Multifidelity Computing for Coupling Full and Reduced Order Models

Hybrid physics-machine learning models are increasingly being used in simulations of transport processes. Many complex multiphysics systems relevant to scientific and engineering applications include multiple spatiotemporal scales and comprise a multifidelity problem sharing an interface between various formulations or heterogeneous computational entities. To this end, we present a robust hybrid analysis and modeling approach combining a physics-based full order model (FOM) and a data-driven reduced order model (ROM) to form the building blocks of an integrated approach among mixed fidelity descriptions toward predictive digital twin technologies. At the interface, we introduce a long short-term memory network to bridge these high and low-fidelity models in various forms of interfacial error correction or prolongation. The proposed interface learning approaches are tested as a new way to address ROM-FOM coupling problems solving nonlinear advection-diffusion flow situations with a bifidelity setup that captures the essence of a broad class of transport processes

Multiscale modeling of granular flows with application to crowd dynamics

In this paper a new multiscale modeling technique is proposed. It relies on a recently introduced measure-theoretic approach, which allows to manage the microscopic and the macroscopic scale under a unique framework. In the resulting coupled model the two scales coexist and share information. This allows to perform numerical simulations in which the trajectories and the density of the particles affect each other. Crowd dynamics is the motivating application throughout the paper.Comment: 30 pages, 9 figure

Multiscale modeling of granular flows with application to crowd dynamics

In this paper a new multiscale modeling technique is proposed. It relies on a recently introduced measure-theoretic approach, which allows to manage the microscopic and the macroscopic scale under a unique framework. In the resulting coupled model the two scales coexist and share information. This allows to perform numerical simulations in which the trajectories and the density of the particles affect each other. Crowd dynamics is the motivating application throughout the paper.Comment: 30 pages, 9 figure

Energy-based operator splitting approach for the time discretization of coupled systems of partial and ordinary differential equations for fluid flows: The Stokes case

The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The proposed algorithm is based on a semi-discretization in time based on operator splitting, whose design is guided by the rationale of ensuring that the physical energy balance is maintained at the discrete level. As a result, unconditional stability with respect to the time step choice is ensured by the implicit treatment of interface conditions within the Stokes substeps, whereas the coupling between Stokes and ODE substeps is enforced via appropriate initial conditions for each substep. Notably, unconditional stability is attained without the need of subiterating between Stokes and ODE substeps. Stability and convergence properties of the proposed algorithm are tested on three specific examples for which analytical solutions are derived

Quasi-simultaneous coupling methods for partitioned problems in computational hemodynamics

The paper describes the numerical coupling challenges in multiphysics problems like the simulation of blood flow in compliant arteries. In addition to an iterative coupling between the fluid flow and elastic vessel walls, i.e. fluid-structure interaction, also the coupling between a detailed 3D local (arterial) flow model and a more global 0D model (representing a global circulation) is analyzed. Most of the coupling analysis is formulated in the more abstract setting of electrical-network models. Both, weak (segregated) and strong (monolithic) coupling approaches are studied, and their numerical stability limitations are discussed. Being a hybrid combination, the quasi-simultaneous coupling method, developed for partitioned problems in aerodynamics, is shown to be a robust and flexible approach for hemodynamic applications too

Hybrid Multi-Objective Optimization of Left Ventricular Assist Device Outflow Graft Anastomosis Orientation to Minimize Stroke Rate

A Left Ventricular Assist Device (LVAD) is a mechanical pump that is utilized as a bridge to transplantation for patients with a Heart Failure (HF) condition. More recently, LVADs have been also used as destination therapy and have provided an increase in the quality of life for patients with HF. However, despite improvements in VAD design and anticoagulation treatment, there remains a significant problem with VAD therapy, namely drive line infection and thromboembolic events leading to stroke. This thesis focuses on a surgical maneuver to address the second of these issues, guided by previous steady flow hemodynamic studies that have shown the potential of tailoring the VAD outflow graft (VAD-OG) implantation in providing up to 50% reduction in embolization rates. In the current study, multi-scale pulsatile hemodynamics of the VAD bed is modeled and integrated in a fully automated multi-objective shape optimization scheme in which the VAD-OG anastomosis along the Ascending Aorta (AA) is optimized to minimize the objective function which include thromboembolic events to the cerebral vessels and wall shear stress (WSS). The model is driven by a time dependent pressure and flow boundary conditions located at the boundaries of the 3D domain through a 50 degree of freedom 0D lumped parameter model (LPM). The model includes a time dependent multi-scale Computational Fluid Dynamics (CFD) analysis of a patient specific geometry. Blood rheology is modeled as using the non-Newtonian Carreua-Yasuda model, while the hemodynamics are that of a laminar and constant density fluid. The pulsatile hemodynamics are resolved using the commercial CFD solver StarCCM+ while a Lagrangian particle tracking scheme is used to track constant density particles modeling thromobi released from the cannula to determine embolization rated of thrombi. The results show that cannula anastomosis orientation plays a large role when minimizing the objective function for patient derived aortic bed geometry used in this study. The scheme determined the optimal location of the cannula is located at 5.5 cm from the aortic root, cannula angle at 90 degrees and coronal angle at 8 degrees along the AA with a peak surface average WSS of 55.97 dy/cm2 and stroke percentile of 12.51%. A Pareto front was generated showing the range of 9.7% to 44.08% for stroke and WSS of 55.97 to 81.47 dy/cm2 ranged over 22 implantation configurations for the specific case studied. These results will further assist in the treatment planning for clinicians when implementing a LVAD