Abstract: Discrete exterior calculus (DEC) is an important class of structure-preserving (mimetic, compatible) discretization method, with discrete analogues of key properties of the continuous exterior calculus such as the exact sequence property, integration by parts and the Hodge decomposition. This permits the design of numerical models with discrete analogues of fundamental physical properties such as conservation laws and involution constraints, along with strong guarantees on numerical stability. Additionally, unlike other SP discretizations such as finite element exterior calculus, it allows the representation of both straight and twisted differential forms. These are needed for certain physical theories, such as electrodynamics. However, conventional DEC is restricted to the case of scalar-valued differential forms (SVDFs). In this talk I will discuss an extension of DEC to the case of (vector) bundle-valued differential forms (BVDFs) in R^3, and demonstrate it's utility in designing a structure-preserving numerical model for compressible flow. If time permits, I will also discuss ideas towards extending DEC to BVDFs on arbitrary manifolds.