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?

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UPDATE:  Mainly I am interested in computing the homology of $M$ without having complete information about the gradient flow of $f$.  In particular, I have a specific smooth function on $\mathbb{R}^9$ coming from some data analysis.  I would like to find the homology of the region $M = $ { $ f \le C $ }.  I have a strategy for finding the critical points of $f$, but determining how they are connected by flow lines seems problematic.  Converting to a discrete problem would, I hope, provide a way around this.