[en] 1 - Description of program or function: NESTLE solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). The NESTLE code can solve the eigenvalue (criticality), eigenvalue adjoint, external fixed-source steady-state, and external fixed-source or eigenvalue initiated transient problems. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two- or four-energy groups can be utilized, with all energy groups being thermal groups (i.e. up-scatter exits) if desired. Core geometries modeled include Cartesian and hexagonal. Three-, two-, and one-dimensional models can be utilized with various symmetries. The thermal conditions predicted by the thermal-hydraulic model of the core are used to correct cross sections for temperature and density effects. Cross sections are parametrized by color, control rod state (i.e., in or out), and burnup, allowing fuel depletion to be modeled. Either a macroscopic or microscopic model may be employed. The December 1996 release of NESTLE V5.02 includes the option to utilize a Weilandt Eigenvalue Shift method in place of the Semi-Implicit Chebyshev Polynomial method to accelerate the outer iterations. In addition, flux, fission source and power density are now exponentially extrapolated to the new time-step time value to improve convergence. Other features added include the following: implicit or explicit transient T-H feedback option, specification of whether convergence after a NEM/T-H update is demanded, frequency of NEM coupling coefficients update based upon L2 fission source relative error reduction, execution time specification of control file name, input echo execution option, and improved run-time statistics. In addition, various minor bugs were fixed, and code restructuring was implemented to increase computational performance and coding clarity. Details of all code changes can be found within subroutine main.f. 2 - Method of solution: The few-group neutron diffusion equation is spatially discretized utilizing the Nodal Expansion Method (NEM). Quartic or quadratic polynomial expansions for the transverse integrated fluxes are employed for Cartesian or hexagonal geometries, respectively. Transverse leakage terms are represented by a quadratic polynomial or constant for Cartesian or hexagonal geometries, respectively. Discontinuity factors are utilized to correct for homogenization errors. Transient problems utilize a user-specified number of delayed-neutron precursor groups. Time-dependent inputs include coolant inlet temperature and flow, soluble poison concentration, and control bank positions. Time discretization is done in a fully implicit manner utilizing a first-order difference operator for the diffusion equation. The precursor equations are analytically solved, assuming the fission rate behaves linearly over a time step. Independent of problem type, an outer-inner iterative strategy is employed to solve the resulting matrix system. Outer iterations can employ Chebyshev acceleration and the fixed-source scaling technique to accelerate convergence. Inner iterations employ either color line or point successive over-relaxation iteration schemes, dependent upon problem geometry. Values of the energy group-dependent optimum relaxation parameter and the number of inner iterations per outer iteration to achieve a specified L2 relative error reduction are determined a priori. The nonlinear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NESTLE can be utilized to solve either the nodal or finite difference method representation of the few-group neutron diffusion equation. Thermal-hydraulic feedback is modeled employing a homogeneous equilibrium mixture (HEM) model, which allows two-phase flow to be treated. However, only the continuity and energy equati ons for the coolant are solved, implying a constant pressure treatment. The slip is assumed to be one in the HEM model. A lumped parameter model is employed to determine the fuel temperature. Decay heat groups are used to model decay heat. All cross sections are expressed in terms of a Taylor's series expansion in coolant density, coolant temperature, effective fuel temperature, and soluble poison number density. 3 - Restrictions on the complexity of the problem: The NEM option works only for two- and four-energy groups, and depletable isotopes are limited to the principle fissile and fertile isotopes and lumped and transient fission products