34 citations · 91 across the 15 of their papers we have counts for
6 papers · 1 filter
Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations
QiZhi He, Alexandre M. Tartakovsky
We propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled advection-dispersion and Darcy flow equations with space-de…
Non-local model for surface tension in fluid-fluid simulations
Amanda A. Howard, Alexandre M. Tartakovsky
We propose a non-local model for surface tension obtained in the form of an integral of a molecular-force-like function with support added to the Navier-Stokes mom…
Analytical steady-state solutions for pressure with a multiscale non-local model for two-fluid systems
Amanda A. Howard, Yongcheng Zhou, Alexandre M. Tartakovsky
We consider the nonlocal multiscale model for surface tension \citep{Tartakovsky2018} as an alternative to the (macroscale) Young-Laplace law. The nonlocal model is obtained in the…
Method of model reduction and multifidelity models for solute transport in random layered porous media
Zhijie Xu, Alexandre M. Tartakovsky
This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to st…
Continuum Model for Nanoscale Multiphase Flows
Alexandre M. Tartakovsky
We propose a nonlocal model for surface tension. This model, in combination with the Landau-Lifshitz-Navier-Stokes equations, describes mesoscale features of the multiphase flow, i…
Persistent incomplete mixing in reactive flows
Alexandre M. Tartakovsky, David Barajas-Solano
We present an effective stochastic advection-diffusion-reaction (SADR) model that explains incomplete mixing typically observed in transport with bimolecular reactions. Unlike trad…