  This is the second in a series of two articles introducing the Gravitas
computational general relativity framework, in which we now focus upon the
design and capabilities of Gravitas's numerical subsystem, including its
ability to perform general 3+1 decompositions of spacetime via the ADM
formalism, its support for the definition and construction of arbitrary Cauchy
surfaces as initial data, its support for the definition and enforcement of
arbitrary gauge and coordinate conditions, its various algorithms for ensuring
the satisfaction of the ADM Hamiltonian and momentum constraints, and its
unique adaptive refinement algorithms based on hypergraph rewriting via Wolfram
model evolution. Particular attention is paid to the seamless integration
between Gravitas's symbolic and numerical subsystems, its ability to configure,
run, analyze and visualize complex numerical relativity simulations and their
outputs within a single notebook environment, and its capabilities for handling
generic curvilinear coordinate systems and spacetimes with general (and often
highly non-trivial) topologies using its specialized and highly efficient
hypergraph-based numerical algorithms. We also provide illustrations of
Gravitas's functionality for the visualization of hypergraph geometries and
spacetime embedding diagrams, the ability for Gravitas's symbolic and numerical
subsystems to be used in concert for the extraction of gravitational wave
signals and other crucial simulation data, and Gravitas's in-built library of
standard initial data, matter distributions and gauge conditions. We conclude
by demonstrating how the numerical subsystem can be used to set up, run,
visualize and analyze a standard yet nevertheless reasonably challenging
numerical relativity test case: a binary black hole collision and merger within
a vacuum spacetime (including the extraction of its outgoing gravitational wave
profile).
