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A robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM\(^+\)-up scheme. (English) Zbl 1192.76030
J. Comput. Phys. 225, No. 1, 840-873 (2007); erratum ibid. 227, No. 10; 5360 (2008).
Summary: We propose a new approach to compute compressible multifluid equations. Firstly, a single-pressure compressible multifluid model based on the stratified flow model is proposed. The stratified flow model, which defines different fluids in separated regions, is shown to be amenable to the finite volume method. We can apply the conservation law to each subregion and obtain a set of balance equations. Secondly, the AUSM\(^{+}\) scheme, which is originally designed for the compressible gas flow, is extended to solve compressible liquid flows. By introducing additional dissipation terms into the numerical flux, the new scheme, called AUSM\(^{+}\)-up, can be applied to both liquid and gas flows. Thirdly, the contribution to the numerical flux due to interactions between different phases is taken into account and solved by the exact Riemann solver. We will show that the proposed approach yields an accurate and robust method for computing compressible multiphase flows involving discontinuities, such as shock waves and fluid interfaces. Several one-dimensional test problems are used to demonstrate the capability of our method, including the Ransom’s water faucet problem and the air-water shock tube problem. Finally, several two dimensional problems will show the capability to capture enormous details and complicated wave patterns in flows having large disparities in the fluid density and velocities, such as interactions between water shock wave and air bubble, between air shock wave and water column(s), and underwater explosion.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76T10 Liquid-gas two-phase flows, bubbly flows
76N15 Gas dynamics (general theory)
Software:
AUSM; HE-E1GODF
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References:
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