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We present a fully-coupled, implicit-in-time framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes system that models two-phase flows. In this work, we extend the block iterative method presented in Khanwale et…
Direct Numerical Simulations (DNSs) are one of the most powerful tools for studying turbulent flows. Even if achievable Reynolds numbers are lower than those obtained with experimental means, there is a clear advantage since the entire…
The task of learning a diffusion-based neural sampler for drawing samples from an unnormalized target distribution can be viewed as a stochastic optimal control problem on path measures. However, the training of neural samplers can be…
We present direct methods and symbolic software for the computation of conservation laws of nonlinear partial differential equations (PDEs) and differential-difference equations (DDEs).The methods are applied to nonlinear PDEs in (1+1)…
Simulations of fluid flow in naturally fractured rocks have implications for several subsurface applications, including energy storage and extraction, and waste storage. We are interested in flow in discrete fracture networks, which…
The potential energy surface (PES) is crucial for interpreting a variety of chemical reaction processes. However, predicting accurate PESs with high-level electronic structure methods is a challenging task due to the high computational…
Modern laboratory techniques like ultrafast laser excitation and shock compression can bring matter into highly nonequilibrium states with complex structural transformation, metallization and dissociation dynamics. To understand and model…
Learning the fine-scale details of a coastal ocean simulation from a coarse representation is a challenging task. For real-world applications, high-resolution simulations are necessary to advance understanding of many coastal processes,…
We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…
While recent approaches, such as the macroscopic forcing method (MFM) or Green's function-based approaches, can be used to compute Reynolds-averaged Navier--Stokes closure operators using forced direct numerical simulations, MFM can also be…
Molecular dynamics (MD) simulations are a central tool in science and engineering enabling the study of dynamical behavior and the link between microscopic structure and macroscopic function. Their high computational cost, however, has…
In this report we briefly summarize the set-up and results for direct numerical simulations (DNS) of turbulent channel flows with riblets. The DNS are carried out with OpenFOAM which allows the use of an unstructured mesh. The present…
Accurately resolving the coupled momentum transfer between the liquid and solid phases of complex fluids is a fundamental problem in multiphase transport processes, such as hydraulic fracture operations. Specifically we need to characterize…
In this paper, we present linearized learning methods to accelerate the convergence of training for stationary nonlinear Navier-Stokes equations. To solve the stationary nonlinear Navier-Stokes (NS) equation, we integrate the procedure of…
In this paper we introduce the concept of Direct Statistical Simulation (DSS) for astrophysical flows. This technique may be appropriate for problems in astrophysical fluids where the instantaneous dynamics of the flows are of secondary…
This study presents the first Direct Numerical Simulation (DNS) of hydrogen combustion in a real-size internal combustion engine, investigating the complex dynamics of ignition, flame propagation, and flame-wall interaction under…
In recent years, convolutional neural networks (CNNs) have experienced an increasing interest in their ability to perform a fast approximation of effective hydrodynamic parameters in porous media research and applications. This paper…
Efficient simulation of the Navier-Stokes equations for fluid flow is a long standing problem in applied mathematics, for which state-of-the-art methods require large compute resources. In this work, we propose a data-driven approach that…
We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule…
We propose a method for the data-driven inference of temporal evolutions of physical functions with deep learning. More specifically, we target fluid flows, i.e. Navier-Stokes problems, and we propose a novel LSTM-based approach to predict…