Power series solutions of the thermal-hydraulic conservation equations

The solution technique presented in this paper is an extension of a method used by Agee (AGEE, 1971) to solve the homogeneous thermal-hydraulic conservation equations used by the FLASH (REDFIELD, 1969) and RELAP (MOORE, 1973) programs. The extension of the method to the more general separated flow case requires the following semi-independent steps: 1) reduce the quasi-linear partial differential equations to a set of K ordinary differentials by use of any general difference formula; 2) form the coefficient series from the known series representation of the dependent variables by algebraic manipulation (i.e., addition, subtraction, multiplication, division, logarithm, and exponential operations) of N-th order power series; 3) solve the resulting set of nonlinear ordinary differential equations by power series methods which are exact to order N; 4) obtain the solution to the coupled set over a 'long' time zone by applying a modified Cauchy-Picard iteration technique; or use the solution obtained in Step 3 over time steps for which the first order coupling is significantly accurate; 5) extend the solution to arbitrary times by utilizing analytical continuation of the existing power series for the dependent variables