The mathematical analysis of the thermal-hydraulic network equations which occur in nuclear reactor safety codes

Thesis/Dissertation · Tue Jan 01 04:00:00 EST 1980

OSTI ID:5328699

Nitao, J J

A mathematical study of a class of two-phase fluid flow equations is presented for RELAP, a safety code for the computer simulation of loss-of-coolant accidents (LOCA's) in light water nuclear reactors. Mathematically, these equations are a system of non-linear stiff ordinary differential equations. Our results on the Jacobian matrix of this system have direct application to their numerical solution. An improvement on the successive overrelaxation method (SOR) in the present linearly implicit scheme is based on the theory of network graphs and M-matrices. A block SOR method is proposed. Estimates and bounds are found for the eigenvalues of the Jacobian matrix with simplifying assumptions. For small break LOCA's eigenvalues with large imaginary parts are present, and therefore, the differential equations is ''stiff oscillatory.'' A numerical investigation of the eigenvalues is also performed for a simple system. Lastly, an estimate for the truncation error of the aforementioned linearly implicit scheme is derived which includes derivative discontinuities due to fluid phase changes and flow reversals. We note the possibility of a lowered numerical stability whenever two flows, one being subcooled, converge, such as, during emergency core cooling system (ECCS) injection.

• Research Organization: California Univ., Berkeley (USA)
• OSTI ID: 5328699
• Country of Publication: United States
• Language: English

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