Time Step and Mesh Size Dependencies in the Heat Conduction Solution of a Semi-Implicit, Finite Difference Scheme for Transient Two-Phase Flow (NUREG/IA-0073, AEEW–M2590)

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Publication Information

Date Published: April 1992

Prepared by:
R. O'Mahoney

Winfrith Technology Centre
United Kingdom Atomic Energy Authority
Dorchester, Dorset, DT2 8DH
United Kingdom

Prepared as part of:
The Agreement on Research Participation and Technical Exchange
under the International Thermal-Hydraulic Code Assessment
and Application Program (ICAP)

Office of Nuclear Regulatory Research
U.S. Nuclear Regulatory Commission
Washington, DC 20555-0001

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This report examines, and establishes the causes of, previously identified time step and mesh size dependencies. These dependencies were observed in the solution of a coupled system of heat conduction and fluid flow equations as used in the TRAC-PFl/MODl computer code.

The TRAC-PF1/MODl computer code employs a semi-implicit, finite difference solution scheme to solve the differential equations describing heat transfer and two-phase fluid flow; it is commonly used to analyse loss-of-coolant accidents in Pressurised Water Reactors.

The report shows that a significant time step size dependency can arise in calculations of the quenching of a previously unwetted surface. The cause of this dependency is shown to be the explicit evaluation, and subsequent smoothing, of the term which couples the heat transfer and fluid flow equations. An axial mesh size dependency is also identified, but this is very much smaller than the time step size dependency.

The report concludes that the time step size dependency represents a potential limitation on the use of large time step sizes for the types of calculation discussed. This limitation affects the present TRAC-PFl/MODl computer code and may similarly affect other semi-implicit finite difference codes that employ similar techniques. It is likely to be of greatest significance in codes where multi-step techniques are used to allow the use of large time steps.

Safety and Engineering Science Division
Winfrith Technology Centre

July 1989

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