- Lander Besabe, Graduate student
- Kamrun Mily, Graduate student co-advised with Dr. D. Labate
- Irina Perepelitsa, Graduate student
Research Projects
The Direct Numerical Simulation (DNS) of the Navier-Stokes equations computes the evolution of all the significant flow structures by resolving them with a properly refined mesh. Unfortunately, when the convection dominates the dynamics - as it happens in many practical applications - this requires very fine meshes, making DNS computationally unaffordable for practical purposes. In particular, we consider new and innovative applications of scientific computing in cardiovascular sciences. There is the crucial need to find a valid alternative to DNS featuring reasonable computational times without sacrificing accuracy for incompressible flow at moderate Reynolds numbers (few thousands).
More details: [1] [2] [3] [4] [5] [6] [7] [8] [9]
In order to meet the growing demand by industrial and clinical research partners for efficient computational tools that enable real-time computations, over the last decade a widespread research effort has been devoted to devise and study reduced order models and methods, which allow to obtain accurate and reliable results at greatly reduced computational costs. These methodologies are readily applied within two contexts: real-time (e.g., parameter estimation and control) and many query (e.g., design and optimization). Both contexts pose a significant, often unsurmountable, challenge to "classical" numerical techniques such as the finite element method.
More details: [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
Numerical simulations of geophysical flows are not only an essential tool for ocean and weather forecast, but they could also provide insights on the mechanisms governing climate change. When a Direct Numerical Simulation(DNS) for geophysical flows is possible, it is usually extremely expensive in terms of computational time and memory demand due to the large amount of degrees of freedom to be considered for a proper description of the flow. In addition, often long time intervals have to be simulated.
We work on: (i) Reduced Order Models (ROMs) that enable fast computations without a significant loss in terms of accuracy and (ii) Large Eddy Simulation (LES) models that allow to use coarser meshes than those required by a DNS thanks to a model for the effect of the small scales that do not get resolved.
More details: [1] [2] [3] [4] [5] [6]
Crowd dynamics
Modeling and simulation of crowd dynamics have fascinated researchers for decades. Academic studies started with empirical observations and continued with the development of models in the field of applied physics and mathematics. The simulation of pedestrian flow has attracted increasing research attention in recent years since a reliable simulation model for pedestrian flow may greatly benefit engineers in mass transportation management, and designers in urban planning and architecture. In addition, if we enrich the crowd dynamics model with the spreading of a disease (like COVID) or an emotion (like fear) we can help address questions related to public safety of crowds in confined environment (like an airport or a concert arena). We work on microscopic (individual-based) and mesoscopic (kinetic) models of crowd dynamics without and with emotional or disease contagion.
More details: [1] [2] [3] [4] [5] [6] [7] [8]
Fluid-Structure Interaction
Fluid-structure interaction (FSI) problems arise in many applications, such as aerodynamics, and biomedical engineering. In applications to hemodynamics, FSI models have been used to describe the interaction between blood and vessel walls, as well as heart valves. Since combining state-of-the-art algorithms with non-invasive clinical measurement tools provides an innovative approach to medical diagnosis and surgical decision making, there is an increasing demand for fast and efficient numerical schemes to solve FSI problems.
More details: [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
Mitral regurgitation (MR) is a valvular disease in which the mitral valve does notclose properly, thereby allowing blood to flow backward from the left ventricle to the left atrium of the heart. MR is among the most prevalent valve problems in the western world. Doppler echocardiography has recently emerged as the method of choice for the non-invasive detection and evaluation of MR severity. However, due to the various color Doppler limitations, the accurate quantification of MR remains one of the major challenges in modern echocardiography. By combining mathematical studies, computer simulations, experimental validation, and clinical experience, it is possible to provide a foundation for new clinical guidelines in echocardiographic assessment of MR.
More details: [1] [2] [3] [4] [5] [6] [7] [8] [9]