Suppose I have a smooth manifold $M$ and a smooth Morse function $f$ on $M$.  Is there a standard way to replace $M$ with a cell complex and $f$ with a discrete Morse function such the resulting homology (via discrete Morse theory) is the same as that of $M$?

My question is motivated by a situation where I know the critical points of $f$, but not how they are connected by gradient flow lines.  So I am interested in a solution which doesn't depend on that information.  I imagine something like the following: Triangulate so that every critical point of $f$ lies on a simplex of the appropriate dimension, then define a discrete vector field by [some process].  This vector field has no nontrivial closed paths [for some reason].  By [some observation], the resulting homology is isomorphic to that of $M$.  

For an expert in Morse theory, does this even sound plausible?  Are there "well-known" methods or results which would fill in the gaps?  Even better, does such a result exist somewhere already?