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In the second paper of this series we pursue two objectives. First, in orderto make the code more sensitive to small effects, we remove many approximationsmade in Paper I. Second, we include turbulence and rotation in thetwo-dimensional framework. The stellar equilibrium is described by means of aset of five differential equations, with the introduction of a new dependentvariable, namely the perturbation to the radial gravity, that is found when thenon-radial effects are considered in the solution of the Poisson equation;following the scheme of the first paper, we write the equations in such a waythat the two-dimensional effects can be easily disentangled. The key conceptintroduced in this series is the equipotential surface. We use the underlyingcause-effect relation to develop a recurrence relation to calculate theequipotential surface functions for uniform rotation, differential rotation,rotation-like toroidal magnetic fields and turbulence. We also develop a moreprecise code to numerically solve the two-dimensional stellar structure andevolution equations based on the equipotential surface calculations. We haveshown that with this formulation we can achieve the precision required byobservations by appropriately selecting the convergence criterion. Severalexamples are presented to show that the method works well. Since we areinterested in modeling the effects of a dynamo-type field on the detailedenvelope structure and global properties of the Sun, the code has beenoptimized for short timescales phenomena (down to 1 yr). The time dependence ofthe code has so far been tested exclusively to address such problems.

Two-Dimensional Stellar Evolution Code Including Arbitrary Magnetic Fields. II. Precision Improvement and Inclusion of Turbulence and Rotation