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Asymptotic-Preserving Weno Schemes for Boltzmann Model Equations and Rarefied Gas Flow Simulation
Jaw-Yen Yang,Manuel Diaz,W. Y. Kang,J. C. Huang 한국전산유체공학회 2014 한국전산유체공학회 학술대회논문집 Vol.2014 No.10
A class of asymptotic-preserving implicit-explicit Runge-Kutta WENO schemes for solving the Boltzmann model equation is presented. The conserved discrete ordinate method for discretize the velocity space is implemented. The asymptotic-preserving time integrating scheme allows larger time step and limiting Euler solution to be approached in the Chapman-Enskog expansion. Computations of rarefied gas flows covering wide Knudsen numbers are given to illustrate the method. The present strategy provides an accurate and robust framework for treating rarefied gas flows. The method is also applicable to semiclassical Boltzmann model equation and its solutions will be also included.
Simulation of Axisymmetric Scramjet Combustion Flowfields Using Weno Navier-Stokes Solvers
Jaw-Yen Yang,J.C. Huang,Y S. Lai,C. S. Kuo 한국전산유체공학회 2014 한국전산유체공학회 학술대회논문집 Vol.2014 No.10
This study is based on the theory of gas dynamics and uses the Navier-Stokes equations as the governing equations to solve the fluid flow field problems of the scramjet. For the turbulent flow, we use the simple Spalart-Allmaras one equation turbulence model (S-A model) which produces better results for near wall and boundary layer flow field problems. The lower-upper symmetric Gauss-Seidel (LU-SGS) implicit scheme, whose results converge efficiently under steady state conditions, is combined with the Weighted Essentially Non-Oscillatory (WENO) scheme to construct a numerical model of the scramjet. Using the WENO scheme’s high-order accuracy and its non-oscillatory solution at discontinuous areas, we can solve supersonic flow field problems with multiple shock wave interactions. This simulation procedure is verified against two partial examples from literature to ensure its accuracy, and is then applied to a complete geometric model of a scramjet with different initial conditions for a full flow field analysis. The Mach number, density, static temperature and pressure are found and the results discussed. It is found that even when the shock waves are very close to each other, the WENO scheme produces better simulation results than other numerical approaches.
Simulation of axisymmetric scramjet inlet flow fields using anti-diffusive WENO Navier-Stokes solver
Juan-Chen Huang,Jaw-Yen Yang,Yu-Hsuan Lai,Jeng-Shan Guo 대한기계학회 2015 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.29 No.5
This study is based on the theory of gas dynamics and uses the Navier-Stokes equations as the governing equations to solve the hypersonicflow problems of the scramjet. For the turbulent flow, we use the Spalart-Allmaras one equation turbulence model, which producesbetter results for near wall and boundary layer flow field problems. The lower-upper symmetric Gauss-Seidel implicit scheme, whichenables results to converge efficiently under steady state conditions, is combined with the anti-diffusive weighted essentially nonoscillatory(WENO) scheme to yield an accurate and efficient simulation tool for an axisymmetric scramjet flow field analysis. Using theWENO scheme’s high-order accuracy and its non-oscillatory solution at discontinuous regions, we can solve the hypersonic flow problemsinvolving complex shock-shock/shock-boundary layer interactions inside the flow path. This simulation procedure is first verifiedagainst two existing partial examples to ensure its accuracy, and is then applied to a complete scramjet model with different initial conditionsfor a full flow field analysis. The aerodynamic data of Mach number, density, static temperature and pressure are obtained and theresults discussed. The anti-diffusive WENO scheme produces more accurate resolution of shock and slip lines and their complex multipleinteractions than other numerical approaches. This is of crucial importance for the scramjet complete flow field analysis as multipleshock-boundary layer and discontinuities interactions often occur within the long flow path.