I have done my PhD research without learning the numerical method details. How can I defend successfully?
Your advisor is giving you good advice. She presumably knows what is required here and will come to your aid if any issue arises. An advisor supporting a candidate in a defense happens in some situations. And the advisor probably knows more about all of your work than any other committee member. 

But if you are using a standard tool in a standard way then it is unlikely that the tool has affected your results. Hopefully you can refer to other, published, studies that use the tool or even marketing material that point to its verification. 

Your field isn't the development of such tools, but their use. Had it been tool development for ME then you'd have a problem. Your undergraduate education probably gives you a general basis for the underlying math/physics/dynamics/whatever. 

Relax. 



Note that my experience is in situations in which the advisor is either a committee member or sits as an advocate. I recognize that there are other traditions in which the committee is independent. But even then, you are unlikely to be strongly challenged for not having details of the tool at hand, beyond general ME principles of analysis.