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We present a new class of integrators for stiff PDEs. These integrators are generalizations of FLow AVeraging integratORS (FLAVORS) for stiff ODEs and SDEs introduced in [Tao, Owhadi and Marsden 2010] with the following properties: (i)…

The accuracy of a large eddy simulation (LES) is determined by the accuracy of the model used to describe the effect of unresolved scales, the numerical errors of the resolved scales, and the optimality of the length scale that separates…

We consider the numerical solution of the scattering of time-harmonic plane waves from an infinite periodic array of reflection or transmission obstacles in a homogeneous background medium, in two dimensions. Boundary integral formulations…

We introduce a new class of integrators for stiff ODEs as well as SDEs. These integrators are (i) {\it Multiscale}: they are based on flow averaging and so do not fully resolve the fast variables and have a computational cost determined by…

Approximately $75 \%$ of the raw material and $50 \%$ of the products in the chemical industry are granular materials. The Discrete Element Method (DEM) provides detailed insights of phenomena at particle scale and it is therefore often…

We study the error scaling properties of large-eddy simulation (LES) in the outer region of wall-bounded turbulence at moderately high Reynolds numbers. In order to avoid the additional complexity of wall-modeling, we perform LES of…

We investigate the performance of wall-modeled LES for external aerodynamics in the NASA Juncture Flow. We characterize the errors in the prediction of mean velocity profiles and pressure coefficient for three different locations over the…

The study presents wall-modeled large-eddy simulations (LES) characterizing the flow features of a neutral atmospheric boundary layer over two urban-like roughness geometries: an array of three-dimensional square prisms and the…

Model-free reinforcement learning attempts to find an optimal control action for an unknown dynamical system by directly searching over the parameter space of controllers. The convergence behavior and statistical properties of these…

Ordinary differential equation (ODE) based generative models have emerged as a powerful approach for producing high-quality samples in many applications. However, the ODE-based methods either suffer the discretization error of numerical…

In this paper we propose an efficient second order well balanced finite volume method for modeling complex free surface flows at the aid of a simple diffuse interface method. The employed physical model is a two-phase model derived from the…

A cell-centered implicit-explicit updated Lagrangian finite volume scheme on unstructured grids is proposed for a unified first order hyperbolic formulation of continuum fluid and solid mechanics. The scheme provably respects the stiff…

A method is proposed for accurately describing arbitrary-shaped free boundaries in single-grid finite-difference schemes for elastodynamics, in a time-domain velocity-stress framework. The basic idea is as follows: fictitious values of the…

We introduce a wall model (WM) for large-eddy simulation (LES) applicable to rough surfaces with Gaussian and non-Gaussian distributions for both transitionally and fully rough regimes. The model is applicable to arbitrary complex…

Accurately, efficiently, and stably computing complex fluid flows and their evolution near solid boundaries over long horizons remains challenging. Conventional numerical solvers require fine grids and small time steps to resolve near-wall…

We develop an enrichment wall-model within the spectral element method (SEM) framework for large-eddy simulations of wall-bounded flows. The method augments the polynomial solution in the wall-adjacent elements with an analytical…

We present a hybrid transformer architecture that replaces discrete middle layers with a continuous-depth Neural Ordinary Differential Equation (ODE) block, enabling inference-time control over generation attributes via a learned steering…

We develop a novel multi-layer predictor-feedback to achieve exact compensation of state-dependent input delay of general nonlinear integro-differential equations. The system of interest is an unconventional mixed Partial Differential…

Under a smart grid paradigm, there has been an increase in sensor installations to enhance situational awareness. The measurements from these sensors can be leveraged for real-time monitoring, control, and protection. However, these…

We present a spectral element model for general-purpose simulation of non-overturning nonlinear water waves using the incompressible Navier-Stokes equations (INSE) with a free surface. The numerical implementation of the spectral element…