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

Communications in Computational Physics 2012年第9期12卷 1070-1095页

作者： Shamsul Qamar munshoor ahmed Ishtiaq Ali Department of Mathematics COMSATS Institute of Information TechnologyPark RoadChak Shahzad IslamabadPakistan Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr.139106 MagdeburgGermany

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

关键词： Reduced model space-time CE/SE method central schemes conservation laws hyperbolic systems shock solutions

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A Gas-Kinetic Scheme for Six-Equation Two-Phase Flow Model

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Applied Mathematics 2014年第3期5卷 453-465页

作者： Saqib Zia munshoor ahmed Shamsul Qamar Department of Mathematics COMSATS Institute of Information Technology Islamabad Pakistan

A kinetic flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation two-phase flow model of Saurel et al. [1]. The model incorporates single velocity, two pressures and relaxation terms. An additional seventh equation, describing the total mixture energy, is added to the model to guarantee the correct treatment of shocks in the single phase limit. Some salient features of the model are that it is hyperbolic with only three wave propagation speeds and the volume fraction remains positive. The proposed numerical scheme is based on the direct splitting of macroscopic flux functions of the system of equations. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Moreover, a pressure relaxation procedure is used to fulfill the interface conditions. For validation, the results of suggested scheme are compared with those from the high resolution central upwind and HLLC schemes. The central upwind scheme is also applied for the first time to this model. The accuracy, efficiency and simplicity of the KFVS scheme demonstrate its potential for modeling two-phase flows.

关键词： Six-Equation Model Kinetic Flux-Vector Splitting Scheme Central Upwind Scheme Non-Conservative System Shock Solution

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