An efficient and robust pressure correction projection method with the CNMT1 finitedifference scheme is presented in this paper for the numerical solution of the incompressible Navier-Stokes equations. It is proved th...
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An efficient and robust pressure correction projection method with the CNMT1 finitedifference scheme is presented in this paper for the numerical solution of the incompressible Navier-Stokes equations. It is proved that on fixed spatial grids the method is of secondorder global accuracy in time; this is confirmed with numerical experiment on an examplewith an exact solution. Then the method is used for numerical simulation of the drivencavity flow problems; the asymptotic periodic solution for Re=10000 is preseated.
高温超导体因其独特的电子性质和非常规超导行为而备受关注。尤其是高能离子注入、压力、电磁场等外部场引起的高温超导材料相变,已成为研究的热点。然而,相关的内在机理仍未完全被揭示。第一性原理计算被广泛认为是一种有效的方法,用以深入探究其内在机理。本研究利用第一性原理计算,探讨了不同泛函(PBE, PBE + U, HSE06)对YBa2Cu3O7 (YBCO7)中氧缺失现象对电子转移性质及超导性能的影响。结果表明,氧的缺失显著改变能带结构,不同泛函预测的结果有很大偏差,三种不同泛函预测的YBa2Cu3O6 (YBCO6)的能隙范围分别为0 eV、0.88 eV和1.69 eV。较大的能隙表明材料呈现绝缘态,而没有能隙则表明材料仍保持金属性。通过与实验结果对比,我们发现HSE06泛函在描述该材料的金属–绝缘性相变方面较为合理,且能隙的存在与否主要受铜的dz2轨道影响,从PBE泛函计算中发现YBCO6没有带隙是因为Cu的dyz轨道占据。此外,O(4)缺失可导致材料c轴伸长,这一现象与实验中He离子辐照后材料的X射线衍射(XRD)分析结果趋势一致。我们的发现将有助于解释YBCO7在外部场作用下,尤其是He离子辐照引发的金属绝缘相变现象,将为高温超导材料及其器件应用提供理论基础和新思路。High-temperature superconductors have attracted significant attention due to their unique electronic properties and unconventional superconducting behavior. In particular, phase transitions of high-temperature superconducting materials induced by external fields such as high-energy ion implantation, pressure, and electromagnetic fields have become a research hotspot. However, the underlying mechanisms remain not fully understood. First-principles calculations are widely regarded as an effective method to explore these intrinsic mechanisms in depth. In this study, first-principles calculations are employed to investigate the effects of oxygen vacancy phenomena on the electronic transfer properties and superconducting performance of YBa2Cu3O7 (YBCO7) under different functionals (PBE, PBE + U, HSE06). The results show that oxygen vacancies significantly alter the band structure, with considerable discrepancies observed in the predictions of different functionals. The calculated band gap for YBa2Cu3O6 (YBCO6) ranges from 0 to 1.69 eV. A larger band gap suggests an insulating state, while the absence of a band gap indicates that the material remains metallic. By comparing the results with the experimental results, we find that the HSE06 functional provides the most reasonable predictions. The presence or absence of a band gap is primarily influenced by copper orbitals. Oxygen vacancy at O(4) can cause the material’s c-axis to elongate,
A second order accurate implicit finite difference scheme CNMT2 is proposed in this paper for the unsteady incompressible Navier-Stokes equations. It is proved that the scheme is unconditionally nonlinearly stable on ...
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A second order accurate implicit finite difference scheme CNMT2 is proposed in this paper for the unsteady incompressible Navier-Stokes equations. It is proved that the scheme is unconditionally nonlinearly stable on smoothly nonuniform halfstaggered meshes; this stability also holds for this scheme with the pressure correction projection method. However, it is found that the pressure correction projection method may lead to deviation problems in practical simulation of high Re flow;the reason and the cure is given in this paper in terms of differential-algebraic equations.
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