“Cross simulation” between analog and digital
Maybe you should read this article.

I do not understand the term "cross simulation" as we normally talk about mixed signal simulation. The "domain crossing" is an integral part of that, I'll explain later.

Mixed signal simulation is a circuit simulation where part of the circuit is described in the analog domain so using transistor level models, capacitor, resistor and inductor models etc. This is needed for analog ciruits.

The rest of the circuit is described as "digital" meaning its behavior is described in Verilog, VHDL or some behavior model language. This describes the circuit in logic expressions like: a = b AND NOT(c) That is much simpler and therefore simulates much faster than analog models. Therefore much more complex (digital) functions can be simulated.

The "domain crossing" happens where the signals travel between the analog and the digital sections. There the analog voltages have to be translated into "zero" or "one" and back (zero or one to an analog voltage). In essence this is usually just a comparator function.