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In this work we design and analyse a Discrete de Rham (DDR) method for the incompressible Navier-Stokes equations. Our focus is, more specifically, on the SDDR variant, where a reduction in the number of unknowns is obtained using…

A recently developed Eulerian finite element method is applied to solve advection-diffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, finite element methods tend to be unstable unless…

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…

We analyze the mixed frame equations of radiation hydrodynamics under the approximations of flux-limited diffusion and a thermal radiation field, and derive the minimal set of evolution equations that includes all terms that are of leading…

This paper introduces the Asymptotic-Preserving Random Feature Method (APRFM) for the efficient resolution of multiscale radiative transfer equations. The APRFM effectively addresses the challenges posed by stiffness and multiscale…

The emergence of diffusion models has significantly advanced generative AI, improving the quality, realism, and creativity of image and video generation. Among them, Stable Diffusion (StableDiff) stands out as a key model for text-to-image…

In order to better understand micromechanical phenomena such as viscoelasticity and plasticity, the thermomechanical viewpoint is of prime importance but requires calorimetric measurements to be performed during a deformation process.…

This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…

We introduce a new regularization of the rotational Navier-Stokes equations that we call the Rotational Approximate Deconvolution Model (RADM). We generalize the deconvolution type model, studied by Berselli and Lewandowski [5], to the RADM…

We consider a stabilization method for divergence-conforming B-spline discretizations of the incompressible Navier--Stokes problem wherein jumps in high-order normal derivatives of the velocity field are penalized across interior mesh…

State-of-the-art atmospheric turbulence image restoration methods utilize standard image processing tools such as optical flow, lucky region and blind deconvolution to restore the images. While promising results have been reported over the…

Even though substantial progress has been made in the numerical approximation of convection-dominated problems, its major challenges remain in the scope of current research. In particular, parameter robust a posteriori error estimates for…

In this paper we present a fourth-order in space and time block-structured adaptive mesh refinement algorithm for the compressible multicomponent reacting Navier-Stokes equations. The algorithm uses a finite volume approach that…

We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…

We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent…

Real-world image super-resolution is particularly challenging for diffusion models because real degradations are complex, heterogeneous, and rarely modeled explicitly. We propose a degradation-aware and structure-preserving diffusion…

The solution of nonsymmetric but positive definite (NSPD) systems arising from advection-diffusion problems is an important research topic in science and engineering. Balancing domain decomposition by constraints with an adaptive coarse…

A growing body of literature has been leveraging techniques of machine learning (ML) to build novel approaches to approximating the solutions to partial differential equations. Noticeably absent from the literature is a systematic…

This article presents stability and convergence analyses of subgrid multiscale stabilized finite element formulation of non-Newtonian power-law fluid flow model strongly coupled with variable coefficients Advection-Diffusion-Reaction…

This paper presents a heterogeneous adaptive mesh refinement (AMR) framework for efficient simulation of moderately stiff reactive problems. This framework features an elaborate subcycling-in-time algorithm along with a specialized…