Characteristics-based modelling of flow problems: Dissertation

Mika Saarinen

Research output: ThesisDissertationCollection of Articles

Abstract

The method of characteristics is in principle an exact way to proceed to the solution of hyperbolic partial differential equations. The numerical solutions, however, are obtained in the fixed computational grid where interpolations of values between the mesh points cause numerical errors. The Piecewise Linear Interpolation Method, PLIM, the utilization of which is based on the method of characteristics, has been developed to overcome these deficiencies. The work concentrates on the following topics: First, the PLIM method has been applied to study the validity of the numerical scheme through solving various difficult flow problems to achieve knowledge for the further development of the method. Second, the mathematical and physical validity and applicability of the two-phase flow equations based on the SFAV (Separation of the two-phase Flow According to Velocities) approach has been studied. Third, the SFAV approach has been further developed for particular cases such as stratified horizontal two-phase flow. In calculating the fluid dynamics of nuclear power plants, two-phase flow has to be considered. Numerical methods that are applied to solve two-phase flow problems are generally inaccurate. The importance of accurate numerical methods is often underestimated because of the difficulties in the physical description of two-phase flow problems. The numerical errors and the deficiencies of the physical model do not correlate; they are separate problems, although and inaccurate numerical solution by itself may lead to nonphysical results. The conventional approach that has been taken to derive one-dimensional two-phase flow equations leads to nonphysical equations and to a mathematically ill-posed initial boundary value problem. Mathematically well-posed and physically reasonable equations can be formed with the SFAV approach. The mathematical and physical justification of these equations has been verified. The applicability of the PLIM code and the various forms of these equations in two-phase flow problems have been studied, especially in the case of horizontal two-phase flow, in which new results have been obtained for the flooding phenomenon.
Original languageEnglish
QualificationDoctor Degree
Awarding Institution
  • Helsinki University of Technology
Award date10 Mar 1994
Place of PublicationEspoo
Publisher
Print ISBNs951-38-4402-1
Publication statusPublished - 1994
MoE publication typeG5 Doctoral dissertation (article)

Fingerprint

two phase flow
modeling
numerical method
interpolation
fluid dynamics
nuclear power plant
flooding
method

Keywords

  • modelling
  • models
  • mathematical models
  • flow models
  • fluid flow
  • two-phase flow
  • nuclear power plants
  • SFAV
  • PLIM
  • equations
  • validation
  • errors

Cite this

Saarinen, M. (1994). Characteristics-based modelling of flow problems: Dissertation. Espoo: VTT Technical Research Centre of Finland.
Saarinen, Mika. / Characteristics-based modelling of flow problems : Dissertation. Espoo : VTT Technical Research Centre of Finland, 1994. 102 p.
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abstract = "The method of characteristics is in principle an exact way to proceed to the solution of hyperbolic partial differential equations. The numerical solutions, however, are obtained in the fixed computational grid where interpolations of values between the mesh points cause numerical errors. The Piecewise Linear Interpolation Method, PLIM, the utilization of which is based on the method of characteristics, has been developed to overcome these deficiencies. The work concentrates on the following topics: First, the PLIM method has been applied to study the validity of the numerical scheme through solving various difficult flow problems to achieve knowledge for the further development of the method. Second, the mathematical and physical validity and applicability of the two-phase flow equations based on the SFAV (Separation of the two-phase Flow According to Velocities) approach has been studied. Third, the SFAV approach has been further developed for particular cases such as stratified horizontal two-phase flow. In calculating the fluid dynamics of nuclear power plants, two-phase flow has to be considered. Numerical methods that are applied to solve two-phase flow problems are generally inaccurate. The importance of accurate numerical methods is often underestimated because of the difficulties in the physical description of two-phase flow problems. The numerical errors and the deficiencies of the physical model do not correlate; they are separate problems, although and inaccurate numerical solution by itself may lead to nonphysical results. The conventional approach that has been taken to derive one-dimensional two-phase flow equations leads to nonphysical equations and to a mathematically ill-posed initial boundary value problem. Mathematically well-posed and physically reasonable equations can be formed with the SFAV approach. The mathematical and physical justification of these equations has been verified. The applicability of the PLIM code and the various forms of these equations in two-phase flow problems have been studied, especially in the case of horizontal two-phase flow, in which new results have been obtained for the flooding phenomenon.",
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author = "Mika Saarinen",
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year = "1994",
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isbn = "951-38-4402-1",
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Saarinen, M 1994, 'Characteristics-based modelling of flow problems: Dissertation', Doctor Degree, Helsinki University of Technology, Espoo.

Characteristics-based modelling of flow problems : Dissertation. / Saarinen, Mika.

Espoo : VTT Technical Research Centre of Finland, 1994. 102 p.

Research output: ThesisDissertationCollection of Articles

TY - THES

T1 - Characteristics-based modelling of flow problems

T2 - Dissertation

AU - Saarinen, Mika

N1 - Project code: ENE040537

PY - 1994

Y1 - 1994

N2 - The method of characteristics is in principle an exact way to proceed to the solution of hyperbolic partial differential equations. The numerical solutions, however, are obtained in the fixed computational grid where interpolations of values between the mesh points cause numerical errors. The Piecewise Linear Interpolation Method, PLIM, the utilization of which is based on the method of characteristics, has been developed to overcome these deficiencies. The work concentrates on the following topics: First, the PLIM method has been applied to study the validity of the numerical scheme through solving various difficult flow problems to achieve knowledge for the further development of the method. Second, the mathematical and physical validity and applicability of the two-phase flow equations based on the SFAV (Separation of the two-phase Flow According to Velocities) approach has been studied. Third, the SFAV approach has been further developed for particular cases such as stratified horizontal two-phase flow. In calculating the fluid dynamics of nuclear power plants, two-phase flow has to be considered. Numerical methods that are applied to solve two-phase flow problems are generally inaccurate. The importance of accurate numerical methods is often underestimated because of the difficulties in the physical description of two-phase flow problems. The numerical errors and the deficiencies of the physical model do not correlate; they are separate problems, although and inaccurate numerical solution by itself may lead to nonphysical results. The conventional approach that has been taken to derive one-dimensional two-phase flow equations leads to nonphysical equations and to a mathematically ill-posed initial boundary value problem. Mathematically well-posed and physically reasonable equations can be formed with the SFAV approach. The mathematical and physical justification of these equations has been verified. The applicability of the PLIM code and the various forms of these equations in two-phase flow problems have been studied, especially in the case of horizontal two-phase flow, in which new results have been obtained for the flooding phenomenon.

AB - The method of characteristics is in principle an exact way to proceed to the solution of hyperbolic partial differential equations. The numerical solutions, however, are obtained in the fixed computational grid where interpolations of values between the mesh points cause numerical errors. The Piecewise Linear Interpolation Method, PLIM, the utilization of which is based on the method of characteristics, has been developed to overcome these deficiencies. The work concentrates on the following topics: First, the PLIM method has been applied to study the validity of the numerical scheme through solving various difficult flow problems to achieve knowledge for the further development of the method. Second, the mathematical and physical validity and applicability of the two-phase flow equations based on the SFAV (Separation of the two-phase Flow According to Velocities) approach has been studied. Third, the SFAV approach has been further developed for particular cases such as stratified horizontal two-phase flow. In calculating the fluid dynamics of nuclear power plants, two-phase flow has to be considered. Numerical methods that are applied to solve two-phase flow problems are generally inaccurate. The importance of accurate numerical methods is often underestimated because of the difficulties in the physical description of two-phase flow problems. The numerical errors and the deficiencies of the physical model do not correlate; they are separate problems, although and inaccurate numerical solution by itself may lead to nonphysical results. The conventional approach that has been taken to derive one-dimensional two-phase flow equations leads to nonphysical equations and to a mathematically ill-posed initial boundary value problem. Mathematically well-posed and physically reasonable equations can be formed with the SFAV approach. The mathematical and physical justification of these equations has been verified. The applicability of the PLIM code and the various forms of these equations in two-phase flow problems have been studied, especially in the case of horizontal two-phase flow, in which new results have been obtained for the flooding phenomenon.

KW - modelling

KW - models

KW - mathematical models

KW - flow models

KW - fluid flow

KW - two-phase flow

KW - nuclear power plants

KW - SFAV

KW - PLIM

KW - equations

KW - validation

KW - errors

M3 - Dissertation

SN - 951-38-4402-1

T3 - VTT Publications

PB - VTT Technical Research Centre of Finland

CY - Espoo

ER -

Saarinen M. Characteristics-based modelling of flow problems: Dissertation. Espoo: VTT Technical Research Centre of Finland, 1994. 102 p.