Is there an equation for the residual strong nuclear force? First of all, note the qualifier "residual".  The present question is not the same as that asked, and answered, in the StackExchange question "Is there an equation for the strong nuclear force?" which was really addressed as though it asked "Is there an equation for the strong interaction between quarks?"
If there is no such equation, is there a numeric simulation program?
 A: There exists the shell model which has been very successful in describing the residual strong force that holds the nucleons in the nucleus and organizes the periodic table of elements. It is based on quantum mechanical analogues.
There are other models: the liquid drop model which is an empirical way of treating the many nucleon system classically like a drop.
There even exists an effective  field theory for nuclear physics .
It depends on the problem one wants to address which of these methods is appropriate.
A: Presently, there are two ways to calculate the nuclear force, or if you prefer, the "residual" strong force, from Quantum Chromodynamics (QCD), which is the fundamental theory for strong interaction. 
1) Using lattice QCD which is based on large-scale simulations performed on supercomputers. A couple of recent papers, e.g. Lattice QCD approach to Nuclear Physics by a Japanese group and 
Light Nuclei and Hypernuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry by a US group. These two groups are the main ones simulating the nuclear force using lattice QCD.
2) Using effective field theory, which was reviewed in, for instance, Modern Theory of Nuclear Forces. Based on the framework of effective field theory, there are also simulations of nuclei. An important example is the success of calculating the Hoyle state of the carbon nucleus.
