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In the present contribution we develop a sharper error analysis for the Virtual Element Method, applied to a model elliptic problem, that separates the element boundary and element interior contributions to the error. As a consequence we…
Immersed boundary-lattice Boltzmann method (IB-LBM) has been widely used for simulation of particle-laden flows recently. However, it was limited to small-scale simulations with no more than O(103) particles. Here, we expand IB-LBM for…
The integral method can be used to model accurately flows down an inclined plane. Such a method consists in projecting the full 3D equations on a lower dimensional representation. The vertical velocity profiles have their functional form…
In this work, we develop a novel Bayesian estimation method for the Dirichlet process (DP) mixture of the inverted Dirichlet distributions, which has been shown to be very flexible for modeling vectors with positive elements. The recently…
We introduce a new Eulerian simulation framework for liquid animation that leverages both finite element and finite volume methods. In contrast to previous methods where the whole simulation domain is discretized either using the finite…
We introduce a particle-based simulation method for granular material in interactive frame rates. We divide the simulation into two decoupled steps. In the first step, a relatively small number of particles is accurately simulated with a…
The study performs large-eddy simulations of supersonic free jet flows using the Discontinuous Galerkin Spectral Element Method (DGSEM). The main objective of the present work is to assess the resolution requirements for adequate simulation…
The simulation of granular media is usually done either with event-driven codes that treat collisions as instantaneous but have difficulty with very dense packings, or with molecular dynamics methods that approximate rigid grains using a…
Discrete fracture networks is a key ingredient in the simulation of physical processes which involve fluid flow in the underground, when the surrounding rock matrix is considered impervious. In this paper we present two different models to…
The need for accurate and fast scale-resolving simulations of fluid flows, where turbulent dispersion is a crucial physical feature, is evident. Large-eddy simulations (LES) are computationally more affordable than direct numerical…
Flow Matching (FM) models achieve remarkable results in generative tasks. Building upon diffusion models, FM's simulation-free training paradigm enables simplicity and efficiency but introduces a train-inference gap: model outputs cannot be…
In this paper we analyze a virtual element method for the two dimensional elasticity spectral problem allowing small edges. Under this approach, and with the aid of the theory of compact operators, we prove convergence of the proposed VEM…
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the…
In this work, we have developed a multiscale computational algorithm to couple finite element method with an open source molecular dynamics code --- the Large scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) --- to perform…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
The present paper deals with the problem of improving the efficiency of large scale turbulent flow simulations. The high-fidelity methods for modelling turbulent flows become available for a wider range of applications thanks to the…
We present a higher order stabilization-free virtual element method applied to plane elasticity problems. We utilize a serendipity approach to reduce the total number of degrees of freedom from the corresponding high-order approximations.…
We present a wavelet-based adaptive method for computing 3D multiscale flows in complex, time-dependent geometries, implemented on massively parallel computers. While our focus is on simulations of flapping insects, it can be used for other…
In this paper, we study applications of the virtual element method (VEM) for simulating the deformation of multiphase composites. The VEM is a Galerkin approach that is applicable to meshes that consist of arbitrarily-shaped polygonal and…
We present an efficient hybrid Neural Network-Finite Element Method (NN-FEM) for solving the viscous-plastic (VP) sea-ice model. The VP model is widely used in climate simulations to represent large-scale sea-ice dynamics. However, the…