With the age of Exascale computing causing a diversification away from traditional CPU-based homogeneous clusters, it is becoming increasingly difficult to ensure that computationally complex codes are able to run on these emerging architectures. This is especially important for large physics simulations that are themselves becoming increasingly complex and computationally expensive. One proposed solution to the problem of ensuring these applications can run on the desired architectures is to develop representative mini-applications that are simpler and so can be ported to new frameworks more easily, but which are also representative of the algorithmic and performance characteristics of the original applications. In this paper we present BookLeaf, an unstructured Arbitrary Lagrangian-Eulerian mini-application to add to the suite of representative applications developed and maintained by the UK Mini-App Consortium (UK-MAC). First, we outline the reference implementation of our application in Fortran. We then discuss a number of alternative implementations using a variety of parallel programming models and discuss the issues that arise when porting such an application to new architectures. To demonstrate our implementation, we present a study of the performance of BookLeaf on number of platforms using alternative designs, and we document a scaling study showing the behaviour of the application at scale.