Explanipedia

Simulation of gas mixture dynamics in a pipeline network using explicit staggered-grid discretization Open

Yan Brodskyi, Vitaliy Gyrya, Anatoly Zlotnik · 2024

Simulation of Gas Mixture Dynamics in a Pipeline Network using Explicit Staggered-Grid Discretization Open

Yan Brodskyi, Vitaliy Gyrya, Anatoly Zlotnik · 2024

We develop an explicit second order staggered finite difference discretization scheme for simulating the transport of highly heterogeneous gas mixtures through pipeline networks. This study is motivated by the proposed blending of hydrogen…

Learning closure models for Turbulence: Calibration of BHR using Machine Learning techniques Open

Ismael Boureima, Vitaliy Gyrya, Juan A. Sáenz, Susan Kurien, Marianne Francois · 2024

Effects of Hydrogen Blending on Natural Gas Pipeline Transients, Capacity, and Economics Open

Anatoly Zlotnik, Saif R. Kazi, Kaarthik Sundar, Vitaliy Gyrya, Luke S. Baker , et al. · 2024

Extension of Finite Element methods to general polygonal (and polyhedral) meshes Open

Vitaliy Gyrya, Konstantin Lipnikov, Gianmarco Manzini, Duncan McGregor · 2024

Pipeline Hydrogen Decarbonization and Repurposing Analyzers (P-HyDRAs) Open

Anatoly Zlotnik, Kaarthik Sundar, Vitaliy Gyrya, Saif R. Kazi, Luke S. Baker , et al. · 2024

The Pipeline Hydrogen Decarbonization and Repurposing Analyzers (P-HyDRAs) are a set of prototype computational tools for simulating and optimizing midstream natural gas pipeline system operations subject to location and time-dependent hyd…

Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks Open

Svetlana Tokareva, Anatoly Zlotnik, Vitaliy Gyrya · 2023

The virtual element method for a 2D incompressible MHD system Open

Sebastián Naranjo Álvarez, L. Beirão da Veiga, Vrushali A. Bokil, Franco Dassi, Vitaliy Gyrya , et al. · 2023

Toward learning Lattice Boltzmann collision operators Open

Alessandro Corbetta, Alessandro Gabbana, Vitaliy Gyrya, Daniel Livescu, Joost Prins , et al. · 2023

Numerical Solution of the Steady-State Network Flow Equations for a Nonideal Gas Open

Shriram Srinivasan, Kaarthik Sundar, Vitaliy Gyrya, Anatoly Zlotnik · 2022

Herein we formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solu…

Towards learning Lattice Boltzmann collision operators Open

Alessandro Corbetta, Alessandro Gabbana, Vitaliy Gyrya, Daniel Livescu, Joost Prins , et al. · 2022

In this work we explore the possibility of learning from data collision operators for the Lattice Boltzmann Method using a deep learning approach. We compare a hierarchy of designs of the neural network (NN) collision operator and evaluate…

Optimization of artificial viscosity in production codes based on Gaussian Regression surrogate models Open

Vitaliy Gyrya, Evan Lieberman, Mark Kenamond, Mikhail Shashkov · 2022

To accurately model flows with shock waves using staggered-grid Lagrangian hydrodynamics, artificial viscosity has to be introduced to convert kinetic energy into internal energy, thereby increasing the entropy across shocks. Determining t…

The NonConforming Virtual Element Method for the Stokes Equations Open

Andrea Cangiani, Vitaliy Gyrya, Gianmarco Manzini · 2022

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while e…

Stochastic Finite Volume Method for Uncertainty Quantification of Transient Flow in Gas Pipeline Networks Open

Svetlana Tokareva, Anatoly Zlotnik, Vitaliy Gyrya · 2022

We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method …

Numerical Solution of the Steady-State Network Flow Equations for a Non-Ideal Gas Open

Shriram Srinivasan, Kaarthik Sundar, Vitaliy Gyrya, Anatoly Zlotnik · 2022

We formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solution fo…

Dynamic calibration of differential equations using machine learning, with application to turbulence models Open

Ismael Boureima, Vitaliy Gyrya, Juan A. Sáenz, Susan Kurien, Marianne Francois · 2022

The virtual element method for resistive magnetohydrodynamics Open

Sebastián Naranjo Álvarez, Vrushali A. Bokil, Vitaliy Gyrya, Gianmarco Manzini · 2021

The virtual element method for the coupled system of magneto-hydrodynamics Open

Sebastian Naranjo-Alvarez, Vrushali A. Bokil, Vitaliy Gyrya, Gianmarco Manzini · 2021

In this work, we review the framework of the Virtual Element Method (VEM) for a model in magneto-hydrodynamics (MHD), that incorporates a coupling between electromagnetics and fluid flow, and allows us to construct novel discretizations fo…

A Virtual Element Method for the Full MHD system Open

Sebastián Naranjo Álvarez, Vrushali A. Bokil, Vitaliy Gyrya, Gianmarco Manzini · 2020

In this manuscript we present a novel discretization for the incompressible MHD system. Our approach follows the framework of the Virtual Element Method and offers two main advantages. The method can be implemented in unstructured meshes m…

Machine-Learning for Rapid Optimization of Turbulence Models Open

Juan A. Sáenz, Ismael Boureima, Vitaliy Gyrya, Susan Kurien · 2020

1. Background and Motivation: What is turbulence; Why is turbulence important; How turbulence is modeled; BHR model; Motivation for a ML framework 2. DNS Database from OES-C4; 3. Machine learning framework: Formulation; Verification; Case …

The virtual element method for resistive magnetohydrodynamics Open

Sebastián Naranjo Álvarez, Vrushali A. Bokil, Vitaliy Gyrya, Gianmarco Manzini · 2020

We present a virtual element method (VEM) for the numerical approximation of the electromagnetics subsystem of the resistive magnetohydrodynamics (MHD) model in two spatial dimensions. The major advantages of the virtual element method inc…

A Low Order Mimetic Finite Difference Method for Resistive Magnetohydrodynamics in 2D Open

Sebastián Naranjo, Vitaliy Gyrya · 2018

We developed a low order Mimetic Finite Difference (MFD) discretization for the equations of magnetohydrodynamics (MHD) in two space dimensions. These equations describe the evolution of the electric and magnetic fields in the presence of …

An explicit staggered-grid method for numerical simulation of large-scale natural gas pipeline networks Open

Vitaliy Gyrya, Anatoly Zlotnik · 2018

A dispersion optimized mimetic finite difference method for Maxwell's equations in metamaterials. Open

Duncan McGregor, Vrushali A. Bokil, Duncan McGregor, Vitaliy Gyrya · 2018

An explicit staggered-grid method for numerical simulation of\n large-scale natural gas pipeline networks Open

Vitaliy Gyrya, Anatoly Zlotnik · 2018

We present an explicit second order staggered finite difference (FD)\ndiscretization scheme for forward simulation of natural gas transport in\npipeline networks. By construction, this discretization approach guarantees\nthat the conservat…

Final Report of the Project "From the finite element method to the virtual element method" Open

Gianmarco Manzini, Vitaliy Gyrya · 2017

The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to gener…

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor Open

Vitaliy Gyrya, Konstantin Lipnikov · 2017

C1-continuous Virtual Element Method for Poisson-Kirchhoff plate problem Open

Vitaliy Gyrya, Hashem M. Mourad · 2016

We present a family of C1-continuous high-order Virtual Element Methods for Poisson-Kirchho plate bending problem. The convergence of the methods is tested on a variety of meshes including rectangular, quadrilateral, and meshes obtained by…

Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom Open

Oleksandr Iaroshenko, Vitaliy Gyrya, Gianmarco Manzini · 2016

In this work we consider a modification to an arbitrary order mixed mimetic finite difference method (MFD) for a diffusion equation on general polygonal meshes [1]. The modification is based on moving some degrees of freedom (DoF) for a fl…

A Dispersion Minimized Mimetic Method for Cold Plasma Open

Vrushali A. Bokil, Vitaliy Gyrya, Duncan McGregor · 2016

In this paper we consider the lowest edge-based mimetic finite difference (MFD) discretization in space for Maxwell's equations in cold plasma on rectangular meshes. The method uses a generalized form of mass lumping that, on one hand, eli…

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