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 twophase flow
equations based on the SFAV
(Separation of the
twophase Flow According to Velocities) approach has been
studied. Third, the
SFAV approach
has been further developed for particular cases such as
stratified horizontal
twophase flow.
In calculating the fluid dynamics of nuclear power
plants, twophase flow has
to be considered.
Numerical methods that are applied to solve twophase
flow problems are
generally inaccurate.
The importance of accurate numerical methods is often
underestimated because of
the difficulties
in the physical description of twophase 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
onedimensional
twophase flow
equations leads to nonphysical equations and to a
mathematically illposed
initial boundary value
problem. Mathematically wellposed 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
twophase flow
problems have been studied, especially in the case of
horizontal twophase
flow, in which new
results have been obtained for the flooding phenomenon.
Original language  English 

Qualification  Doctor Degree 
Awarding Institution 

Award date  10 Mar 1994 
Place of Publication  Espoo 
Publisher  
Print ISBNs  9513844021 
Publication status  Published  1994 
MoE publication type  G5 Doctoral dissertation (article) 
Keywords
 modelling
 models
 mathematical models
 flow models
 fluid flow
 twophase flow
 nuclear power plants
 SFAV
 PLIM
 equations
 validation
 errors
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Saarinen, M. (1994). Characteristicsbased modelling of flow problems: Dissertation. VTT Technical Research Centre of Finland.