Engineered living materials (ELMs) propose the integration of living microbial agents to achieve novel functionalities. The synthesis of mycelium-based ELMs can be framed as a fermentation process within a regulated, coupled organism-environment system on which we can intervene through a control vector. The non-local interactions, large dimensionality, low observability and highly non-linear nature of such systems make the realization of high-resolution objectives (for example, locally steering network formation and cellular differentiation towards mechanical objectives) challenging. Holistic mathematical modelling may provide an approach to address both the non-trivial representational and process control challenges that the production of desired and designed outcomes presents. However, existing models of fungal growth are selectively delimited in scale and scope and operate under simplifying conditions of homogeneity, symmetry and reduced dimensionality. Here we present a simple multiphysics modelling approach for macroscopic mycelium growth in heterogeneous 3D environments. The mathematical model is formulated as a system of partial differential equations integrating metabolism, transport, morphogenesis and environmental dynamics within a single framework. The theoretical model is complemented by a real-time numerical solver implemented in a browser environment using the cross-platform WebGPU API for hardware acceleration. Our results demonstrate the tractability and accessibility of macroscopic simulation of organism and environment in concert for scenarios corresponding to mycelium-based ELM synthesis. This lays the basis for the simulation tool to be productively engaged in goal-oriented design and engineering activities that span from explorative and curiosity driven exploration of design outcomes, to closed-loop production, to life-cycle/career simulation within use-case scenarios.