相关论文: Transitions from Monotonicity to Chaos in Gas Mixt…
The stable operation of gas networks is an important optimization target. While for this task commonly finite volume methods are used, we introduce a new finite difference approach. With a summation by part formulation for the spatial…
This work presents a novel, dimensionless model that results in a dimensionless algebraic equation that can be used to quantify the pressure drop associated with the steady state, isothermal flow through a straight, horizontal pipeline, of…
In this article we survey recent progress on mathematical results on gas flow in pipe networks with a special focus on questions of control and stabilization. We briefly present the modeling of gas flow and coupling conditions for flow…
We formulate an economic optimal control problem for transport of natural gas over a large-scale transmission pipeline network under transient flow conditions. The objective is to maximize economic welfare for users of the pipeline system,…
We consider the simulation of barotropic flow of gas in long pipes and pipe networks. Based on a Hamiltonian reformulation of the governing system, a fully discrete approximation scheme is proposed using mixed finite elements in space and…
In many parts of the world, electric power systems have seen a significant shift towards generation from renewable energy and natural gas. Because of their ability to flexibly adjust power generation in real time, gas-fired power plants are…
In this paper, we study hydrogen-natural gas mixtures transported through pipeline networks. The flow is modeled by the isothermal Euler equations with a pressure law involving a non-constant, composition-dependent compressibility factor.…
We consider balanced flows in a natural gas transmission network and discuss computationally hard problems such as establishing if solution of the underlying nonlinear gas flow equations exists, if it is unique, and finding the solution.…
As a common practice, the direction of natural gas flow in every pipeline is determined ex-ante for simplification purposes, and treated as a given parameter within the scheduling problem. However, in integrated gas and electric power…
The coordinated dispatch of power and gas in the electricity-gas integrated energy system (EG-IES) is fundamental for ensuring operational security. However, the gas dynamics in the natural gas system (NGS) are governed by the nonlinear…
We prove an existence result for the steady state flow of gas mixtures on networks. The basis of the model are the physical principles of the isothermal Euler equation, coupling conditions for the flow and pressure, and the mixing of…
We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…
Optimizing the transient control of gas networks is a highly challenging task. The corresponding model incorporates the combinatorial complexity of determining the settings for the many active elements as well as the non-linear and…
The structure of a network has a major effect on dynamical processes on that network. Many studies of the interplay between network structure and dynamics have focused on models of phenomena such as disease spread, opinion formation and…
This paper examines aspirational requirements for software addressing mixed-integer optimization problems constrained by the nonlinear Shallow Water partial differential equations (PDEs), motivated by applications such as river-flow…
We introduce a general, analytical framework to express and to approximate partial differential equations (PDEs) numerically on graphs and networks of surfaces---generalized by the term hypergraphs. To this end, we consider PDEs on…
Hydrogen's growing role in the transition towards climate-neutral energy systems necessitates structured modeling frameworks. Existing gas network models, largely developed for natural gas, fail to capture hydrogen systems distinct…
Hydrogen is produced from water using renewable electricity. Unlike electricity, hydrogen can be stored in large quantities for long periods. This storage ability acts as a green battery, allowing solar and wind energy to be generated and…
In this paper, we consider the problem of regulating the outlet pressure of gas flowing through a pipeline subject to uncertain and variable outlet flow. Gas flow through a pipe is modeled using the coupled isothermal Euler equations, with…
Mixed dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimension. Such equations naturally arise in a wide range of scientific fields including geology,…