Physical units in UFL

The Unified Form Language (UFL) is a domain-specific language designed for finite element discretisation of partial differential equations (PDEs). However, UFL does not natively support the representation of physical units, which can lead to inconsistencies when formulating PDEs involving different physical quantities. In this work, we introduce a framework to manage physical units in UFL expressions through two key steps: (1) units transformation and (2) homogeneous factorisation. During the transformation step, dimensional quantities are incorporated into existing UFL expressions. These quantities are derived from the physical unit system provided by SymPy. The subsequent factorisation step enables the extraction of dimensional quantities from homogeneous expressions. This framework offers multiple levels of consistency checks, including dimensional consistency, unit consistency, and scaling consistency. It can be used to validate existing UFL codes, analyse the scaling of terms in PDEs, and derive dimensionless numbers, providing valuable insights and reducing potential model flaws. This functionality is implemented in the dolfiny framework.