Non-intrusive data-driven ROM framework for hemodynamics problems

Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PED) by properly combining the high-fidelity solutions of the problem obtained for several configurations, i.e. for several properly chosen values of the physical/geometrical parameters characterizing the problem. By starting from a database of high-fidelity solutions related to a certain values of the parameters, we apply the proper orthogonal decomposition with interpolation (PODI) and then reconstruct the variables of interest for new values of the parameters, i.e. different values from the ones included in the database. Furthermore, we present a preliminary web application through which one can run the ROM with a very user-friendly approach, without the need of having expertise in the numerical analysis and scientific computing field. The case study we have chosen to test the efficiency of our algorithm is represented by the aortic blood flow pattern in presence of a left ventricular (LVAD) assist device when varying the pump flow rate.