Numerical Discretization of Coupling Conditions by High-Order Schemes

Banda, Mapundi K.; Häck, Axel-Stefan; Herty, Michaël

doi:10.1007/s10915-016-0185-x

Cited by 12 publications

(10 citation statements)

References 39 publications

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“…For the mimmod scheme we need a second ghost cell ξ−1. In principle it should be possible to use the time derivative of the coupling condition as in [BHH16] or [BK14], but in our setting it is much easier to simply use a first order extrapolation through the first couple of inner cell values and the newly-computed boundary value from (22).…”

Section: Coupling Conditionsmentioning

confidence: 99%

On the relation of powerflow and Telegrapher's equations: continuous and numerical Lyapunov stability

Fokken,

Göttlich

2021

Preprint

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In this contribution we analyze the exponential stability of power networks modeled with the Telegrapher's equations as a system of balance laws on the edges. We show the equivalence of periodic solutions of these Telegrapher's equations and solutions to the well-established powerflow equations. In addition we provide a second-order accurate numerical scheme to integrate the powerflow equations and show (up to the boundary conditions) Lyapunov stability of the scheme.

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Section: Coupling Conditionsmentioning

confidence: 99%

On the relation of powerflow and Telegrapher's equations: continuous and numerical Lyapunov stability

Fokken,

Göttlich

2021

Preprint

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“…Also, the algorithm is second-order in the pipe but it may reduce to first order at the coupling condition. The algorithm can be extended to second-order across the nodal point using techniques presented in [2]. However, note that the steady state is constant and therefore the scheme preserves the steady state to any order across the nodal point.…”

Section: Well-balanced Scheme For Flows In Network 669mentioning

confidence: 99%

“…where the flux terms are as defined in (2) and S j i is the source term given in (2) at the point U j i . The coupling conditions (15), (18) are used to calculate the density and momentum at a node.…”

Section: Numerical Testsmentioning

confidence: 99%

See 1 more Smart Citation

Well-balanced scheme for gas-flow in pipeline networks

Mantri¹,

Herty²,

Noelle³

2019

Networks &Amp; Heterogeneous Media

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Gas flow through pipeline networks can be described using 2 × 2 hyperbolic balance laws along with coupling conditions at nodes. The numerical solution at steady state is highly sensitive to these coupling conditions and also to the balance between flux and source terms within the pipes. To avoid spurious oscillations for near equilibrium flows, it is essential to design well-balanced schemes. Recently Chertock, Herty &Özcan[11] introduced a well-balanced method for general 2 × 2 systems of balance laws. In this paper, we simplify and extend this approach to a network of pipes. We prove wellbalancing for different coupling conditions and for compressors stations, and demonstrate the advantage of the scheme by numerical experiments.2010 Mathematics Subject Classification. Primary: 35L60, 35L65, 76M12.

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“…Particular results for the coupling of Euler equations with Euler equations exist and have been studied, eg, in Colombo and Mauri . Numerical approaches have been proposed, eg, in Godlewski et al and Banda et al Coupling the dynamic requires to postulate conditions to be fulfilled at the interface x n =0 for a.e. t ≥0.…”

Section: Description Of the Model Problemmentioning

confidence: 99%

Fluid‐structure coupling of linear elastic model with compressible flow models

Herty

Müller

Gerhard

et al. 2017

Numerical Methods in Fluids

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Summary Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.

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Numerical Discretization of Coupling Conditions by High-Order Schemes

Cited by 12 publications

References 39 publications

On the relation of powerflow and Telegrapher's equations: continuous and numerical Lyapunov stability

On the relation of powerflow and Telegrapher's equations: continuous and numerical Lyapunov stability

Well-balanced scheme for gas-flow in pipeline networks

Fluid‐structure coupling of linear elastic model with compressible flow models

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