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Summary We introduce an immersed high‐order discontinuous Galerkin method for solving the compressible Navier‐Stokes equations on non–boundary‐fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are advanced in time with an explicit time marching scheme. The discretisation meshes may contain simplicial (triangular or tetrahedral) elements of different sizes and need not be structured. On the discretisation mesh, the fluid domain boundary is represented with an implicit signed distance function. The cut‐elements partially covered by the solid domain are integrated after tessellation with the marching triangle or tetrahedra algorithms. Two alternative techniques are introduced to overcome the excessive stable time step restrictions imposed by cut‐elements. In the first approach, the cut‐basis functions are replaced with the extrapolated basis functions from the nearest largest element. In the second approach, the cut‐basis functions are simply scaled proportionally to the fraction of the cut‐element covered by the solid. To achieve high‐order accuracy, additional nodes are introduced on the element faces abutting the solid boundary. Subsequently, the faces are curved by projecting the introduced nodes to the boundary. The proposed approach is verified and validated with several two‐ and three‐dimensional subsonic and hypersonic low Reynolds number flow applications, including the flow over a cylinder, a space capsule, and an aerospace vehicle.

The monitoring of infrastructure assets using sensor networks is becoming increasingly prevalent. A digital twin in the form of a finite element (FE) model, as commonly used in design and construction, can help make sense of the copious amount of collected sensor data. This paper demonstrates the application of the statistical finite element method (statFEM), which provides a principled means of synthesizing data and physics-based models, in developing a digital twin of a self-sensing structure. As a case study, an instrumented steel railway bridge of $ 27.34\hskip1.5pt \mathrm{m} $ length located along the West Coast Mainline near Staffordshire in the UK is considered. Using strain data captured from fiber Bragg grating sensors at 108 locations along the bridge superstructure, statFEM can predict the “true” system response while taking into account the uncertainties in sensor readings, applied loading, and FE model misspecification errors. Longitudinal strain distributions along the two main I-beams are both measured and modeled during the passage of a passenger train. The statFEM digital twin is able to generate reasonable strain distribution predictions at locations where no measurement data are available, including at several points along the main I-beams and on structural elements on which sensors are not even installed. The implications for long-term structural health monitoring and assessment include optimization of sensor placement and performing more reliable what-if analyses at locations and under loading scenarios for which no measurement data are available.