相关论文: Natural Gas Flow Equations: Uniqueness and an MI-S…
This paper presents $\Psi$-GNN, a novel Graph Neural Network (GNN) approach for solving the ubiquitous Poisson PDE problems with mixed boundary conditions. By leveraging the Implicit Layer Theory, $\Psi$-GNN models an "infinitely" deep…
Stand-alone direct current (DC) microgrids may belong to different owners and adopt various control strategies. This brings great challenge to its optimal operation due to the difficulty of implementing a unified control. This paper…
A reduced level of system inertia due to renewable integration increases the need for cost-effective provision of ancillary services, such as Frequency Response (FR). In this paper we propose a closed-form solution to the differential…
We perform numerical experiments on the Serre-Green-Naghdi (SGN) equations and a fully dispersive "Whitham-Green-Naghdi" (WGN) counterpart in dimension 1. In particular, solitary wave solutions of the WGN equations are constructed and their…
The Grad-Shafranov (GS) equation is a nonlinear elliptic partial differential equation that governs the ideal magnetohydrodynamic equilibrium of a tokamak plasma. Previous studies have demonstrated the existence of multiple solutions to the…
A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our…
The present paper deals with a modified Serre-Green-Naghdi (mSGN) system that has been introduced by Clamond et al. to improve the dispersion relation. We present a precise blow-up scenario of the mSGN equations and we prove the existence…
In many astrophysical plasmas, the Coulomb collision is insufficient to maintain an isotropic temperature, and the system is driven to the anisotropic regime. In this case, magnetohydrodynamic (MHD) models with anisotropic pressure are…
Recent increases in gas-fired power generation have engendered increased interdependencies between natural gas and power transmission systems. These interdependencies have amplified existing vulnerabilities to gas and power grids, where…
Simulation and control of the transient flow in natural gas networks involve solving partial differential equations (PDEs). This paper proposes a semi-analytical solutions (SAS) approach for fast and accurate simulation of the natural gas…
A two-stage multi-period mixed-integer linear stochastic programming model is proposed to assist qualified operators in long-term generation and transmission expansion planning of electricity and gas systems to meet policy objectives. The…
In the study of gas dynamics, theoretical modeling and numerical simulation are mostly set up with deterministic settings. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between flow-field…
In this paper, we propose a graph neural network architecture to solve the AC power flow problem under realistic constraints. To ensure a safe and resilient operation of distribution grids, AC power flow calculations are the means of choice…
Accurate and efficient numerical simulation of unconventional reservoirs is challenging. Long periods of transient flow and steep potential gradients occur due to the extreme conductivity contrast between matrix and fracture. Detailed…
Computational models corresponding to supply security in natural gas networks aim to describe flows and consumption values in the case of component failures or unforseen pipeline shutdowns. The role of natural gas reservoires in this…
In this paper we study a gradient flow generated by the Landau-de Gennes free energy that describes nematic liquid crystal configurations in the space of $Q$-tensors. This free energy density functional is composed of three quadratic terms…
We are concerned with the three dimensional incompressible Navier--Stokes equations driven by an additive stochastic forcing of trace class. First, for every divergence free initial condition in $L^{2}$ we establish existence of infinitely…
We derive conditions for monotonicity properties that characterize general flows of a commodity over a network, where the flow is described by potential and flow dynamics on the edges, as well as potential continuity and Kirchhoff-Neumann…
The optimal power flow (OPF) problem determines power generation/demand that minimize a certain objective such as generation cost or power loss. It is nonconvex. We prove that, for radial networks, after shrinking its feasible set slightly,…
We prove that in the absence of topological changes, the notion of BV solutions to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical) non-uniqueness. Our approach is based on the local structure of the…