On the Riemann problem for liquid or gas‐liquid media

Chen, Tze-Jang; Cooke, Charlie H.

doi:10.1002/fld.1650180507

Cited by 12 publications

(14 citation statements)

References 6 publications

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“…In order to directly apply the numerical methods [39][40][41][42][43] developed for compressible gas flow to the water medium, an expression for the internal energy associated with the Tait's equation of state was proposed in [49]. A set of Roe-averaged values is defined bỹ…”

Section: Case Iii: Collapse Of 2d Air Bubble Under Strong Shock In Watermentioning

confidence: 99%

Adaptive multi-resolution method for compressible multi-phase flows with sharp interface model and pyramid data structure

Han

Adams

2014

Journal of Computational Physics

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Section: Case Iii: Collapse Of 2d Air Bubble Under Strong Shock In Watermentioning

confidence: 99%

Adaptive multi-resolution method for compressible multi-phase flows with sharp interface model and pyramid data structure

Han

Adams

2014

Journal of Computational Physics

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“…This is applied to liquid as well as gas flows 18, 19, and γ, e , and p c are the specific heat ratio, internal energy, and pressure constant, respectively. The effect of the fluid–structure interaction is not taken into consideration in the present work.…”

Section: Ghost Junction Methodsmentioning

confidence: 99%

A new finite volume method on junction coupling and boundary treatment for flow network system analyses

Hong¹,

Kim²

2011

Numerical Methods in Fluids

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To adequately analyze the flow in a pipe or duct network system, traditional node-based junction coupling methods require junction losses, which are specified by empirical or analytic correlations. In this paper, a new finite volume junction coupling method using a ghost junction cell is developed by considering the interchange of linear momentum as well as the important wall effect at the junction without requiring any correlation on the junction loss. Also, boundary treatment is modified to preserve the stagnation enthalpy across boundaries, such as the pipe end and the interface between the junction and the branch.The computational accuracy and efficiency of Godunov-type finite volume schemes are investigated by tracing the total mechanical energy of rapid transients due to sudden closure of a valve at the downstream end. Among the approximate Riemann solvers, the proposed RoeM scheme turns out to be more suitable for finite volume junction treatment than the original Roe's approximate Riemann solver because of conservation of the stagnation enthalpy across the geometric discontinuity. From the viewpoint of computational cost, the implicit LU-SGS time integration is appropriate for steady and slow transients, while the explicit third-order TVD Runge-Kutta scheme is advantageous for rapid transients.(iii) A single momentum flow exists at the junction node: lim x i →0 + s i ( p + U 2 ) i = P (iv) A geometry and flow-dependent pressure loss exists: pk = p k −f (k,k) Here, x i and s i denote the axial distance from the junction node, and the cross-section area of pipe i, respectively.f (k,k) is the pressure loss along the streamline (k,k). k andk indicate the ingoing and outgoing pipe indices, respectively.Guinot [8] introduced a Godunov-type finite volume scheme for one-dimensional pipe flow, and proposed an iterative junction coupling method to specify boundary conditions for adjacent pipes from the coupling conditions (i) and (iv). Kiuchi [9], Guy [10], and Osiadacz [11] proposed another iterative method to calculate the junction pressure. Recently, Banda et al. [14] analyzed the coupling conditions (i) and (ii) or (i) and (iv) from a mathematical point of view, and proved the well-posedness. Colombo and Garavello [12] have proposed similar coupling conditions (i) and (iii), and proved the well-posedness.The traditional node-based junction treatments depend on many loss coefficients at the junction, as shown in the coupling condition (iv), to properly reflect the momentum interaction at the junction. However, the junction losses are often incorrectly assigned or unwillingly neglected in complex flow network applications when the connected branch angle is arbitrarily three-dimensional and/or the number of branches is greater than four. In this case, the analytic correlations are very difficult to derive, and empirical correlations are rarely available. In practical engineering design, the junction losses are negligible in most long-pipe systems, but the losses are no longer trivial for short-pipe systems bec...

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“…note that for the water medium, what we have actually used is the Tait EOS [9,14,28,36], and we need to usep = p + γB instead of p in all the above formulae, whereB = B − A, A = 1.0E5 Pa and B = 3.31E8 Pa. For water, γ = 7.15, and the displayed pressure for the water in Sect. 8 is p, notp.…”

Section: Two-medium Flow Model For Nonconservative Euler Equationsmentioning

confidence: 98%

WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-Dimensional Compressible Two-Medium Flows

2012

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High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in (Parés, SIAM this approach may have some computational issues and shortcomings. In this paper, a modification to the high order path-conservative scheme in (Castro et al., Math. Comput. 75:1103-1134, 2006) is proposed to improve its computational performance and to overcome some of the shortcomings. This modification is based on the high order finite volume WENO scheme with subcell resolution and it uses an exact Riemann solver to catch the right paths at the discontinuities. An application to one-dimensional compressible two-medium flows of nonconservative or primitive Euler equations is carried out to show the effectiveness of this new approach.

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On the Riemann problem for liquid or gas‐liquid media

Cited by 12 publications

References 6 publications

Adaptive multi-resolution method for compressible multi-phase flows with sharp interface model and pyramid data structure

Adaptive multi-resolution method for compressible multi-phase flows with sharp interface model and pyramid data structure

A new finite volume method on junction coupling and boundary treatment for flow network system analyses

WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-Dimensional Compressible Two-Medium Flows

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