اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدReconstructing fluid dynamics with micro-finite element
66
0
0.0
(
0
)
تأليف
Wennan Zou
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In the theory of the Navier-Stokes equations, the viscous fluid in incompressible flow is modelled as a homogeneous and dense assemblage of constituent fluid particles with viscous stress proportional to rate of strain. The crucial concept of fluid flow is the velocity of the particle that is accelerated by the pressure and viscous interaction around it. In this paper, by virtue of the alternative constituent micro-finite element, we introduce a set of new intrinsic quantities, called the vortex fields, to characterise the relative orientation between elements and the feature of micro-eddies in the element, while the description of viscous interaction in fluid returns to the initial intuition that the interlayer friction is proportional to the slip strength. Such a framework enables us to reconstruct the dynamics theory of viscous fluid, in which the flowing fluid can be modelled as a finite covering of elements and consequently indicated by a space-time differential manifold that admits complex topological evolution.
قيم البحث
اقرأ أيضاً
Capillary phenomena are involved in many industrial processes, especially those dealing with composite manufacturing. However, their modelling is still challenging. Therefore, a finite element setting is proposed to better investigate this complex is
sue. The variational formulation of a liquid-air Stokes system is established, while the solid substrate is described through boundary conditions. Expressing the weak form of Laplaces law over liquid-air, liquid-solid and air-solid interfaces, leads to a natural enforcement of the mechanical equilibrium over the wetting line, without imposing explicitly the contact angle itself. The mechanical problem is discretized by using finite elements, linear both in velocity and pressure, stabilized with a variational multiscale method, including the possibility of enrichment of the pressure space. The moving interface is captured by a Level-Set methodology, combined with a mesh adaptation technique with respect to both pressure and level-set fields. Our methodology can simulate capillary-driven flows in 2D and 3D with the desired precision: droplet spreading, droplet coalescence, capillary rise. In each case, the equilibrium state expected in terms of velocity, pressure and contact angle is reached.
Diving induces large pressures during water entry, accompanied by the creation of cavity and water splash ejected from the free water surface. To minimize impact forces, divers streamline their shape at impact. Here, we investigate the impact forces
and splash evolution of diving wedges as a function of the wedge opening angle. A gradual transition from impactful to smooth entry is observed as the wedge angle decreases. After submersion, diving wedges experience significantly smaller drag forces (two-fold smaller) than immersed wedges. Our experimental findings compare favorably with existing force models upon the introduction of empirically-based corrections. We experimentally characterize the shapes of the cavity and splash created by the wedge and find that they are independent of the entry velocity at short times, but that the splash exhibits distinct variations in shape at later times. We propose a one-dimensional model of the splash that takes into account gravity, surface tension and aerodynamics forces. The model shows, in conjunction with experimental data, that the splash shape is dominated by the interplay between a destabilizing Venturi-suction force due to air rushing between the splash and the water surface and a stabilizing force due to surface tension. Taken together, these findings could direct future research aimed at understanding and combining the mechanisms underlying all stages of water entry in application to engineering and bio-related problems, including naval engineering, disease spreading or platform diving.
Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at scale rema
ins daunting, limited by the computational cost of resolving the smallest spatiotemporal features. This leads to unfavorable trade-offs between accuracy and tractability. Here we use end-to-end deep learning to improve approximations inside computational fluid dynamics for modeling two-dimensional turbulent flows. For both direct numerical simulation of turbulence and large eddy simulation, our results are as accurate as baseline solvers with 8-10x finer resolution in each spatial dimension, resulting in 40-80x fold computational speedups. Our method remains stable during long simulations, and generalizes to forcing functions and Reynolds numbers outside of the flows where it is trained, in contrast to black box machine learning approaches. Our approach exemplifies how scientific computing can leverage machine learning and hardware accelerators to improve simulations without sacrificing accuracy or generalization.
Herein, the Karman vortex system is considered to be a large recurrent neural network, and the computational capability is numerically evaluated by emulating nonlinear dynamical systems and the memory capacity. Therefore, the Reynolds number dependen
ce of the Karman vortex system computational performance is revealed and the optimal computational performance is achieved near the critical Reynolds number at the onset of Karman vortex shedding, which is associated with a Hopf bifurcation. Our finding advances the understanding of the relationship between the physical properties of fluid dynamics and its computational capability as well as provides an alternative to the widely believed viewpoint that the information processing capability becomes optimal at the edge of chaos.
Truncated Taylor expansions of smooth flow maps are used in Hamiltons principle to derive a multiscale Lagrangian particle representation of ideal fluid dynamics. Numerical simulations for scattering of solutions at one level of truncation are found
to produce solutions at higher levels. These scattering events to higher levels in the Taylor expansion are interpreted as modeling a cascade to smaller scales.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
