A Second-Order Accurate Capturing Scheme for 1D Inviscid Flows of Gas and Water with Vacuum Zones

Tang, Hao; Huang, De

doi:10.1006/jcph.1996.0212

Cited by 40 publications

(30 citation statements)

References 11 publications

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“…In addition, fractures within a solid are treated as vacuums. Consequently, solutions to relevant solid phase Riemann problems can be constructed and obtained by methods similar to those employed for gas-water-vacuum Riemann problems in [12]. All these elements will be incorporated into the new solid phase scheme.…”

Section: Introductionmentioning

confidence: 99%

“…Miller and Puckett [10] also reported that Colella et al [11] proposed a Godunov method for two or more gases. Tang and Huang [12] extended the standard MUSCL scheme developed by van Leer [13] to flows of gas and water with vacuum zones. For the extension several techniques were presented to prevent the computed density from becoming smaller than its lower bound.…”

Section: Introductionmentioning

confidence: 99%

“…Given the existing E-MUSCL scheme [12] for coupled gas and water systems with vacuum zones, to accomplish this objective a new solid phase formulation must be developed that can be naturally incorporated into it. A major difference between responses of a solid and those of a fluid is that the former usually behaves as a shape-memory material.…”

Section: Introductionmentioning

confidence: 99%

“…The resulting scheme, denoted as an E-MUSCL scheme, can capture shocks, gas/water interfaces, as well as vacuum zones and takes into account water's capability to resist tensile stresses. The E-MUSCL scheme was applied to study cavitation phenomena within a water shock tube [12,14].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Second-Order Godunov Method for Wave Problems in Coupled Solid–Water–Gas Systems

Tang

Sotiropoulos

1999

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Second-Order Godunov Method for Wave Problems in Coupled Solid–Water–Gas Systems

Tang

Sotiropoulos

1999

Journal of Computational Physics

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“…The numerical scheme should also be robust enough to deal with the enormous instability problems caused by the cavitating flows. Various numerical methods, such as the method of characteristics [8] and high resolution upwind schemes for capturing the interface of two phase flows [11], have been developed to study cavitating flows.…”

Section: Introductionmentioning

confidence: 99%

Direct Calculations of Cavitating Flows in Fuel Delivery Pipe by the Space-Time CE/SE Method

Qin¹,

Yu²,

Lai³

1999

SAE Technical Paper Series

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In this paper, we report direct calculations of cavitating pipe flows by the method of Space-Time Conservation Element and Solution Element, or the CE/SE method for short. The tenet of the CE/SE method is treating space and time as one entity, and the calculation of flow properties is based on the local and global space-time flux conservation. As a contrast to the modern upwind schemes, no Riemann solver is used, thus the logic of the present scheme for cavitating flows is much simpler. Two numerical examples are reported in this paper: (1) a hydraulic shock problem, and (2) a cavitating pipe flow. For the hydraulic shock problem, we demonstrate the capability of the CE/SE method for capturing contact discontinuities in cavitating fluids. For the pipe flows, a two-phase homogeneous equilibrium cavitation model is employed. In both cases, numerical results compared favorably with the experimental data and analytical solution.

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Numerical study of wave propagation in compressible two‐phase flow

Zeidan

Romenski

Slaouti

et al. 2006

Numerical Methods in Fluids

105

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SUMMARYWe propose a new model and a solution method for two-phase two-fluid compressible flows. The model involves six equations obtained from conservation principles applied to a one-dimensional flow of gas and liquid mixture completed by additional closure governing equations. The model is valid for pure fluids as well as for fluid mixtures. The system of partial differential equations with source terms is hyperbolic and has conservative form. Hyperbolicity is obtained using the principles of extended thermodynamics. Features of the model include the existence of real eigenvalues and a complete set of independent eigenvectors. Its numerical solution poses several difficulties. The model possesses a large number of acoustic and convective waves and it is not easy to upwind all of these accurately and simply. In this paper we use relatively modern shock-capturing methods of a centred-type such as the total variation diminishing (TVD) slope limiter centre (SLIC) scheme which solve these problems in a simple way and with good accuracy. Several numerical test problems are displayed in order to highlight the efficiency of the study we propose. The scheme provides reliable results, is able to compute strong shock waves and deals with complex equations of state.

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A Second-Order Accurate Capturing Scheme for 1D Inviscid Flows of Gas and Water with Vacuum Zones

Cited by 40 publications

References 11 publications

A Second-Order Godunov Method for Wave Problems in Coupled Solid–Water–Gas Systems

A Second-Order Godunov Method for Wave Problems in Coupled Solid–Water–Gas Systems

Direct Calculations of Cavitating Flows in Fuel Delivery Pipe by the Space-Time CE/SE Method

Numerical study of wave propagation in compressible two‐phase flow

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