On a third order CWENO boundary treatment with application to networks of hyperbolic conservation laws

Naumann, Alexander; Kolb, Oliver; Semplice, Matteo

doi:10.1016/j.amc.2017.12.041

Cited by 11 publications

(29 citation statements)

References 33 publications

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“…Within the following numerical examples, we consider two different discretization schemes. The first is a third-order CWENO scheme (CWENO3) with suitable boundary treatment [20,23], which relies on a local Lax-Friedrichs flux function for the inner discretization points of each pipe and handles coupling points by explicitly solving equation (27). The second scheme is an implicit box scheme (IBOX) [21], suitable for sub-sonic flows.…”

Section: Numerical Resultsmentioning

confidence: 99%

Modeling and simulation of gas networks coupled to power grids

2019

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In this paper, a mathematical framework for the coupling of gas networks to electric grids is presented to describe in particular the transition from gas to power. The dynamics of the gas flow are given by the isentropic Euler equations, while the power flow equations are used to model the power grid. We derive pressure laws for the gas flow that allow for the wellposedness of the coupling and a rigorous treatment of solutions. For simulation purposes, we apply appropriate numerical methods and show in a experimental study how gas-to-power might influence the dynamics of the gas and power network, respectively.

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Section: Numerical Resultsmentioning

confidence: 99%

Modeling and simulation of gas networks coupled to power grids

2019

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“…For example, close to the top‐left boundary of the domain, one may use only

{\overset{u}{true}}_{0}, ⋯, {\overset{u}{true}}_{8}, {\overset{u}{true}}_{11}, {\overset{u}{true}}_{12}

to determine an optimal polynomial of degree 3, the standard polynomial of degree 2 in the south‐west direction, and three first‐degree polynomials in the other directions. In order to obtain reconstructions that do not require ghost cells, one may investigate the adaption to the 2D case of a technique that avoids altogether the use of ghost cells …”

Section: Central Weighted Essentially Nonoscillatory Reconstruction (mentioning

confidence: 99%

“…In order to obtain reconstructions that do not require ghost cells, one may investigate the adaption to the 2D case of a technique that avoids altogether the use of ghost cells. 30…”

Section: Boundary Treatmentmentioning

confidence: 99%

Third‐ and fourth‐order well‐balanced schemes for the shallow water equations based on the CWENO reconstruction

Castro

Semplice

2018

Numerical Methods in Fluids

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Summary High‐order finite volume schemes for conservation laws are very useful in applications, due to their ability to compute accurate solutions on quite coarse meshes and with very few restrictions on the kind of cells employed in the discretization. For balance laws, the ability to approximate up to machine precision relevant steady states allows the scheme to compute accurately, also on coarse meshes, small perturbations of such states, which are very relevant for many applications. In this paper, we propose third‐ and fourth‐order accurate finite volume schemes for the shallow water equations. The schemes have the well‐balanced property thanks to a path‐conservative approach applied to an appropriate nonconservative reformulation of the equations. High‐order accuracy is achieved by designing truly two‐dimensional (2D) reconstruction procedures of the central WENO (CWENO) type. The novel schemes are tested for accuracy and well‐balancing and shown to maintain positivity of the water height on wet/dry transitions. Finally, they are applied to simulate the Tohoku 2011 tsunami event.

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“…A different approach, entirely based on extrapolation is studied in [2,3]. In [29] a different strategy was considered. There, in a one-dimensional finite volume context, ghost values are entirely avoided and the point value reconstruction at the boundary is performed with a type reconstruction that makes use only of interior cell averages.…”

Section: Introductionmentioning

confidence: 99%

One- and Multi-dimensional CWENOZ Reconstructions for Implementing Boundary Conditions Without Ghost Cells

Semplice

Travaglia

Puppo

2021

Commun. Appl. Math. Comput.

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We address the issue of point value reconstructions from cell averages in the context of third-order finite volume schemes, focusing in particular on the cells close to the boundaries of the domain. In fact, most techniques in the literature rely on the creation of ghost cells outside the boundary and on some form of extrapolation from the inside that, taking into account the boundary conditions, fills the ghost cells with appropriate values, so that a standard reconstruction can be applied also in the boundary cells. In Naumann et al. (Appl. Math. Comput. 325: 252–270. 10.1016/j.amc.2017.12.041, 2018), motivated by the difficulty of choosing appropriate boundary conditions at the internal nodes of a network, a different technique was explored that avoids the use of ghost cells, but instead employs for the boundary cells a different stencil, biased towards the interior of the domain. In this paper, extending that approach, which does not make use of ghost cells, we propose a more accurate reconstruction for the one-dimensional case and a two-dimensional one for Cartesian grids. In several numerical tests, we compare the novel reconstruction with the standard approach using ghost cells.

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On a third order CWENO boundary treatment with application to networks of hyperbolic conservation laws

Cited by 11 publications

References 33 publications

Modeling and simulation of gas networks coupled to power grids

Modeling and simulation of gas networks coupled to power grids

Third‐ and fourth‐order well‐balanced schemes for the shallow water equations based on the CWENO reconstruction

One- and Multi-dimensional CWENOZ Reconstructions for Implementing Boundary Conditions Without Ghost Cells

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