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We present a dynamic model for the optimal control problem (OCP) of hydrogen blending into natural gas pipeline networks subject to inequality constraints. The dynamic model is derived using the first principles partial differential…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
A comprehensive scheme for the spatial discretisation of continuity equation, momentum advection and normal and shear stresses at the fluid interfaces is presented for numerically simulating the incompressible two phase flows based on the…
This paper presents an implicit method for the discrete unified gas-kinetic scheme (DUGKS) to speed up the simulations of the steady flows in all flow regimes. The DUGKS is a multi-scale scheme finite volume method (FVM) for all flow…
We consider a distributed stochastic optimization problem in networks with finite number of nodes. Each node adjusts its action to optimize the global utility of the network, which is defined as the sum of local utilities of all nodes.…
There are proposed models of contracts, technological equipment and gas networks and methods of their optimization. The flow in network undergoes restrictions of contracts and equipment to be operated. The values of sources and sinks are…
We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic…
We analyze two types of summation-by-parts finite difference operators for approximating the second derivative with variable coefficient. The first type uses ghost points, while the second type does not use any ghost points. A previously…
Existing techniques for the cost optimization of water distribution networks either employ meta-heuristics, or try to develop problem-specific optimization techniques. Instead, we exploit recent advances in generic NLP solvers and explore a…
We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula,…
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…
There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in…
The current energy transition promotes the convergence of operation between the power and natural gas systems. In that direction, it becomes paramount to improve the modeling of non-convex natural gas flow dynamics within the coordinated…
We examine the problem of optimal transport capacity expansion planning for a gas pipeline network to service the growing demand of gas-fired power plants that are increasingly used to provide base load, flexibility, and reserve generation…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
We consider the method of mappings for performing shape optimization for unsteady fluid-structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes…
In this paper, authors focus effort on improving the conventional discrete velocity method (DVM) into a multiscale scheme in finite volume framework for gas flow in all flow regimes. Unlike the typical multiscale kinetic methods unified…
We present Finite Volume methods for diffusion equations on generic meshes, that received important coverage in the last decade or so. After introducing the main ideas and construction principles of the methods, we review some literature…
We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution and of its gradient. In the case of simplicial meshes, the…
We present an economic optimization problem for allocating the flow of natural gas and hydrogen blends through a large-scale transportation pipeline network. Physical flow of the gas mixture is modeled using a steady-state relation between…