Yerbol Palzhanov, Graduate student co-advised with Dr. M. Olshanskii
Qi Sun, Graduate student co-advised with Dr. M. Olshanskii
Quang Hoang, Undergraduate student co-advised with Dr. M. Olshanskii
Kaylie O'Connell, Undergraduate student co-advised with Dr. W. Ott

Research Projects

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]

Flow at moderately high Re

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]

Reduced Order Modeling

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]

Simulations for diagnosis of mitral valve regurgitation

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]