A Versatile Reduced Order Model of Urban Boundary Layer Dynamics in the Center of Paris

The computational demands of Computational Fluid Dynamics (CFD) often limit its real-time or large-scale applications, particularly in scenarios requiring multiple simulations based on varying input parameters. This study introduces a surrogate reduced order model (ROM) that not only addresses the computational challenges of CFD but also underscores its potential for broad applicability.

We focus on the dynamics of the Urban Boundary Layer (UBL), a key factor in understanding urban microclimates and their impact on energy consumption, thermal comfort, and local weather phenomena. Using a representative urban test case from the city center of Paris, we illustrate the effectiveness of our approach. During the offline phase, the ROM is constructed by assembling a database of Dynamic Mode Decomposition (DMD) modes [1] associated with various aspects of UBL dynamics, such as temperature distribution, wind patterns, and turbulence characteristics. These modes are determined based on a set of meteorological conditions defined through k-means clustering analysis. During the online phase, we interpolate these DMD modes from the database, enabling us to determine the dynamic characteristics of the UBL within the domain without initiating computationally intensive code_saturne calculations.

Our validation for the UBL dynamics in central Paris indicates that the online phase can achieve a Normalized Root Mean Square Error (NRMSE) of 2-8%. A distinctive aspect of our approach is the incorporation of DMD during the code_saturne computation process. Some modifications of DMD can be seamlessly integrated into numerous code_saturne simulations, harnessing the advantages of DMD with minimal computational trade-offs. This ROM approach offers a promising tool for urban climate studies, urban planning, and environmental management, providing a more efficient means to simulate and understand the complex dynamics of the Urban Boundary Layer.