Commun. Comput. Phys., 12 (2012), pp. 1070-1095.


The Space-Time CE/SE Method for Solving Reduced Two-Fluid Flow Model

Shamsul Qamar 1*, Munshoor Ahmed 2, Ishtiaq Ali 2

1 Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad Islamabad, Pakistan; and Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany.
2 Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad Islamabad, Pakistan.

Received 21 February 2011; Accepted (in revised version) 1 November 2011
Available online 28 March 2012
doi:10.4208/cicp.210211.011111a

Abstract

The space-time conservation element and solution element (CE/SE) method is proposed for solving a conservative interface-capturing reduced model of compressible two-fluid flows. The flow equations are the bulk equations, combined with mass and energy equations for one of the two fluids. The latter equation contains a source term for accounting the energy exchange. The one and two-dimensional flow models are numerically investigated in this manuscript. The CE/SE method is capable to accurately capture the sharp propagating wavefronts of the fluids without excessive numerical diffusion or spurious oscillations. In contrast to the existing upwind finite volume schemes, the Riemann solver and reconstruction procedure are not the building block of the suggested method. The method differs from the previous techniques because of global and local flux conservation in a space-time domain without resorting to interpolation or extrapolation. In order to reveal the efficiency and performance of the approach, several numerical test cases are presented. For validation, the results of the current method are compared with other finite volume schemes.

AMS subject classifications: 76T99, 65Y99, 65M99, 35L45, 35L65, 35L67

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Key words: Reduced model, space-time CE/SE method, central schemes, conservation laws, hyperbolic systems, shock solutions.

*Corresponding author.
Email: shamsul.qamar@comsats.edu.pk (S. Qamar), manshoor@comsats.edu.pk (M. Ahmed), ishtiaqali@comsats.edu.pk (I. Ali)
 

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