This paper is concerned with the development of a hybrid data-driven technique for unsteady fluid-structure interaction systems. The proposed data-driven technique combines the deep learning framework with a projection-based low-order modeling. While the deep learning provides low-dimensional approximations from datasets arising from black-box solvers, the projection-based model constructs the low-dimensional approximations by projecting the original high-dimensional model onto a low-dimensional subspace. Of particular interest of this paper is to predict the long time series of unsteady flow fields of a freely vibrating bluff-body subjected to wake-body synchronization. We consider convolutional neural networks (CNN) for the learning dynamics of wake-body interaction, which assemble layers of linear convolutions with nonlinear activations to automatically extract the low-dimensional flow features. Using the high-fidelity time series data from the stabilized finite element Navier-Stokes solver, we first project the dataset to a low-dimensional subspace by proper orthogonal decomposition (POD) technique. The time-dependent coefficients of the POD subspace are mapped to the flow field via a CNN with nonlinear rectification, and the CNN is iteratively trained using the stochastic gradient descent method to predict the POD time coefficient when a new flow field is fed to it. The time-averaged flow field, the POD basis vectors, and the trained CNN are used to predict the long time series of the flow fields and the flow predictions are quantitatively assessed with the full-order (high-dimensional) simulation data. The proposed POD-CNN model based on the data-driven approximation has a remarkable accuracy in the entire fluid domain including the highly nonlinear near wake region behind a freely vibrating bluff body.
In this paper, we propose a hybrid lattice Boltzmann method (HLBM) for solving fluid-structure interaction problems. The proposed numerical approach is applied to model the flow induced by a vibrating thin lamina submerged in a viscous quiescent fluid. The hydrodynamic force exerted by the fluid on the solid body is described by means of a complex hydrodynamic function, whose real and imaginary parts are determined via parametric analysis. Numerical results are validated by comparison with those from other numerical as well as experimental works available in the literature. The proposed hybrid…
An existing hybrid MPI-OpenMP scheme is augmented with a CUDA-based fine grain parallelization approach for multidimensional distributed Fourier transforms, in a well-characterized pseudospectral fluid turbulence code. Basics of the hybrid scheme are reviewed, and heuristics provided to show a potential benefit of the CUDA implementation. The method draws heavily on the CUDA runtime library to handle memory management, and on the cuFFT library for computing local FFTs. The manner in which the interfaces are constructed to these libraries, and ISO bindings utilized to facilitate platform portab…
We simulate the two-dimensional fluid flow around National Advisory Committee for Aeronautics (NACA) 0012 airfoil using a hybrid lattice Boltzmann method (HLBM), which combines the standard lattice Boltzmann method with an unstructured finite-volume formulation. The aim of the study is to assess the numerical performances and the robustness of the computational method. To this purpose, after providing a convergence study to estimate the overall accuracy of the method, we analyze the numerical solution for different values of the angle of attack at a Reynolds number equal to $10^3$. Subsequentl…
We present a novel partitioned iterative formulation for modeling of fluid-structure interaction in two-phase flows. The variational formulation consists of a stable and robust integration of three blocks of differential equations, viz., incompressible viscous fluid, a rigid or flexible structure and two-phase indicator field. The fluid-fluid interface between the two phases, which may have high density and viscosity ratios, is evolved by solving the conservative phase-field Allen-Cahn equation in the arbitrary Lagrangian-Eulerian coordinates. While the Navier-Stokes equations are solved by a …
We propose a hybrid moment method for the multi-scale kinetic equations in the framework of the regularized moment method [7]. In this method, the fourth order moment system is chosen as the governing equations in the fluid region. When transiting from the fluid regime to the kinetic regime, the maximum entropy principle is adopted to reconstruct the kinetic distribution function, so that the information in the fluid region can be utilized thoroughly. Moreover, only one uniform set of numerical scheme is needed for both the fluid and kinetic regions. Numerical tests show the high efficiency of…
We present a particle method for estimating the curvature of interfaces in volume-of-fluid simulations of multiphase flows. The method is well suited for under-resolved interfaces, and it is shown to be more accurate than the parabolic fitting that is employed in such cases. The curvature is computed from the equilibrium positions of particles constrained to circular arcs and attracted to the interface. The proposed particle method is combined with the method of height functions at higher resolutions, and it is shown to outperform the current combinations of height functions and parabolic fitt…
We present a new hybrid algorithm implemented in the code CHIEF (Code Hybrid with Inertial Electron Fluid) for simulations of electron-ion plasmas. The algorithm treats the ions kinetically, modeled by the Particle-in-Cell (PiC) method, and electrons as an inertial fluid, modeled by electron fluid equations without any of the approximations used in most of the other hybrid codes with an inertial electron fluid. This kind of code is appropriate to model a large variety of quasineutral plasma phenomena where the electron inertia and/or ion kinetic effects are relevant. We present here the govern…
In this paper, we develop a simplified hybrid weighted essentially non-oscillatory (WENO) method combined with the modified ghost fluid method (MGFM) [28] to simulate the compressible two-medium flow problems. The MGFM can turn the two-medium flow problems into two single-medium cases by defining the ghost fluids status in terms of the predicted the interface status, which makes the material interface "invisible". For the single medium flow case, we adapt between the linear upwind scheme and the WENO scheme automatically by identifying the regions of the extreme points for the reconstruction p…
Solving complex fluid-structure interaction (FSI) problems, which are described by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics based solvers are inadequate to handle the increasing demand for large-scale and long-period simulations. The ever-increasing availability of data and rapid advancement in deep learning (DL) have opened new avenues to tackle these challenges through data-enabled modeling. The seamless integration of DL and classic numerical techniques through the differentiable program…
The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. Here, a novel, implicit, particle-in-cell based scheme for the hybrid model is derived for multi-dimensional electromagnetic problems with multiple ion species, which features global mass, momentum and energy conservation. The scheme includes sub-cycling and orbit averaging of the ions, with cell-centered finite differences and implicit midpoint time advance. To reduce discrete particle noise, the scheme allo…
In this paper, we describe a soil-fluid-structure interaction model that combines soil mechanics (saturated sediments), fluid mechanics (seawater or air), and solid mechanics (structures). The formulation combines the Material Point Method, which models large deformation of the porous media and the structure, with the Implicit Continuous-fluid Eulerian, which models complex fluid flows. We validate the model and simulate the whole process of earthquake-induced submarine landslides. We show that this model captures complex interactions between saturated sediment, seawater, and structure, so we …
We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. We interchangeably use particle and grid representations of transported quantities to balance efficiency and accuracy. A novel Backward Semi-Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of Burgers' equation. We solve this equation using Newton's method enabled by $C^1$ continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection t…
The hybrid kinetic-ion fluid-electron plasma model is widely used to study challenging multi-scale problems in space and laboratory plasma physics. Here, a novel conservative scheme for this model employing implicit particle-in-cell techniques is extended to arbitrary coordinate systems via curvilinear maps from logical to physical space. The scheme features a fully non-linear electromagnetic formulation with a multi-rate time advance - including sub-cycling and orbit-averaging for the kinetic ions. By careful choice of compatible particle-based kinetic-ion and mesh-based fluid-electron discre…
This paper describes a new code for simulating astrophysical plasmas that solves a hybrid model composed of gyrokinetic ions (GKI) and an isothermal electron fluid (ITEF) [A. Schekochihin et al., Astrophys. J. Suppl. \textbf{182}, 310 (2009)]. This model captures ion kinetic effects that are important near the ion gyro-radius scale while electron kinetic effects are ordered out by an electron-ion mass ratio expansion. The code is developed by incorporating the ITEF approximation into {\tt AstroGK}, an Eulerian $δf$ gyrokinetics code specialized to a slab geometry [R. Numata et al., J. Compute.…
A hybrid kinetic-fluid model is used to study ionization waves (striations) in a low-current plasma column of DC discharges in noble gases. Coupled solutions of a kinetic equation for electrons, a drift-diffusion equation of ions, and a Poisson equation for the electric field are obtained to clarify the nature of plasma stratification in the positive column and near-electrode effects. A simplified two-level excitation-ionization model is used for the conditions when the nonlinear effects due to stepwise ionization, gas heating, and Coulomb interactions among electrons are negligible. It is con…
The quasi-neutral hybrid particle-in-cell algorithm with kinetic ions and fluid electrons is a popular model to study multi-scale problems in laboratory, space, and astrophysical plasmas. Here, it is shown that the treatment of ions as finite-size particles and electrons as a grid-based fluid can cause significant numerical wave dispersion errors in the magnetohydrodynamic limit ($kd_i \ll 1$, where $d_i$ is the ion skin-depth). Practical requirements on the mesh spacing $Δx/d_i$ are suggested to bound these errors from above.
