افزايش پايداري شبكه بولتزمن در اعداد رينولدز بالا براي جريان تراكم ناپذير

چكيده انگليسي :

Stability Improvement of Lattice Boltzmann Method for High Reynolds Number Incompressible Flows Amin Pesaran Behbahani a pesaranbehbahani@me iut ac ir Date of Submission 2013 3 14 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Mahmud Ashrafizaadeh email Mahmud@cc iut ac ir Abstract In recent years the Lattice Boltzmann method LBM has become attractive Since the incompressible Navier Stokes equations in theory and applications are important it is essential to develop a lattice Boltzmann Equation LBE which can precisely model the incompressible Navier Stokes NS equations in general It is well known that the small Mach number limit is equal to the incompressible limit so it is possible to develop a LBE which can correctly model the incompressible NS equations only with the small Mach number limit Compared to the NS equation based approach the method of LBE offers an alternative treatment for fluid dynamics The LBE often employs uniform lattices to maintain a compact and efficient computational procedure which makes it less efficient to perform flow simulations when there is a need for high resolution near the body and or there is a far field boundary To resolve these difficulties a multi block method is developed An accurate conservative interface treatment between neighboring blocks is adopted and demonstrated that it satisfies the continuity of mass momentum and stresses across the interface Several test cases are employed to assess accuracy improvement with respect to grid refinement the impact of the corner singularity and the Reynolds number scaling The present multi block method can substantially improve the accuracy and computational efficiency of the LBE for viscous flow computations From a computational view point the notable advantages of LBM are its parallelism simplicity of programming and ease of incorporating microscopic interactions However despite the notable success of the LBM some shortcoming of the LB model are apparent For instance the model may lead to numerical instability when the dimensionless relaxation time is close to 0 5 To overcome this shortcoming different method has been suggested like Multi Relaxation Time MRT Two Relaxation Time TRT and multi block The MRT LB model is of better numerical stability and has more degrees of freedom than the commonly used Single Relaxation Time SRTLB model The main idea of the MRT LB model is that the advection is mapped onto the momentum space by a linear transformation and the flux is still finished in the velocity space Most of the existing MRT LB models are constructed for the compressible NS equations in the low Mach number limit and it is well understood that compressible error exits for simulating incompressible fluid flows The recovered macroscopic equations from the existing MRT LB model is the approximate incompressible NS equations through the Chapman Enskog CE expansion Considering the significance of the incompressible NS equations in theory and applications it is necessary to establish an MRT LB model which can exactly model the incompressible NS equations In this work MRT TRT and SRT models has been used to simulate cavity and flow on airfoil and studying stability of each one Then for increasing the stability of each collision model they have been combined with a multi block method Also using the multi block model for improve the stability needs to identify area subjected to numerical instability in the computational domain Another algorithm that has been introduced in this thesis is a combination of different collision models namely multi collision A comparison between its stability and that of the MRT TRT and etc has been given Keywords Lattice Boltzmann Stability Improvement Multi Block Multi Collision PDF created with pdfFactory trial version www pdffactory com

پسران بهبهاني، امين

افزايش پايداري شبكه بولتزمن در اعداد رينولدز بالا براي جريان تراكم ناپذير

ضريب تخفيف منفرد , ضريب تخفيف دوگانه , ضريب تخفيف چندگانه , روش چند بلوكي , روش چند برخوردي