Related papers: Continuous Data Assimilation for Displacement in a…
Conventional recursive filtering approaches, designed for quantifying the state of an evolving uncertain dynamical system with intermittent observations, use a sequence of (i) an uncertainty propagation step followed by (ii) a step where…
This article presents a priori error estimates of the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the $H(\rm div)$ conforming virtual element method (VEM) for the approximation of the…
This article reports on the efficiency of a co-located diffuse approximation method coupled with a projection algorithm for the solution of two and three-dimensional incompressible flow equations. Three typical examples show the accuracy of…
In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of…
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
In this work, we characterize the water absorption properties of selected porous materials through a combined approach that integrates laboratory experiments and mathematical modeling. Specifically, experimental data from imbibition tests…
Several natural and industrial processes involve the extraction or retention of a solute by a fluid invading a network of channels. Examples include aquifer contamination, chemical filtration, and coffee extraction. We propose a continuum…
Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…
We study compressible fluid flow in narrow two-dimensional channels using a novel molecular dynamics simulation method. In the simulation area, an upstream source is maintained at constant density and temperature while a downstream…
Turbulent flow over permeable interface is omnipresent featuring complex flow topology. In this work, a data driven, end to end machine learning model has been developed to model the turbulent flow in porous media. For the same, we have…
In this paper, we propose an adaptive sieving (AS) strategy for solving general sparse machine learning models by effectively exploring the intrinsic sparsity of the solutions, wherein only a sequence of reduced problems with much smaller…
In this study, we conduct parameter estimation analysis on a data assimilation algorithm for two turbulence models: the simplified Bardina model and the Navier-Stokes-{\alpha} model. Our approach involves creating an approximate solution…
The use of data assimilation technique to identify optimal topography is discussed in frames of time-dependent motion governed by non-linear barotropic ocean model. Assimilation of artificially generated data allows to measure the influence…
Mathematical modeling of fluid flow in a porous medium is usually described by a continuity equation and a chosen constitutive law. The latter, depending on the problem at hand, may be a nonlinear relation between the fluid's pressure…
Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using…
In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by…
Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…
Reactive transport in permeable porous media is relevant for a variety of applications, but poses a significant challenge due to the range of length and time scales. Multiscale methods that aim to link microstructure with the macroscopic…
Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…