An Integrated RELAP5-3D and Multiphase CFD Code System Utilizing a Semi Implicit Coupling Technique Page: 3 of 12
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2001 RELAP5 International Users Seminar
Sun Valley, Idaho
September 5-7, 2001
stability issues related to thermal-hydraulic code
coupling. A brief discussion of the methodology is
presented later in this paper.
The most important features of the semi-implicit
coupling methodology are its generality and its use of
the Parallel Virtual Machine (PVM) software package
(Geist, 1994) to allow communication among the
programs. These features allow additional programs to
be added to the integrated code system in a very straight
forward manner. Additionally, by creating this generic
interface, the development of all of the programs in the
integrated system can proceed independently of each
other, provided the interface is maintained. This
approach is contrasted with the "hard-wired" approach
used in COBRA/TRAC where the programs are
conjoined to form one new program. This approach
makes code maintenance and development more
difficult. This may partially explain why the
COBRA/TRAC program has not kept current with the
development of either the COBRA or TRAC programs.
Semi-Implicit Coupling Algorithm
A complete description of the semi-implicit coupling
algorithm is provided by Weaver (2000); what follows is
a brief synopsis of the methodology. A coupled code
system performs a domain decomposition of the
complete problem to allow each program to solve a
piece of the problem. This is shown schematically in
Figure 1. The advantage of the semi-implicit coupling
technique is that it is more numerically stable than
simpler, explicit coupling schemes.
The use of implicit velocities and pressures in the
discretized conservation equations in the semi-implicit
numerical method (Liles, 1978) provides numerical
stability for time step sizes smaller than the material
Courant limit. One feature of this method is that a single
matrix containing only new-time pressures can be
developed. This matrix contains the effect of all of the
new-time variables. This feature is the key to the semi-
implicit coupling algorithm.
Using the nomenclature of Weaver (2000), RELAP5-3D
will be the master process and the CFD program will be
the slave process in this system. The semi-implicit
coupling methodology modifies the solution procedure
in the RELAP5-3D program for the junctions
representing the connections between the two systems.
The pressure equation for the volume attached to the
coupling location in the RELAP5-3D computational
domain is modified by retaining the mass, energy,
volume and non-condensable gas flow rates as
By retaining these terms, the changes in the pressures in
all of the volumes in the computational domain can be
computed in terms of the flow rates in the coupling
SP+1 = ak + bk, jng J +
ck, jugj + d juf1 +
n+1 n+ 1
ek, mgj + fk, jmf, j+
k, jw + hk, jw
where ng, ug, u, mg, mi, wg and w, represent the flow
rate of non-condensable gas, and the phasic flow rates of
energy, mass and volume at the coupling locations, and
NC is the number of coupling junctions. The coefficients
a through h for the volumes attached to the coupling
junctions in the RELAP5-3D computational domain
(volumes 1 and 2 in Figure 1) are then transmitted to the
CFD program. The CFD solution uses coefficients a
through h to calculate the interdependence of pressure
and flow rates consistent with RELAP5-3D solution
strategy. This consistency is the key to the semi-implicit
coupling methodology. When the mass, energy, volume
and non-condensable flow rates in the coupling
junctions have been received from the slave process,
Equation (1) can be evaluated for the change in the
pressure in each volume in the RELAP5-3D system.
Once the changes in the pressures in the volumes have
been computed, the time advancement may be
completed in the normal manner.
The semi-implicit coupling algorithm is numerically
stable subject to certain limitations. The master process
(RELAP5-3D in this application) must use semi-
implicit numerics and the material Courant limit must
not be violated in the master process or at the coupling
location. The semi-implicit coupling algorithm does not
influence the stability of the slave process (the CFD
program in this application). At this point, a few words
concerning stability of the CFD program are
appropriate. The CFD program which was chosen for
this work uses a fully-implicit solution procedure.
Through the use of fully-implicit numerics, the CFD
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Aumiller, D.L.; Tomlinson, E.T. & Weaver, W.L. An Integrated RELAP5-3D and Multiphase CFD Code System Utilizing a Semi Implicit Coupling Technique, article, June 21, 2001; United States. (https://digital.library.unt.edu/ark:/67531/metadc783173/m1/3/: accessed March 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.