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Numerical methods for multi-scale modeling of non-Newtonian flows.

機譯：非牛頓流多尺度建模的數值方法。

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This work presents numerical methods for the simulation of Non-Newtonian fluids in the continuum as well as the mesoscopic level. The former is achieved with Direct Numerical Simulation (DNS) spectral h/p methods, while the latter employs the Dissipative Particle Dynamics (DPD) technique. Physical results are also presented as a motivation for a clear understanding of the underlying numerical approaches.; The macroscopic simulations employ two non-Newtonian models, namely the Reiner-Ravlin (RR) and the viscoelastic FENE-P model. (1) A spectral viscosity method defined by two parameters &egr;, M is used to stabilize the FENE-P conformation tensor c. Convergence studies are presented for different combinations of these parameters. Two boundary conditions for the tensor c are also investigated. (2) Agreement is achieved with other works for Stokes flow of a two-dimensional cylinder in a channel. Comparison of the axial normal stress and drag coefficient on the cylinder is presented. Further, similar results from unsteady two- and three-dimensional turbulent flows past a flat plate in a channel are shown. (3) The RR problem is formulated for nearly incompressible flows, with the introduction of a mathematically equivalent tensor formulation. A spectral viscosity method and polynomial over-integration are studied. Convergence studies, including a three-dimensional channel flow with a parallel slot, investigate numerical problems arising from elemental boundaries and sharp corners. (4) The round hole pressure problem is presented for Newtonian and RR fluids in geometries with different hole sizes. Comparison with experimental data is made for the Newtonian case. The flaw in the experimental assumptions of undisturbed pressure opposite the hole is revealed, while good agreement with the data is shown. The Higashitani-Pritchard kinematical theory for RR, fluids is recovered for round holes and an approximate formula for the RR Stokes hole pressure is presented.; The mesoscopic simulations assume bead-spring representations of polymer chains and investigate different integrating schemes of the DPD equations and different intra-polymer force combinations. (1) A novel family of time-staggered integrators is presented, taking advantage of the time-scale disparity between polymer-solvent and solvent-solvent interactions. Convergence tests for relaxation parameters for the velocity-Verlet and Lowe's schemes are presented. (2) Wormlike chains simulating lambda- DNA molecules subject to constant shear are studied, and direct comparison with Brownian Dynamics and experimental results is made. The effect of the number of beads per chain is examined through the extension autocorrelation function. (3) The Schmidt number (Sc) for each numerical scheme is investigated and the dependence on the scheme's parameters is shown. Re-visiting the wormlike chain problem under shear, we recover a better agreement with the experimental data through proper adjustment of Sc.
機譯：這項工作提出了數值方法來模擬連續(xù)體以及介觀層面的非牛頓流體。前者是通過直接數值模擬（DNS）光譜h / p方法實現的，而后者則采用了耗散粒子動力學（DPD）技術。物理結果也被提出來作為對潛在的數值方法的清晰理解的動力。宏觀模擬采用兩個非牛頓模型，即Reiner-Ravlin（RR）模型和粘彈性FENE-P模型。 （1）使用由兩個參數＆egr ;, M定義的光譜粘度法來穩(wěn)定FENE-P構象張量c。提出了針對這些參數的不同組合的收斂性研究。還研究了張量c的兩個邊界條件。 （2）對于通道中二維圓柱的斯托克斯流，與其他工作達成了協議。給出了圓柱體上軸向法向應力和阻力系數的比較。此外，示出了通過通道中的平板的不穩(wěn)定二維和三維湍流的相似結果。 （3）通過引入數學上等效的張量公式，為幾乎不可壓縮的流量公式化了RR問題。研究了光譜粘度法和多項式超積分。收斂性研究（包括帶有平行槽的三維通道流）研究了元素邊界和尖角引起的數值問題。 （4）提出了具有不同孔徑的幾何形狀的牛頓流體和RR流體的圓孔壓力問題。對于牛頓情況，與實驗數據進行了比較。揭示了與孔相對的不受擾動壓力的實驗假設中的缺陷，同時顯示了與數據的良好一致性。 Higashitani-Pritchard的RR運動學理論，為圓孔回收流體，并給出了RR Stokes孔壓力的近似公式。介觀模擬假定聚合物鏈為珠狀彈簧，并研究了DPD方程的不同積分方案和不同的聚合物內力組合。 （1）利用聚合物-溶劑相互作用和溶劑-溶劑相互作用之間的時標差異，提出了一個新的時間交錯積分器族。提出了速度-Verlet和Lowe方案的松弛參數的收斂性測試。 （2）研究了蠕蟲樣鏈模擬恒定剪切作用下的lambda DNA分子，并與Brownian Dynamics進行了直接比較和實驗結果。通過擴展自相關函數檢查每條鏈的珠子數量的影響。 （3）研究了每種數值方案的施密特數（Sc），并顯示了對方案參數的依賴性。重新研究剪切下的蠕蟲狀鏈問題，我們通過適當調整Sc可以恢復與實驗數據的更好一致性。

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