .

ACTA APPLICANDAE MATHEMATICAE, 2014, 129 (01) :1-21

[3] 2-PHASE FLOW EQUATIONS FOR A DILUTE DISPERSION OF GAS-BUBBLES IN LIQUID [J].

BIESHEUVEL, A ;

VANWIJNGAARDEN, L .

JOURNAL OF FLUID MECHANICS, 1984, 148 (NOV) :301-318

[4] Well-balanced high-order centred schemes for non-conservative hyperbolic systems. Applications to shallow water equations with fixed and mobile bed [J].

Canestrelli, Alberto ;

Siviglia, Annunziato ;

Dumbser, Michael ;

Toro, Eleuterio F. .

ADVANCES IN WATER RESOURCES, 2009, 32 (06) :834-844

[5] A Riemann solver and upwind methods for a two-phase flow model in non-conservative form [J].

Castro, CE ;

Toro, EF .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2006, 50 (03) :275-307

[6] ACCURATE NUMERICAL DISCRETIZATIONS OF NON-CONSERVATIVE HYPERBOLIC SYSTEMS [J].

Fjordholm, Ulrik Skre ;

Mishra, Siddhartha .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2012, 46 (01) :187-206

[7] An exact multiphase Riemann solver for compressible cavitating flows [J].

Jafarian, Ali ;

Pishevar, Ahmadreza .

INTERNATIONAL JOURNAL OF MULTIPHASE FLOW, 2017, 88 :152-166

[8]

Lagumbay R.S., 2007, International Journal for Numerical Methods in Fluids, V4, P1

[9]

LIUZZI D, 2012, THESIS

[10] ON THE EFFECT OF TEMPERATURE AND VELOCITY RELAXATION IN TWO-PHASE FLOW MODELS [J].

Martinez Ferrer, Pedro Jose ;

Flatten, Tore ;

Munkejord, Svend Tollak .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2012, 46 (02) :411-442

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