Bulletin of the American Physical Society
77th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 24–26, 2024; Salt Lake City, Utah
Session ZC13: CFD: Algorithms II |
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Chair: Gretar Tryggvason, Johns Hopkins University Room: 155 C |
Tuesday, November 26, 2024 12:50PM - 1:03PM |
ZC13.00001: Preconditioned Adjoint Data-Assimilation for Two-dimensional Decaying Isotropic Turbulence Carol Klingler, Qi Wang The inverse problem of reconstructing the history of flow from sparse measurements using the Navier-Stokes equations is formulated as a constrained cost minimization, where the cost function is defined as the mismatch between the true and modeled measurements. The adjoint fields assist in efficiently evaluating the gradient of the cost function with respect to the initial condition of the flow evolution. Our previous studies indicate that the adjoint fields grow exponentially in backward time and favor small-scale structures in the initial condition, complicating adjoint-based data assimilation. To achieve favorable reconstruction quality across scales, the optimization process is preconditioned by modifying the inner product definition for the forward-adjoint duality relation with a weighting kernel in Fourier space. We demonstrate that this approach of preconditioning resembles the adjoint of large-eddy simulations, with the flexibility to adjust the filter as needed. We focus on two-dimensional decaying isotropic turbulence within a periodic domain and perform data assimilation using a discrete adjoint solver. The results with different preconditioned adjoint solvers are discussed and compared, highlighting the potential of preconditioned adjoint in data assimilation techniques. |
Tuesday, November 26, 2024 1:03PM - 1:16PM |
ZC13.00002: Enabling Large-Scale Simulations of Flows Driven by Atomistic Effects Tim Linke, Dane M Sterbentz, Jean-Pierre Delplanque, Jonathan L Belof Hydrodynamic flows can be strongly influenced by molecular effects. Nonequilibrium behavior encountered in phase transitions, chemical reactions and diffusion processes fundamentally alter the fluid, thereby affecting the flow field. In particular, capturing an accurate flow field response in high-energy-density applications, such as inertial confinement fusion experiments, presents several major challenges. Significant advances in modeling these extreme conditions are achieved by coupling macroscopic solvers with atomistic simulations, such as molecular dynamics. However, the practicality of this approach is limited by the high computational costs of concurrently running molecular models with the flow solver. We present a strategy that allows continuum-atomistic frameworks to extend far into macroscopic length and time scales. By leveraging exascale computing architectures to optimize the balance between performance and accuracy, we achieve large-scale simulations. This contributes substantially to the effort of gaining first-principle insight into the material behavior of hydrodynamic models. |
Tuesday, November 26, 2024 1:16PM - 1:29PM |
ZC13.00003: Fredholm Integral Equations Neural Operator (FIE-NO) for Data-Driven Boundary Value Problems Haoyang Jiang, Yongzhi Qu In this paper, we present a novel Fredholm Integral Equations Neural Operator (FIE-NO) method, an integration of Random Fourier Features (RFF) and Fredholm Integral Equations (FIE) into the deep learning framework, tailored for solving data-driven Boundary Value Problems (BVPs) with a particular focus on challenges posed by irregular boundaries. Unlike traditional computational approaches that struggle with the computational intensity and complexity of such problems, our method offers a robust, efficient, and accurate solution mechanism. By harnessing the power of physics-guided operator learning, FIE-NO demonstrates superior performance in addressing BVPs. Notably, our approach is designed to generalize across multiple scenarios, including those with unknown equation forms and intricate boundary shapes, after being trained on a singular boundary condition type. Experimental validation demonstrates that the FIE-NO method performs well in various fluid mechanics scenarios. Utilizing the Darcy flow equation and typical PDEs such as the Laplace and Helmholtz equations, the method exhibits robust performance across different boundary conditions. Experimental results indicate that FIE-NO achieves higher accuracy and stability compared to other methods when addressing complex boundary value problems with varying numbers of interior points. |
Tuesday, November 26, 2024 1:29PM - 1:42PM |
ZC13.00004: A reconstruction based exponentially accurate spectral method to solve Elliptic Partial Differential Equations with discontinuous coefficients and complex shaped interfaces Sandeep Saha, Aman K Singh, Sudipta Ray Elliptic Partial Differential Equations (EPDE) with discontinuous coefficients are essential for modelling physical phenomena in media with varying material properties across sharp interfaces with complex geometry. The well-known exponential convergence of spectral methods for differential equations, reduces to algebraic convergence due to the Gibbs-Wilbraham phenomenon due to the discontinuity, thus limiting their application to EPDEs. To overcome Gibbs-Wilbraham phenomenon we propose a reconstruction technique that decomposes the solution into a C∞ smooth function and a modified Heaviside function, where a C∞ correction function modifies the Heaviside step function. In our previous work we proposed a weak formulation for the correction function. We now propose a novel strong form approach where the correction function is obtained by solving the Cauchy problem spanning over sub-domains separated by the interface and imposing conditions on the interface. The smooth function, is also obtained from the solution of the EPDE without the interface. We showcase exponential accuracy while resolving discontinuities at a sharp interfaces using the Helmholtz and Poisson equations for two- and three-dimensional problems, from acoustics and fluid dynamics. |
Tuesday, November 26, 2024 1:42PM - 1:55PM |
ZC13.00005: Improving the performance of regularized Stokeslet simulations using linearly implicit integrators Moslem Uddin, Lisa J Fauci, Ricardo Cortez, Tommaso Buvoli Using the test problem of a flexible, undulating filament in a viscous fluid, we explore the computational performance of different time integrators in regularized Stokeslet simulations. While explicit integrators are commonly used, stability considerations require prohibitively small time steps. While fully implicit methods have no such restrictions, these require the solution of nonlinear equations at each time step. To address these difficulties, here we consider both Rosenbrock and Implicit-Explicit (IMEX) methods, which are linearly implicit integrators. Using these methods, we have achieved approximately 50 times speedup in simulation timings compared to explicit methods. We will discuss these successes, as well as challenges and directions of further improvements. |
Tuesday, November 26, 2024 1:55PM - 2:08PM |
ZC13.00006: A high-order structured multiblock solver exploiting task-parallelism for compressible multiphase flows Alboreno Voci, Mario Di Renzo, Henry Collis, Sanjiva K Lele, Gianluca Iaccarino The solver combines curvilinear coordinates and multiple rectangular blocks, thus maintaining the advantage of structured solvers while not being limited to simulations of simplistic geometries. The solver uses a high order finite difference scheme, which is hybridized with more dissipative schemes close to physical or mesh discontinuities. It builds on top of the HTR solver [Di Renzo et al., Comp. Phys. Comm. 2020], which uses Legion as a runtime for task scheduling and resource utilization. Different from a classic MPI approach, the solver uses Legion's own data structures combined with task requirements to become self-aware of the data communication and synchronization when run in distributed memory. This automation is shown in this work to provide an explicit advantage in the curvilinear multiblock solver, where memory access patterns are often non-trivial and involve geometrical transformations. Such cases arise sometimes when the blocks are (in the physical domain) skewed/rotated to obtain a better mesh quality, leading to the formation of polyjunctions (grid singularities). At those locations, it can be shown that the geometric conservation laws do not hold, hence significant errors causing simulation failure are encountered. Two approaches to accounting for the grid singularities are presented in this work. These are tested against a suite of problems designed to stress each capability of the solver, including accuracy, compressibility, multispecies reacting flows and multiphase flows. |
Tuesday, November 26, 2024 2:08PM - 2:21PM |
ZC13.00007: A Lattice Boltzmann method for two-phase flows on adaptive Cartesian grids Julian Vorspohl, Matthias Meinke, Wolfgang Schröder We present a numerical scheme, which is capable of predicting liquid-gas multiphase flows on adaptive Cartesian grids. Each of the two fluid phases is modeled by a separate solver using a Lattice Boltzmann Method (LBM) such that density and viscosity can be controlled independently, and high density and viscosity ratios can be achieved. To capture the motion of the liquid-gas interface, a level-set method is used, which is advected by the local fluid velocity. It is used to impose the boundary conditions in the phase boundary cells by evaluating the boundary normal and curvature, e.g., for the determination of the surface tension. The stress tensor on both sides of the interface is evaluated to obtain a correction term for the bounce back boundary condition such that the kinematic coupling condition and the jump condition for the pressure is fulfilled. All solvers, i.e., the LBM solvers for the liquid and gas phase, and the level set solver, operate on a joint hierarchical Cartesian grid, which facilitates an efficient parallelization and enables adaptive mesh refinement with a dynamic load balancing. The presented method is validated by generic test cases for two-phase bubble flows. Details of the numerical method, results of the validation, and its application to the analysis of multiphase flow problems will be presented. |
Tuesday, November 26, 2024 2:21PM - 2:34PM |
ZC13.00008: ABSTRACT WITHDRAWN
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Tuesday, November 26, 2024 2:34PM - 2:47PM |
ZC13.00009: Generalized aliasing in large data-sets: Lessons from pseudo-spectral methods Jared P Whitehead, Gus L.W. Hart, Mark K Transtrum, Tyler Jarvis Effects of aliasing are commonly seen in signals processing and direct numerical simulations of fluid dynamics, particularly for pseudo-spectral methods. These aliasing effects have been well studied and are accounted for in most high level simulations. The advent of 'artificial intelligence' and massive data sets in recent years has led to the breakdown of the traidtional bias-vairance tradeoff commonly used in statistics to explain the so-called 'sweet-spot' necessary to achieve the best model fit to known data. This tradeoff fails to explain the success of deep neural networks and other recent advances where the 'sweet-spot' in interpolation space yields far more erros than an over-parameterized fit does. |
Tuesday, November 26, 2024 2:47PM - 3:00PM |
ZC13.00010: An Adjoint-Based Data Assimilation Algorithm using the Hybridizable Discontinuous Galerkin Framework Gao Jun Wu, Sreevatsa Anantharamu, Krishnan Mahesh CFD and experiments are often used as separate lenses to study the same flow physics. Data assimilation integrates both views by finding a solution to the modeled equations that best fits the measurements. This work presents an adjoint-based data assimilation algorithm for flows governed by the incompressible Navier-Stokes (N-S) equations, aiming to minimize discrepancies between simulations and experiments due to uncertainties in the initial and boundary conditions. |
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