As a new faculty, I lack the knowledge of fundamentals in my field. What should be the course of action under my special circumstance? Academics are supposed to be an expert in their field and should have a firm grasp on their subject of research. For example, my research is focused on Computational fluid dynamics (CFD) and using finite volume method is my bread and butter. However due to various error in decision making, I never took a course on the subject. I just had an introductory course on transport phenomena and actual numerical method knowledge was acquired while pursuing research on a very practical basis.
My applied research involves using fluent software and I am able to produce decent publications using the software.
Now, as a faculty member, I am supposed to teach CFD to undergrad and graduate students.
How do I address my lack of structured fundamental knowledge on the topic? I will have to start teaching from next semester and I have the course material from a previous instructor, but I am clueless about half of the stuff as that never came across during my research. Also, it's mathematics heavy, I did not come across that in my research papers.
Do I take up the recommended book and study the entire thing, solving selected examples over the course of one month. Or any other way to expedite the process? Please advise.
You indeed need to master the topic that you will teach. So before each lecture, you need to make sure that you master the content to be able to teach it and to answer potential questions from students.
Having said that, you still have some control over the content that you teach during each lecture and how you teach it. Thus, you can sometimes select some parts that you prefer to teach over others. If you use some good textbook, then your job will be much easier.  So looking for a good textbook or teaching content online can help. And you only need to master the parts that you will teach.
Normally, you should be able to prepare 2 hours of lecture in 1 day or less, even if you are not very familiar with the topic. But if you have a good textbook it can be easier. So if you have one month, you have a lot of time in front of you.
Having said that, the life of a new faculty member is generally hard the first one or two years because of all the new courses that we usually have to teach. But then it gets easier as you teach the same courses again.
When I started to teach, I had to teach three new courses on a 1 week notice, including one that I was not familiar about computer networks. That semester, I worked hard everyday from morning to evening and took a one month online course at the same time to master the topic that I would teach the next semester. Then, after the first year, things got easier, and I focused more on research again.