Session T08: Computational Fluid Dynamics: General III

A novel Fourier-based (pseudo)spectral framework for 1D hemodynamics and wave propagation in the entire human circulatory system

Fast and accurate numerical simulation of blood flow is necessary to study and identify important physical and physiological quantities as well as their relationships to cardiovascular functions. Comprehensive analysis requires simulating pressure and flow waves that travel, reflect and attenuate through a complex vascular network that is also coupled to organs. This work introduces a new numerical framework for modeling such wave propagation in the complete circulation, employing a (pseudo)spectral approach for resolving the reduced-order (1D) Navier-Stokes PDEs that govern the corresponding fluid-structure dynamics in each vascular segment. The solver has a number of appealing properties: it is high-order in both space and time; it faithfully preserves the diffusion/dispersion characteristics of the underlying continuous problems (errors do not compound as waves propagate through vasculature); it has mild CFL constraints on explicit time integrators; it is parallelizable; and it incorporates the nonlinear and nonstationary coupling of other cardiovascular system components (a hybrid ODE heart model). The physiological accuracy and computational performance of this framework is demonstrated by a variety of well-established benchmarks.    

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The dynamics of a particle confined to a fluid interface are strongly connected to the motion and geometry of the interface itself. In this work, a numerical framework is presented to study this connection for the case of a particle straddling a fluid interface at low Reynolds number flows. The approach utilizes a chimera (also called overset) grid in which a local body-fitted mesh attached to the particle is coupled to a fixed, global Cartesian grid covering the entire computational domain. Solutions to the governing equations are computed on each mesh independently and are then coupled via interpolation. Motion of the fluid interface is captured by the level set method and the effect of surface tension is modeled as a volumetric forcing term. The efficacy of the method is demonstrated in a series of two-dimensional simulations with an assumed constant three-phase contact angle. In particular, the effect of interfacial deformations on the drag force and torque for a particle translating between parallel plates is investigated.   

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Can deep learning or symbolic regression supplement traditional simulators in fluid dynamics?  How well do such models generalize outside of the dataset they learn from, and how well do they preserve statistical properties of the simulated fluid?  In this talk, I will present some key observations from our recent research in this area, which aims to answer these questions. I will highlight our new method: "Disentangled Sparsity Networks," which allow one to interpret the internals of a neural network trained on fluids simulation. Not only does this give us a way of interrogating how the deep learning model is making predictions, but it also allows one to replace the learned model with a symbolic expression and embed that model inside a traditional solver. We show that this technique can improve the applicability of symbolic regression to high-dimensional datasets, such as those in fluid dynamics, without imposing priors on the recovered symbolic equation.   

Physics-Informed PointNet: A Deep Learning Strategy for Solving Nonlinear PDEs on Unseen Irregular Geometries

Physics Informed Neural Network (PINN) is a semi-supervised deep learning methodology for solving partial differential equations (PDEs) governing physical phenomena. In PINNs, instead of using labeled data for training, the physics is incorporated in the loss function as the mean squared residuals of the governing PDEs and the associated boundary conditions. However, current versions of PINNs are restricted to a fixed geometry that was used in the training, requiring retraining of the network for any new geometry. Thus, the goal of using deep learning for accelerating geometric optimization in industrial designs is currently unreachable through PINNs. To obviate this limitation, we introduce a Physics Informed PointNet (PIPN) framework. PIPN, once trained, can predict the solution of PDEs of interest not only without labeled data but also on an unseen set of irregular geometries. As a test case, we consider PDEs of conservation of mass, momentum, and energy for incompressible flow with two specific examples: the method of manufactured solution in nontrivial geometries; and natural convection in a square enclosure with a cylinder with various shapes for its cross section. A study of prediction accuracy and obtained speedup factor compared to regular CFD solvers is presented.   

A Study of Microgravity on Fluid Instabilities in Microfluidic domain

Computational fluid dynamics (CFD) analysis is applied to increase the understanding of gravity on fluid instability phenomenon. The effort specifically studies viscous fingering patterns in a microfluidic device. In addition, the effort aims to support microgravity experiments that will utilize imagery using a lens free imaging (LFI) system to capture the data. The purpose of the study is to provide preliminary data using CFD analysis software STAR-CCM+ to predict how a suborbital flight experiment using microfluidic flow will transpire. Lab experiments were conducted to observe Saffman-Taylor or viscous fingering instability in microfluidic devices using liquids that include water, ethanol, and corn syrup. A study was done to quantify the viscous finger length and width with respect to the microfluidic device chamber size. The results show a correlation between viscous finger patterns and the device geometry.  A second study was done to analyze the effects of gravity and microgravity on the viscous fingering phenomenon. Microgravity is simulated using CFD to refine the experiments a priori the suborbital flight later. This study shows the effects of the force of gravity may have on viscous finger patterns. The comparison of the data captured in the lab and suborbital flight experiment to the CFD results provide further insight into the accuracy of the CFD modeling with respect to microfluidics behavior in microgravity.   

Variational quantum algorithm towards quantum computing for fluid mechanics

Quantum computation has shown a fast development trend in the past few years.  The quantum devices, superposition state, and the representability of the Hilbert space span by the quantum vectors show great potentials for achieving exponential speedup over classical computers, which have stimulated great interests in quantum computing in many fields, such as communication, finance, and life sciences.  The study of quantum algorithms for fluid mechanics problems is still at an infancy stage.  Here we present a variational quantum algorithm for solving key building blocks of the Navier-Stokes equations.  Using a parameterized quantum circuit, solutions can be obtained through a training process.  Using numerical experiments, we compare the computational cost of the algorithm with the previous methods and the results indicate that a significant speedup is possible.   

Large-eddy simulation of dominant wind and contaminate transport in New York City

The danger of pollutants, biological agents and poisonous chemicals released in urban locations has become a major concern for public safety. While past studies have investigated contaminant transport in small city sections, this research seeks to address the transport of a point-source pollutant in a 3 km-long and highly-populated area of the Lower Manhattan. The study area includes southern Manhattan from the southern tip north all the way to Canal St. A computational grid system with approximately 76 million grid points is used to resolve the flow while the immersed boundary method is employed to resolve the geometry of the buildings, roads, and other objects including many skyscrapers of varying heights. The large-eddy simulation method is used to resolve the wind flow within the urban area. A Eulerian transport model is coupled with LES to compute the concentration field of the pollutant. We found that the pollutant propagates downwind at 42% of the prevailing wind velocity of 3.6 m/s. Once the pollutant source is removed, the pollutant plume propagates out of the study area at 20% of the prevailing wind velocity.   

Two-compartment modeling of a hospital isolation room informed by CFD

Computational fluid dynamics (CFD) will be used to inform a lower order modeling approach, namely the well-known box or compartment models of indoor air quality, to obtain rapid and accurate prediction of aerosol concentrations in isolation rooms. Compartment modeling of pollutants (including infectious aerosols) in ventilated spaces has a rich history in the occupational hygiene community and, to the knowledge of the authors, this marks the first time it will be informed through CFD. The isolation room will be represented by two compartments, an inner and an outer compartment, with each compartment assumed to be perfectly mixed, but with different aerosol concentrations. In this model, the patient (or source of aerosols) occupies the inner or sub-compartment located within the parent compartment, the latter corresponding to the isolation room. Compartment model equations consist of initial value, coupled linear ordinary differential equations describing aerosol mass balance for each compartment. Parameters in the model equations associated with short-circuiting intensity (between the inner compartment and the air exhaust vent in the outer compartment) and flow exchange between the two compartments will be calibrated via the CFD.   

Temporal accuracy of FastRK3

FastRK3 is an explicit, three-stage, third-order Runge-Kutta (RK3) based projection-method which requires solving the Poisson equation for pressure only once per time step versus three times of standard RK3 methodology (Aithal & Ferrante, J. Comp. Phys., 2020). The present work is focused on the temporal accuracy of FastRK3 in comparison with the underlying standard RK3 methodology. We derive theoretically and show numerically that, for free-shear flows, FastRK3 is third-order and second-order accurate in time for velocity and pressure, respectively, when the RK3 coefficients and the pressure extrapolation scheme satisfy specific conditions herein derived. For wall-bounded flows, specifically the lid-driven polar cavity, we show numerically that the temporal accuracy of velocity and pressure is second-order for both FastRK3 and standard RK3. In summary, we derive theoretically and verify numerically the conditions that the RK3 coefficients and the pressure extrapolation scheme need to satisfy in order for FastRK3 to preserve the temporal accuracy of the underlying RK3 methodology.   

Analysis of downscaled branches and Receptive field on a CNN-based incompressible solver

Convolutional Neural Networks (CNN) are widely used in the CFD community due to their fast predictions and capabilities to extract topological information from fluid flows. While standalone CNNs have been extensively studied, their coupling with a CFD solver still remains unclear, in particular for time-evolving problems. This work focuses on a CNN embedded into an incompressible solver. The neural network solves the Poisson equation, necessary to update the velocity field provided by the resolution of the advection equation. Several U-Net architectures, parametrized by their number of downscaled branches (DBs) and receptive field (RF), are evaluated on the Von Karman oscillations generated by a 2D cylinder at low Reynolds numbers. Results are compared with other standard Poisson and CFD solvers, revealing that the Von Karman oscillations can be reproduced accurately using the CNN-based solver with fast inference time. To further analyze the error, Dynamic Mode Decomposition (DMD) is applied on the solutions, revealing the key effects of both DBs and RF on the modes accuracy, shedding new light on the behavior and limitations of CNN when interacting with CFD solvers.   

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Recent advancements in artificial intelligence have generated a lot of interest in the area of machine learning (ML) for fluid dynamics. This is important, especially for time-sensitive industrial applications, since it can provide a more efficient way of running CFD simulations, for instance, for design optimization that is inherently computationally demanding.

One class of ML algorithms commonly applied to fluid dynamics problems is the convolutional neural network (CNN). Although several different architectures of this type of neural network have been applied to fluid dynamics problems, they all rely on the basic convolutional operation. Reliance on the convolutional operation assumes that the flow domain has to be discretized using a Cartesian grid and the most common geometric representation uses the signed distance field. While this representation might be sufficient for simple problems; in situations where the geometry changes, for instance in design optimization studies, it is important to have geometric representations that can better capture the subtle differences in design options.

In this work we propose a new approach, taking into account geometric features, for representing the geometry used in CNNs applied for flow field predictions in fluid dynamics problems.   

A multigrid solver for the coupled pressure-temperature equations in an all-Mach solver with VoF

We present a generalisation of the all-Mach solver in Fuster & Popinet (2018) to account for heat diffusion between two different compressible phases. By solving a two-way coupled system of equations for pressure and temperature using a multigrid solver, the current code is shown to increase the robustness and accuracy of the solver with respect to classical explicit discretization schemes. Different test cases are proposed to validate the correct implementation of the thermal effects: an Epstein-Plesset like problem for temperature is shown to compare well with a spectral method solution. The code also reproduces free small amplitude oscillations where analytical solutions showing the transition between isothermal and adiabatic regimes are available. In addition, we show results of a single sonoluminescent bubble (SBSL) in standing waves, where the result of the DNS is compared with that of other methods in the literature. Finally, the collapse of a bubble near a rigid boundary is studied reporting the change of heat flux as a function of the stand-off distance.