I have finished reading through some good texts on numerical methods for partial differential equations, including the books by LeVeque on Finite Differences and Finite Volume methods, and the Chapra and Canale book, Numerical Methods for Engineers. So I understand the basic numerical mathematics to solve simple to intermediate partial differential equations. But what I am missing is some sort of reference book or set of examples of people actually implementing/computing these methods to solve problems.
For examples, I have a few different projects I would like to implement, such as simulating a chemotaxis equation on a simple domain, implementing the shallow water equation on a simple and complicated domain, etc. I want to understand how to setup the computation for these problems.
So I am basically looking for a book that has tutorials on setting up the computation for solving different PDEs. Does anyone know of any good books or tutorials like that? Every tutorial I have found so far implements the simplest examples--such as 1-dimensional heat equation on a rod, which are really not so useful a bridge to more complicated problems. I understand that for PDEs, there are usually packages to handle discretizing the domain and handling the matrix solves for banded matrices, etc. So I don't have to program these things myself.I would just like to see multiple examples of how other people have taken a PDE and then programmed the solvers.
Any suggestions would really be appreciated, even if they are links to Arxiv tutorials or blog posts, etc.
Please note, I did check the following SE posts and they were not relevant to this question.
reference request : Numerical techniques for partial differential equations