ترغب بنشر مسار تعليمي؟ اضغط هنا

Limitation of Finite Difference Scheme in Electroconvection with Unipolar Charge Injection: A base-state Analysis

61   0   0.0 ( 0 )
 نشر من قبل Yifei Guan
 تاريخ النشر 2020
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

The 1D hydrostatic base state of electroconvection driven by unipolar charge injection between two parallel electrodes is investigated using a finite difference method. A boundary layer near the anode surface is derived analytically. The computational grid is required to resolve this boundary layer to maintain high order accuracy.

قيم البحث

اقرأ أيضاً

In this work, the electrohydrodynamic (EHD) instability induced by a unipolar charge injection is extended from a single-phase dielectric liquid to a two-phase system that consists of a liquid-air interface. A volume of fluid (VOF) model based two-ph ase solver was developed with simplified Maxwell equations implemented in the open-source platform OpenFOAMtextsuperscript. The numerically obtained critical value for the linear stability matches well with the theoretical values. To highlight the effect of the slip boundary at interface, the deformation of the interface is ignored. A bifurcation diagram with hysteresis loop linking the linear and finite amplitude criteria, which is Uf = 0.059, was obtained in this situation. It is concluded that the lack of viscous effect at interface leads to a significant increase in the flow intensity, which is the reason for the smaller instability threshold in two-phase system. The presence of interface also changes the flow structure and makes the flow vortices shift closer to the interface.
We present a fully conservative, skew-symmetric finite difference scheme on transformed grids. The skew-symmetry preserves the kinetic energy by first principles, simultaneously avoiding a central instability mechanism and numerical damping. In contr ast to other skew-symmetric schemes no special averaging procedures are needed. Instead, the scheme builds purely on point-wise operations and derivatives. Any explicit and central derivative can be used, permitting high order and great freedom to optimize the scheme otherwise. This also allows the simple adaption of existing finite difference schemes to improve their stability and damping properties.
We analyze the linear stability of the base state of the problem of coupled flow and deformation in a long and shallow rectangular soft hydraulic conduit with a thick top wall. Specifically, the steady base state is computed at low but finite Reynold s number. Then, we show that with the upstream flux fixed and the outlet pressure set to gauge, the flow is linearly stable to infinitesimal flow-wise perturbations. Multiple oscillatory but stable eigenmodes are computed in a range of the reduced Reynolds number, $hat{Re}$, and the so-called fluid--structure interaction (FSI) parameter, $lambda$, indicating the stiffness of this FSI system. These results provide a framework to address, in future work, the individual effects of various aspects of two-way FSI coupling on instability and flow transition in soft hydraulic conduits.
In scalar turbulence it is sometimes the case that the scalar diffusivity is smaller than the viscous diffusivity. The thermally-driven turbulent convection in water is a typical example. In such a case the smallest scale in the problem is the Batche lor scale $l_b$, rather than the Kolmogorov scale $l_k$, as $l_b = l_k/Sc^{1/2}$, where Sc is the Schmidt number (or Prandtl number in the case of temperature). In the numerical studies of such scalar turbulence, the conventional approach is to use a single grid for both the velocity and scalar fields. Such single-resolution scheme often over-resolves the velocity field because the resolution requirement for scalar is higher than that for the velocity field, since $l_b<l_k$ for $Sc>1$. In this paper we put forward an algorithm that implements the so-called multiple-resolution method with a finite-volume code. In this scheme, the velocity and pressure fields are solved in a coarse grid, while the scalar field is solved in a dense grid. The central idea is to implement the interpolation scheme on the framework of finite-volume to reconstruct the divergence-free velocity from the coarse to the dense grid. We demonstrate our method using a canonical model system of fluid turbulence, the Rayleigh-Benard convection. We show that, with the tailored mesh design, considerable speed-up for simulating scalar turbulence can be achieved, especially for large Schmidt (Prandtl) numbers. In the same time, sufficient accuracy of the scalar and velocity fields can be achived by this multiple-resolution scheme. Although our algorithm is demonstrated with a case of an active scalar, it can be readily applied to passive scalar turbulent flows.
65 - Julius Reiss 2014
A simple scheme for incompressible, constant density flows is presented, which avoids odd-even decoupling for the Laplacian on a collocated grids. Energy stability is implied by maintaining strict energy conservation. Momentum is conserved. Arbitrary order in space and time can easily be obtained. The conservation properties hold on transformed grids.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا