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We introduce a residual-based stabilized formulation for incompressible Navier-Stokes flow that maintains discrete (and, for divergence-conforming methods, strong) mass conservation for inf-sup stable spaces with $H^1$-conforming pressure…
In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with…
Simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment related activities. The numerical simulators used for modeling such processes rely on spatial and temporal…
We present results of direct numerical simulation of incompressible fluid flow over a thick bed of mobile, spherically-shaped particles. The algorithm is based upon the immersed boundary technique for fluid-solid coupling and uses a…
Nonlinear electromagnetic (EM) inverse scattering is a quantitative and super-resolution imaging technique, in which more realistic interactions between the internal structure of scene and EM wavefield are taken into account in the imaging…
We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…
Magnetic soft continuum robots (MSCRs) have emerged as a promising technology for minimally invasive interventions, offering enhanced dexterity and remote-controlled navigation in confined lumens. Unlike conventional guidewires with…
We present a general procedure to introduce electronic polarization into classical Molecular Dynamics (MD) force-fields using a Neural Network (NN) model. We apply this framework to the simulation of a solid-liquid interface where the…
We report on simulations of two-phase flows with deforming interfaces at various density contrasts by solving thermodynamically consistent Cahn-Hilliard Navier-Stokes equations. An (essentially) unconditionally energy-stable…
We describe tests validating progress made toward acceleration and automation of hydrodynamic codes in the regime of developed turbulence by three Deep Learning (DL) Neural Network (NN) schemes trained on Direct Numerical Simulations of…
Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of science and engineering, but their numerical solvers often…
Modeling hysteretic switching dynamics in memristive devices is computationally demanding due to coupled ionic and electronic transport processes. This challenge is particularly relevant for emerging two-dimensional (2D) devices, which…
Finite element modeling of charged species transport has enabled analysis, design, and optimization of a diverse array of electrochemical and electrokinetic devices. These systems are represented by the Poisson-Nernst-Planck equations…
We investigate the large-scale influence of numerical noises as tiny artificial stochastic disturbances on a sustained turbulence. Using the two-dimensional (2D) turbulent Rayleigh-B\'enard (RB) convection as an example, we numerically…
The provision of reliable connectivity is envisioned as a key enabler for future autonomous driving. Anticipatory communication techniques have been proposed for proactively considering the properties of the highly dynamic radio channel…
Variational multiscale (VMS) methods offer a robust framework for handling under-resolved flow scales without resorting to problem-specific turbulence models. Here, we propose and assess a dynamic, term-by-term VMS stabilized formulation…
The Direct Simulation Monte Carlo (DSMC) method is the gold standard for non-equilibrium rarefied gas dynamics, yet its computational cost can be prohibitive, especially for near-continuum regimes and high-fidelity \emph{ab initio}…
In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…
To fully evaluate a turbulent flow, Direct Numerical Simulation (DNS) is the most accurate method by far and requires considerable computational power and time; not optimum for industry standards. Developing an alternative model, providing…
The deep neural network multigrid solver (DNN-MG) combines a coarse-grid finite element simulation with a deep neural network that corrects the solution on finer grid levels, thereby improving the computational efficiency. In this work, we…