The calculation of the energy release typified by Eqs. (4.15)-(4.22) is complicated by the need to solve spatial as well as temporal derivatives in a finite difference manner. Thus computer solutions are needed, and the available codes reflect improvements in the analysis over the past two decades (see also the Appendix).

(a) AX-1 (13a). This is a one-dimensional spherical model with a linear equation of state. It accepted only a step of reactivity and had no Doppler feedback.

(b) АХ-TNT (13b). This development of AX-1 was also one-dimensional but it included a linear or Clausius-Clapeyron equation of state. It had partial Doppler feedback, and it accepted reactivity ramps as well as steps. It had a total of 320 mesh points and it used an additional routine to cal­culate the available work energy in terms of TNT equivalent.

(c) WEAK EXPLOSION (14). Still a one-dimensional spherical model code, it included an equation of state of the form p = В exp [—A/(E + Eq)] and a Doppler feedback which depended on E1/2. This code had no calcula­tion of the work energy available for damage to structure.

(d) MARS (15). This code is two dimensional (r, z). It allows in its modified form all types of equations of state, all forms of reactivity addi­tions and allows the input of tabulated power distributions. Six core regions involving a total of 380 mesh points each can be used to map the core. Doppler feedback is included. A modified version of MARS calculated the available work as an isentropic expansion of fuel following termination of the transient by the dispersion of the core. However, modifications to the core model have allowed the available work to be calculated as a function of the amount of sodium present in the core into which energy is deposited by the molten fuel. This sodium is then assumed to undergo isentropic expansion.

(e) VENUS (12b). This latest code is still under development at ANL. It combines a comprehensive hydrodynamic code that calculates the move­ment of fuel and structural material allowing a pointwise variation of density with time, with a point kinetic model of the kind used in MARS. The code is produced as a module in a much larger series of codes which starts with a dynamic module and ends with damage calculations within the vessel. It is the first to avoid the use of constant density, although the results do not differ greatly from MARS except in special cases.