Reaction–diffusion mechanisms are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns formed by vegetation in semi-arid landscapes. Moreover, domain growth is an important process for embryonic growth and wound healing. There are many numerical modelling frameworks capable of simulating such systems on growing domains; however, each of these may be well suited to different spatial scales and particle numbers. Recently, spatially extended hybrid methods on static domains have been produced to bridge the gap between these different modelling paradigms in order to represent multi-scale phenomena. However, such methods have not been developed with domain growth in mind. In this paper, we develop three hybrid methods on growing domains, extending three of the prominent static-domain hybrid methods. We also provide detailed algorithms to allow others to employ them. We demonstrate that the methods are able to accurately model three representative reaction–diffusion systems accurately and without bias.

反应扩散机制是一种强大的范式，可用于在多个空间尺度上表示许多生物和物理现象。应用包括细胞内动力学、细胞迁移和半干旱景观中植被形成的模式。此外，域生长是胚胎生长和伤口愈合的重要过程。有许多数值建模框架能够在不断增长的领域中模拟此类系统；然而，这些中的每一个都可能非常适合不同的空间尺度和粒子数。最近，已经产生了静态域上的空间扩展混合方法，以弥合这些不同建模范式之间的差距，以表示多尺度现象。然而，这些方法的开发并未考虑到域的增长。在本文中，我们在增长领域开发了三种混合方法，扩展了三种突出的静态域混合方法。我们还提供详细的算法以允许其他人使用它们。我们证明了这些方法能够准确无偏地准确地模拟三个具有代表性的反应扩散系统。