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Development of a less-dissipative hybrid AUSMD scheme for multi-component flow simulations

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Abstract

In this study, a less-dissipative hybrid AUSMD scheme considering the linearized approximated solution around the material interfaces of compressible multi-component flows is proposed. A high-resolution reconstruction scheme, so-called MUSCL + THINC, has been devised by combining the MUSCL method with the Tangent of Hyperbola for Interface Capturing technique (THINC) under the boundary variation diminishing concept, which is used to determine the cell-interface values to evaluate the AUSMD flux. Several perfect gas and multi-component flow problems are selected as the benchmark test cases. The flow models we use here are the perfect gas Euler equations and the multi-phase five-equation flow model. We compared the proposed MUSCL + THINC-type AUSMD scheme with the original MUSCL-type AUSMD scheme to verify its capability of capturing shock waves, expansion fans, and material interfaces, which are identified as a well-defined sharp jump in volume fraction. Numerical results of all benchmark tests show that the MUSCL + THINC-type AUSMD solver is superior to the original MUSCL-type AUSMD in resolving shock waves, expansion fans, and interfaces. In particular, the solution quality for expansion fans and interfaces on coarse grids is greatly improved by the MUSCL + THINC-type AUSMD scheme.

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Abbreviations

a :

Sound speed

E :

Total mixture energy

F :

Inviscid flux

H :

Enthalpy

M :

Mach number

p :

Pressure

p ∞ :

Pressure-like constant

Q :

Conserved variable

u :

Mixture velocity

U :

Conserved variable flux

α :

Volume fraction

ρ :

Fluid density

γ :

Specific heat ratio

i + 1/2:

Cell interface

L:

Left state of cell interface

R:

Right state of cell interface

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Acknowledgements

The author wishes to acknowledge the financial support sponsored by the National Science Council of Taiwan, ROC under Contract MOST 103-2221-E-032-024-MY3. The first author also appreciates late Meng-Sing Liou’s fruitful discussions about the development of AUSMD scheme since 1997. The first author also cherishes the unreserved sharing of his life experiences and encouragement.

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Authors and Affiliations

  1. Department of Aerospace Engineering, Tamkang University, New Taipei City, Taiwan, ROC

    Y.-Y. Niu & Y.-C. Chen

  2. Corning Display Technologies Taiwan, Tainan, Taiwan, ROC

    T.-Y. Yang

  3. Department of Mechanical Engineering, Tokyo Institute of Technology, Tokyo, Japan

    F. Xiao

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  1. Y.-Y. Niu
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  2. Y.-C. Chen
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  4. F. Xiao
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Correspondence to Y.-Y. Niu.

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Communicated by C.-H. Chang.

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Niu, YY., Chen, YC., Yang, TY. et al. Development of a less-dissipative hybrid AUSMD scheme for multi-component flow simulations. Shock Waves 29, 691–704 (2019). https://doi.org/10.1007/s00193-018-0872-7

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