• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Physics-informed deep learning for incompressible laminar flows

    2020-07-01 05:14:02ChengpingRoHoSunYngLiu

    Chengping Ro, Ho Sun*, Yng Liu,*

    a Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115, USA

    b Department of Civil and Environmental Engineering, Northeastern University, Boston, MA 02115, USA

    c Department of Civil and Environmental Engineering, MIT, Cambridge, MA 02139, USA

    Keywords:Physics-informed neural networks(PINN)Deep learning Fluid dynamics Incompressible laminar flow

    ABSTRACT Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training a reliable model. This can be achieved by incorporating the residual of physics equations into the loss function. Through minimizing the loss function, the network could approximate the solution. In this paper, we propose a mixed-variable scheme of physics-informed neural network (PINN) for fluid dynamics and apply it to simulate steady and transient laminar flows at low Reynolds numbers. A parametric study indicates that the mixed-variable scheme can improve the PINN trainability and the solution accuracy. The predicted velocity and pressure fields by the proposed PINN approach are also compared with the reference numerical solutions. Simulation results demonstrate great potential of the proposed PINN for fluid flow simulation with a high accuracy.

    Deep learning (DL) has attracted tremendous attentions in recent years in the field of computational mechanics due to its powerful capability in nonlinear modeling of complex spatiotemporal systems. According to a technical report [1] by U.S.Department of Energy, a DL-based approach should be featured with the domain-aware, interpretable and robust to be a general approach for solving the science and engineering problems. Recent studies of leveraging DL to model physical system include,just to name a few [2-6]. These applications can be categorized into two types based on how the DL model is constructed: in either data-driven or physics-informed manner. In a data-driven framework, the DL model is constructed as a black-box to learn a surrogate mapping from the formatted input x ∈Rmto the output y ∈Rn. The exceptional approximation ability of deep neural network (DNN) makes possible to learn the mapping even when the dimensionality m and n are very high. The training dataset { x,y}, typically very rich, can be obtained by conducting high-fidelity simulations using exact solvers (e.g., see Refs.[3, 4, 7]). Nevertheless, obtaining a rich and sufficient dataset from simulations for training a reliable DL model is computationally expensive and requires careful case design. To address this fundamental challenge, physics-informed DL explicitly embed the physical laws (e.g., the governing partial differential equations (PDEs), initial/boundary conditions, etc.) into the DNN, constraining the network's trainable parameters within a feasible solution space. The objective of exploiting physical laws in DNN is assumed to (1) reduce the large dependency of the model on available dataset in terms of both quality and quantity,and (2) improve the robustness and interpretability of the DL model. In this regard, DNN essentially has the capacity of approximating the latent solutions for PDEs [8, 9], with distinct benefits summarized as follows: (1) the superior interpolation ability of DNN, (2) the approximated solution has a close form with its infinite derivative continuous, and (3) state-of-the-art hardware advances make the numerical implementation and parallelization extremely convenient.

    More recently, Raissi et al. [5, 6] introduced a general framework of PINN and demonstrated its capacity in modeling complex physical systems such as solving/identifying PDEs. A huge difference from some of the previous studies is that, in addition to the physical laws, the PINN can also exploit the available measurement data, making it possible to discover the systems whose physics are not fully understood. In particular, seminal contributions of using PINN to model fluid flows have been made recently. For example, Kissas et al. [10] employed PINN to predict the arterial blood pressure based on the MRI data and the conservation laws. Sun et al. [11] proposed a PINN approach for surrogate modeling of fluid flows without any simulation data. Zhu et al. [12] proposed a physics-constrained convolutional encoder-decoder network and a generative model for modeling of stochastic fluid flows.

    In this paper, we formulate a mixed-variable PINN scheme for simulation of viscous incompressible laminar flows without any measurement data. The remaining this paper is organized as follows. We will introduce the methodology of the mixed-variable PINN and the mathematical formulation for fluid dynamics.The steady and transient laminar flows passing a circular cylinder will be modeled using the proposed PINN scheme without any simulation data. A comparison study is made to demonstrate the improved solution accuracy and network trainability by the proposed scheme.

    Let us consider the incompressible Newtonian flow governed by the following Navier–Stokes equations:

    where ? is the Nabla operator, v =(u, v) is the velocity vector, p is the pressure, μ is the viscosity of the fluid, ρ is the density of fluid and g is the gravitational acceleration. When leveraging PINN to solve the aforementioned PDEs, minimizing a complex residual loss resulted from Eq. (2) is intractable due to its complex form with multiple latent variables (e.g., v and p) and high-order derivatives (e.g., ?2). In order to design an easily trainable PINN, we convert the Navier–Stokes equation in Eq. (2)to the following continuum and constitutive formulations:

    where σ is the Cauchy stress tensor and p =?trσ/2. The benefits of using the continuum-mechanics-based formulation are twofold: (1) reducing the order of derivatives when a mixed-variable scheme in PINN is used and (2) improved trainability of DNN as found in the comparison of numerical results.

    The proposed mixed-variable scheme is used in this paper to solve the aforementioned PDEs (see Eqs. (1), (3) and (4)) that govern the laminar flow dynamics. The salient feature of PINN is that the physical fields are approximated globally by a DNN. In free condition of the flow. In this way, the continuity equation will be satisfied automatically. For a two-dimensional problem,the velocity components can be computed by particular, the DNN maps the spatiotemporal variables { t,x}Tto the mix-variable solution { ψ, p,σ}, where the stream function ψ is employed rather than the velocity v to ensure the divergence[u,v,0]=?×[0,0,ψ]. Note that v =[u,v] is taken as the latent vari-

    able. The automatic differentiation is used to obtain the partial derivatives of the DNN output regarding the time and space(e.g., t , x and y). The loss function is composed of the data loss Jd(if measurements are available) and the physics loss Jp. The physics loss Jpis the summation of the governing equation loss Jgand the initial and boundary condition loss Ji/bc, given by

    where r(·)denotes the residual, | |·|| denotes the ?2norm and N(·)denotes the number of collocation points (subscripts g for governing equation, I for initial condition, n b for Neumann boundary, and d b for Dirichlet boundary). The total physics loss Jpis defined as

    where β >0 is a user-defined weighting coefficient for initial and boundary condition loss. Noteworthy, having the measurement data makes the fluid flow modeling data-driven, which is however not a prerequisite. The architecture of the proposed PINN for fluid dynamics simulation is presented in Fig. 1. In this paper, no measurement data from simulations or physical experiments is used for training the PINN.

    In this section, we employ the proposed PINN to model the steady and transient flows passing a circular cylinder. A parabolic velocity profile is applied on the inlet while the zero pressure condition is applied on the outlet, as shown in Fig. 2. Non-slip conditions are enforced on the wall and cylinder boundaries.The gravity is ignored in both two cases. The proposed PINN is implemented on the TensorFlow [13] and the source codes can be found in https://github.com/Raocp/PINN-laminar-flow.

    For the steady case, the dynamic viscosity and density of the fluid is 2×10-2kg/(m·s) and 1 kg/m3respectively. The normal velocity profile is defined as

    Fig. 1. Architecture of the physics-informed neural network for fluid dynamics. Note that α is a user-defined weighting coefficient. w and b are weights and biases for the DNN. The constraint of initial and boundary conditions can be converted as residuals adding to the loss function based on Lagrangian multipliers. The data loss Jd is present only when data is available.

    Fig. 2. Diagram of the computation model

    with Umaxequal to 1.0 m/s which results in a small Reynolds number so that the flow is dominated by laminar flow. A total number of Ng=50000 collocation points, which includes Ndb=1200 Dirichlet boundary (cylinder, wall, inlet) points and Nnb=200 Neumann boundary (outlet) points, are generated using Latin hypercube sampling (LHS) for the training the network. It should be noted that the collocation points are refined near the cylinder to better capture the details of the flow.A grid search strategy is used to find an optimal combination of depth and width for the network. The relative ?2error defined by

    is used as the metric for comparison, where f is the physical quantity of interest, and M is the total number of reference points. Adam [14] and Limited-memory BFGS (L-BFGS)optimizer [15] is employed to train the DNN due to their good convergence speed demonstrated in the tests. We also implement the traditional scheme for fluid dynamics employed in [5,6] where the stream function and pressure { ψ, p} act as the output variables. From the relative ?2errors of the velocity field (see Table 1), it can be seen that the network of 8×40 achieves the best result among all the configurations. The mixed-variable PINN improves the accuracy of numerical results over the traditional PINN.

    The predicted velocity and pressure fields by the PINNs with mixed-variable and traditional scheme are shown in Fig. 3(b, c).

    Table 1 Relative ?2 errors (unit: 1 0?2) of the velocity field for different DNN configurations with β =2 (left: the traditional scheme; right: the proposed mixed-variable scheme)

    The reference solution is obtained from the ANSYS Fluent 18.1 package (finite volume-based) [16] (see Fig. 3a). It can be observed that the PINN with the traditional scheme fails to model the flow. In particular, the traditional scheme fails to enforce the non-slip condition on the lower and upper boundaries.However, the steady velocity and pressure fields are well reproduced by the PINN with mixed-variable scheme. It is worth mentioning that the pressure distribution on the cylinder surface is typically of interest for computing the resultant drag and lift forces. Therefore, we compare the pressure distributions obtained by two types of PINN and ANSYS Fluent as shown in Fig.4. The overall agreement between the mixed-variable PINN and ANSYS Fluent is very good.

    We also compare the performance of these two schemes under various β which controls the weight of the boundary condition loss. As shown in Fig. 5, the convergence of the traditional scheme is significantly affected by β, though the final loss can be reduced by increasing the value of β up to 10. However, the mixed-variable scheme yields consistent results for various β.The improvement by the mixed-variable scheme is thanks to the reduced order of derivatives required to construct the loss function, in comparison with the traditional scheme [5, 6], which makes the optimization problem easier.

    The transient flow with the same computation domain depicted in Fig. 2 is considered in this case. The dynamic viscosity of the flow is μ=5×10?3kg/(m·s) while the density is ρ=1 kg/m3. The time duration for the modeling is 0.5 s. Three virtual pressure probes P1(0.15, 0.2) m, P2(0.2, 0.25) m and P3(0.25, 0.2) m are installed on the surface of the cylinder. The flow is initially still while a time-varying parabolic inlet velocity profile is applied subsequently, which is defined as

    Fig. 3. Velocity and pressure fields of the steady flow passing a circular cylinder. a Reference solution from ANSYS Fluent. b Mixed-variable scheme solution with 8×40 network. c Traditional scheme solution with 8×40 network. The hyperparameters and collocation points for training these two PINNs are kept same.

    Fig. 4. Distribution of pressure on cylinder. Network of 8×40 and β=2 are used.

    Fig. 5. Comparison of convergence curves with respect to coefficient β. Network of 8×40 is used in all the cases. 10000 iterations trained with Adam optimizer followed by L-BFGS optimizer

    Fig. 6. Transient normal velocity profile.

    where Umaxequals to 0.5 m/s and the period T is 1.0 s. The remaining boundary conditions are the same as those in the previous example. The inflow velocity as a function of t and y is visualized in Fig. 6. The width and depth of the network are selected to be 50 and 7 respectively while the coefficient β is set to be 2. A total number of Ng=120000 collocation points, which include Ndb=9600 points on cylinder, wall and inlet boundaries,Nnb=3200 points on outlet, and NI=3500 points at initial time,are used to train the network.

    Fig. 7. Snapshots of the PINN-predicted transient flow fields passing a circular cylinder

    Fig. 8. Pressure time histories on a P1, b P2 and c P3 probes.

    Three snapshots of the predicted flow fields are presented in Fig. 7 which shows the evolution of the flow as the inlet velocity increases over time. The reference flows obtained by ANSYS Fluent are not shown here since the PINN-predicted result matches very well with them. The pressure time histories on three probes obtained from the proposed PINN are compared with those from ANSYS Fluent, as depicted in Fig. 8. It can be seen that the proposed PINN approach can well predict the pressure time histories in a transient flow.

    We propose a mixed-variable PINN scheme for modeling fluid flows, with particular applications to incompressible laminar flows. The salient features of the proposed scheme include (1)employing the general continuum equations together with the material constitutive law rather than the derived Navier–Stokes equations, and (2) using stream function to ensure the divergence free condition of the flow in a mixed-variable setting. The comparison study indicates the benefits (high accuracy and good trainability) of the proposed mixed-variable scheme. In both the steady and transient flow cases, the result produced by the PINN shows a good agreement with the reference numerical solutions.

    It is notable that the applications in this paper are limited to the laminar flows at low Reynolds numbers, although the approach is in theory applicable to turbulent flows at large Reynolds numbers. However, it requires discretizing the computation domain with much finer collocation points which will lead to computer memory issues and drastically increase the computational cost. Our future work aims to address this challenge by developing a "divide-and-conquer" training scheme in the context of transfer learning, that is to divide the time domain into multiple steps and re-train the network partially while fixing the weights and the biases from the previous step [17].

    亚洲在线观看片| 国产极品天堂在线| 久久久成人免费电影| 美女xxoo啪啪120秒动态图| av女优亚洲男人天堂| 欧美成人免费av一区二区三区| 亚洲av成人精品一区久久| 搞女人的毛片| 精品久久久久久久久亚洲| 嫩草影院精品99| 成人av在线播放网站| 中文字幕制服av| 欧美高清成人免费视频www| 人妻夜夜爽99麻豆av| 久久99热这里只有精品18| 91在线精品国自产拍蜜月| 美女高潮的动态| 赤兔流量卡办理| 日本黄大片高清| 亚洲国产精品专区欧美| 欧美zozozo另类| 最近的中文字幕免费完整| 大又大粗又爽又黄少妇毛片口| 欧美区成人在线视频| 少妇被粗大猛烈的视频| av卡一久久| 99热6这里只有精品| 久久精品熟女亚洲av麻豆精品 | 亚洲激情五月婷婷啪啪| 国产一区二区在线av高清观看| 日本一二三区视频观看| 国产欧美日韩精品一区二区| 午夜福利在线观看免费完整高清在| 麻豆久久精品国产亚洲av| 免费无遮挡裸体视频| 成人av在线播放网站| 国产美女午夜福利| 久久久欧美国产精品| 欧美一区二区精品小视频在线| 亚洲av免费在线观看| 午夜福利在线观看吧| 内地一区二区视频在线| 美女脱内裤让男人舔精品视频| 亚洲av成人精品一二三区| av在线播放精品| 免费看av在线观看网站| 大香蕉久久网| 亚洲综合色惰| 国产真实乱freesex| 精品国内亚洲2022精品成人| 寂寞人妻少妇视频99o| 亚洲18禁久久av| 国产精品熟女久久久久浪| 欧美3d第一页| 乱系列少妇在线播放| 精品久久久久久久久亚洲| 亚洲国产精品sss在线观看| 熟女电影av网| 亚洲欧美日韩高清专用| 在线观看美女被高潮喷水网站| 精品一区二区免费观看| 国产精品福利在线免费观看| 久久欧美精品欧美久久欧美| 久久久亚洲精品成人影院| 欧美日韩精品成人综合77777| 亚洲av免费在线观看| 一夜夜www| 亚洲国产精品成人久久小说| 久久精品国产99精品国产亚洲性色| 干丝袜人妻中文字幕| 十八禁国产超污无遮挡网站| 国产淫语在线视频| 欧美不卡视频在线免费观看| av免费在线看不卡| 99久久精品国产国产毛片| 精品久久久久久久久久久久久| 在线观看66精品国产| 99久久精品热视频| 男女视频在线观看网站免费| 国产大屁股一区二区在线视频| 成人亚洲欧美一区二区av| www.色视频.com| 欧美xxxx黑人xx丫x性爽| 别揉我奶头 嗯啊视频| .国产精品久久| 亚洲综合色惰| 午夜激情欧美在线| 看免费成人av毛片| 美女黄网站色视频| 简卡轻食公司| 欧美激情国产日韩精品一区| 久久精品国产自在天天线| 性插视频无遮挡在线免费观看| 99久久人妻综合| 色网站视频免费| 亚洲伊人久久精品综合 | 啦啦啦啦在线视频资源| 色综合色国产| 国产男人的电影天堂91| 国产中年淑女户外野战色| 亚洲欧美成人精品一区二区| 日本色播在线视频| 一区二区三区免费毛片| 亚洲美女搞黄在线观看| 三级国产精品欧美在线观看| 中国国产av一级| 免费看av在线观看网站| 波野结衣二区三区在线| 国产成人精品婷婷| 三级毛片av免费| 国产精品不卡视频一区二区| 黄片无遮挡物在线观看| 午夜福利在线观看吧| 日本一本二区三区精品| 国产av在哪里看| 天美传媒精品一区二区| 国产在线一区二区三区精 | 亚洲欧美日韩卡通动漫| 国产高清三级在线| 村上凉子中文字幕在线| 欧美zozozo另类| 国产亚洲av片在线观看秒播厂 | 久久99蜜桃精品久久| 日日干狠狠操夜夜爽| 欧美高清性xxxxhd video| .国产精品久久| 五月玫瑰六月丁香| 麻豆精品久久久久久蜜桃| 久久精品国产亚洲av涩爱| 91av网一区二区| 毛片一级片免费看久久久久| 联通29元200g的流量卡| 亚洲精品日韩av片在线观看| 精品久久久久久久末码| 成人综合一区亚洲| 精品人妻视频免费看| 日日摸夜夜添夜夜爱| 亚洲美女搞黄在线观看| 国产一级毛片七仙女欲春2| 成年女人永久免费观看视频| 特大巨黑吊av在线直播| 寂寞人妻少妇视频99o| 淫秽高清视频在线观看| 尤物成人国产欧美一区二区三区| 神马国产精品三级电影在线观看| 毛片一级片免费看久久久久| 中文字幕av在线有码专区| 亚洲欧美日韩无卡精品| 免费观看的影片在线观看| 成人午夜精彩视频在线观看| 精品国产三级普通话版| 日韩亚洲欧美综合| 久久精品国产亚洲av涩爱| 国产成人91sexporn| 日韩亚洲欧美综合| 黄色配什么色好看| 一本—道久久a久久精品蜜桃钙片 精品乱码久久久久久99久播 | 长腿黑丝高跟| 久热久热在线精品观看| 国产精品一区二区性色av| 久久精品影院6| 狠狠狠狠99中文字幕| www.av在线官网国产| 国产精品.久久久| 亚洲自拍偷在线| av卡一久久| 国产成人精品一,二区| 国产精品国产三级专区第一集| 最近中文字幕高清免费大全6| 99久久成人亚洲精品观看| 寂寞人妻少妇视频99o| 嫩草影院精品99| 亚洲人成网站在线播| 人体艺术视频欧美日本| 成人漫画全彩无遮挡| 国产精品久久电影中文字幕| 日韩一本色道免费dvd| 观看美女的网站| 精品久久久久久久久久久久久| 人妻夜夜爽99麻豆av| 青青草视频在线视频观看| 中文字幕免费在线视频6| 亚洲经典国产精华液单| 在线天堂最新版资源| 国产一级毛片在线| 午夜精品一区二区三区免费看| 欧美+日韩+精品| 2022亚洲国产成人精品| 综合色av麻豆| 日本黄色片子视频| 波多野结衣巨乳人妻| 精品熟女少妇av免费看| 爱豆传媒免费全集在线观看| 免费观看的影片在线观看| 亚洲国产成人一精品久久久| 高清在线视频一区二区三区 | 国产老妇女一区| 国产不卡一卡二| 日韩成人av中文字幕在线观看| 一级黄片播放器| 看黄色毛片网站| 国产精品综合久久久久久久免费| 男人舔奶头视频| 国产av不卡久久| 最近手机中文字幕大全| 99久久成人亚洲精品观看| 黄色配什么色好看| 精品久久久久久电影网 | 日本五十路高清| 亚洲婷婷狠狠爱综合网| 久久久欧美国产精品| 久久99热这里只有精品18| 日韩 亚洲 欧美在线| 看免费成人av毛片| 最近视频中文字幕2019在线8| 国产在视频线在精品| 蜜臀久久99精品久久宅男| 少妇猛男粗大的猛烈进出视频 | 久久精品国产鲁丝片午夜精品| 男的添女的下面高潮视频| 日日干狠狠操夜夜爽| 亚洲三级黄色毛片| 亚洲怡红院男人天堂| 免费黄色在线免费观看| 国产熟女欧美一区二区| 卡戴珊不雅视频在线播放| 成人一区二区视频在线观看| eeuss影院久久| 久99久视频精品免费| 国产精品.久久久| 成人特级av手机在线观看| 蜜桃久久精品国产亚洲av| 亚洲精品亚洲一区二区| 1024手机看黄色片| 少妇的逼水好多| 国产三级中文精品| 国产老妇伦熟女老妇高清| 成人高潮视频无遮挡免费网站| 亚洲国产欧美在线一区| 男人狂女人下面高潮的视频| 亚洲精品日韩在线中文字幕| 国产精品熟女久久久久浪| 亚洲国产精品合色在线| 久久久久久国产a免费观看| 色尼玛亚洲综合影院| 亚洲精品,欧美精品| 日本一二三区视频观看| 看免费成人av毛片| 免费观看人在逋| 久久久精品大字幕| 99久久精品热视频| 久久久久久久国产电影| 国产av在哪里看| 在现免费观看毛片| 成人亚洲欧美一区二区av| 深爱激情五月婷婷| 18+在线观看网站| 高清日韩中文字幕在线| 欧美极品一区二区三区四区| 少妇人妻一区二区三区视频| 水蜜桃什么品种好| 午夜福利网站1000一区二区三区| 18禁裸乳无遮挡免费网站照片| av在线亚洲专区| 七月丁香在线播放| 亚洲久久久久久中文字幕| 国产av在哪里看| 亚洲欧美日韩高清专用| 美女脱内裤让男人舔精品视频| 一夜夜www| 精品久久久久久久人妻蜜臀av| 国产私拍福利视频在线观看| 国产单亲对白刺激| 久久久午夜欧美精品| 国产在视频线精品| 国产成人freesex在线| 国产成人福利小说| 大又大粗又爽又黄少妇毛片口| 婷婷六月久久综合丁香| 国产亚洲一区二区精品| 国产精品国产三级专区第一集| 国产精品熟女久久久久浪| 亚洲成色77777| 一个人免费在线观看电影| 成人一区二区视频在线观看| 国产亚洲91精品色在线| 国产精品伦人一区二区| 岛国毛片在线播放| 男女下面进入的视频免费午夜| 成人午夜高清在线视频| 欧美丝袜亚洲另类| 国产精品.久久久| 九九热线精品视视频播放| 高清毛片免费看| 汤姆久久久久久久影院中文字幕 | 最近视频中文字幕2019在线8| 欧美高清性xxxxhd video| 国产女主播在线喷水免费视频网站 | 久久久亚洲精品成人影院| 国产黄色小视频在线观看| 蜜桃亚洲精品一区二区三区| 亚洲,欧美,日韩| 色噜噜av男人的天堂激情| 午夜免费激情av| 真实男女啪啪啪动态图| 国产精品综合久久久久久久免费| 国国产精品蜜臀av免费| 亚洲人与动物交配视频| 欧美日韩国产亚洲二区| 一本—道久久a久久精品蜜桃钙片 精品乱码久久久久久99久播 | 欧美激情国产日韩精品一区| 欧美bdsm另类| 性插视频无遮挡在线免费观看| 国产色婷婷99| 亚洲欧美日韩无卡精品| 毛片女人毛片| 欧美变态另类bdsm刘玥| av免费观看日本| 午夜老司机福利剧场| 真实男女啪啪啪动态图| 天天躁夜夜躁狠狠久久av| 99九九线精品视频在线观看视频| 久久久久久久国产电影| 国产免费福利视频在线观看| or卡值多少钱| 女的被弄到高潮叫床怎么办| 日本-黄色视频高清免费观看| 欧美性猛交黑人性爽| 成人二区视频| 亚洲中文字幕日韩| АⅤ资源中文在线天堂| 简卡轻食公司| 欧美人与善性xxx| 少妇丰满av| 精品免费久久久久久久清纯| 一级av片app| 国产伦在线观看视频一区| 国产精品无大码| 女人十人毛片免费观看3o分钟| 欧美成人午夜免费资源| 纵有疾风起免费观看全集完整版 | 两个人的视频大全免费| 国产欧美另类精品又又久久亚洲欧美| 欧美色视频一区免费| 天堂av国产一区二区熟女人妻| 亚洲第一区二区三区不卡| 亚洲av福利一区| 久久精品夜色国产| 国产精品不卡视频一区二区| 精华霜和精华液先用哪个| 亚洲婷婷狠狠爱综合网| 99热这里只有是精品50| 欧美日韩一区二区视频在线观看视频在线 | 久久久精品94久久精品| 亚洲人成网站在线播| 我的老师免费观看完整版| 搡老妇女老女人老熟妇| 久久人妻av系列| av在线观看视频网站免费| 亚洲高清免费不卡视频| 波多野结衣巨乳人妻| 99久久精品热视频| 中文字幕精品亚洲无线码一区| 老司机影院毛片| 在线观看美女被高潮喷水网站| 亚洲av成人精品一区久久| 日本色播在线视频| 午夜爱爱视频在线播放| 国产精品一区二区三区四区免费观看| 国产亚洲91精品色在线| 久久久久网色| 日韩视频在线欧美| 91午夜精品亚洲一区二区三区| 一级毛片久久久久久久久女| 国产高清三级在线| 少妇被粗大猛烈的视频| 亚洲国产精品久久男人天堂| 2021天堂中文幕一二区在线观| 久久国内精品自在自线图片| 91狼人影院| 精品久久久久久久久亚洲| 久久久久九九精品影院| 国产精品野战在线观看| 亚洲综合色惰| 久久99热6这里只有精品| 国产精品人妻久久久久久| 亚洲av中文av极速乱| 亚洲最大成人av| 午夜视频国产福利| 18禁在线播放成人免费| 久久鲁丝午夜福利片| 女人十人毛片免费观看3o分钟| 黄色一级大片看看| 美女内射精品一级片tv| 99视频精品全部免费 在线| 日本一二三区视频观看| 国产精品综合久久久久久久免费| 麻豆乱淫一区二区| 日本午夜av视频| 欧美成人精品欧美一级黄| 色噜噜av男人的天堂激情| 亚洲美女搞黄在线观看| 最近最新中文字幕免费大全7| 男女那种视频在线观看| 成年女人永久免费观看视频| 色5月婷婷丁香| 日本爱情动作片www.在线观看| 黄色配什么色好看| 性色avwww在线观看| 天堂中文最新版在线下载 | 国产高清视频在线观看网站| 国产欧美日韩精品一区二区| 欧美性感艳星| 国产精品国产高清国产av| 色播亚洲综合网| 国产精品1区2区在线观看.| videossex国产| 欧美三级亚洲精品| 欧美xxxx性猛交bbbb| 婷婷色麻豆天堂久久 | 亚洲伊人久久精品综合 | 婷婷六月久久综合丁香| 亚洲人成网站高清观看| 色哟哟·www| 国产午夜精品一二区理论片| 校园人妻丝袜中文字幕| 国产高清不卡午夜福利| 久久久色成人| 国产爱豆传媒在线观看| a级毛色黄片| 亚洲精品成人久久久久久| 中文字幕免费在线视频6| 亚洲国产精品专区欧美| 99热精品在线国产| 18禁在线播放成人免费| 亚洲色图av天堂| 国产精品久久久久久av不卡| 日本黄大片高清| 亚洲人与动物交配视频| 精华霜和精华液先用哪个| 色尼玛亚洲综合影院| 国产一区亚洲一区在线观看| 亚洲成av人片在线播放无| 国产黄片视频在线免费观看| 九九在线视频观看精品| 国产麻豆成人av免费视频| 黄片无遮挡物在线观看| 欧美高清性xxxxhd video| 一本—道久久a久久精品蜜桃钙片 精品乱码久久久久久99久播 | 在现免费观看毛片| 国产极品天堂在线| 国产精品久久电影中文字幕| 亚洲aⅴ乱码一区二区在线播放| 黄色一级大片看看| 免费观看的影片在线观看| 在线观看av片永久免费下载| 国产精品久久久久久久久免| 国产成人91sexporn| 国产探花在线观看一区二区| 超碰av人人做人人爽久久| 久久久久久久久久久免费av| 大香蕉97超碰在线| 寂寞人妻少妇视频99o| 国产亚洲av嫩草精品影院| 老司机影院毛片| 91精品伊人久久大香线蕉| 色5月婷婷丁香| 九色成人免费人妻av| 中文字幕人妻熟人妻熟丝袜美| 亚洲自拍偷在线| 国产视频内射| 午夜日本视频在线| 亚洲最大成人手机在线| 精品国产露脸久久av麻豆 | 我的女老师完整版在线观看| 国产乱人偷精品视频| 日韩中字成人| 国产成人aa在线观看| 永久免费av网站大全| 亚洲成人久久爱视频| 亚洲av中文av极速乱| 一卡2卡三卡四卡精品乱码亚洲| 亚洲精品乱久久久久久| 国产亚洲精品av在线| 久久韩国三级中文字幕| 纵有疾风起免费观看全集完整版 | 亚洲天堂国产精品一区在线| 精品久久国产蜜桃| 看免费成人av毛片| 最近中文字幕高清免费大全6| 尾随美女入室| 一级毛片我不卡| av.在线天堂| 久久久色成人| 午夜福利网站1000一区二区三区| videossex国产| 亚洲精华国产精华液的使用体验| 高清日韩中文字幕在线| 亚洲美女搞黄在线观看| 久久亚洲精品不卡| 亚洲av电影不卡..在线观看| 久久99蜜桃精品久久| 少妇熟女欧美另类| 国内少妇人妻偷人精品xxx网站| 成人av在线播放网站| 亚洲精品aⅴ在线观看| 99在线视频只有这里精品首页| 麻豆久久精品国产亚洲av| 好男人在线观看高清免费视频| 欧美三级亚洲精品| 一本一本综合久久| av在线蜜桃| 亚洲欧美日韩高清专用| 亚洲av日韩在线播放| 亚洲国产色片| 午夜福利网站1000一区二区三区| 精品欧美国产一区二区三| 亚洲成色77777| 天天躁日日操中文字幕| 女人久久www免费人成看片 | 精品少妇黑人巨大在线播放 | av专区在线播放| 久久精品影院6| 中文字幕久久专区| 99久久精品热视频| 国产精品久久久久久久久免| 国产精品福利在线免费观看| 精品无人区乱码1区二区| 亚洲精品自拍成人| 99热这里只有是精品在线观看| 亚洲精品久久久久久婷婷小说 | 欧美日本视频| 久久久精品欧美日韩精品| 久久亚洲国产成人精品v| 国产精品精品国产色婷婷| 伦精品一区二区三区| av在线播放精品| 网址你懂的国产日韩在线| 久久午夜福利片| 国产熟女欧美一区二区| 亚洲精品国产av成人精品| 九九在线视频观看精品| 老司机影院成人| 日韩av不卡免费在线播放| 国产精品一二三区在线看| 久久国产乱子免费精品| 一卡2卡三卡四卡精品乱码亚洲| 亚洲伊人久久精品综合 | 精品国产一区二区三区久久久樱花 | 日本免费在线观看一区| av国产久精品久网站免费入址| 亚洲国产精品合色在线| 日本av手机在线免费观看| 久久久久国产网址| av在线播放精品| 波野结衣二区三区在线| 日本一二三区视频观看| 亚洲欧美精品自产自拍| av女优亚洲男人天堂| 久久久亚洲精品成人影院| 特大巨黑吊av在线直播| 成年女人永久免费观看视频| 人妻制服诱惑在线中文字幕| 午夜爱爱视频在线播放| 午夜a级毛片| 国产 一区 欧美 日韩| 变态另类丝袜制服| 成年版毛片免费区| 精品无人区乱码1区二区| 国产精品久久久久久精品电影| 中文资源天堂在线| 亚洲av免费高清在线观看| 少妇被粗大猛烈的视频| 少妇的逼水好多| 国产在视频线精品| 哪个播放器可以免费观看大片| 成人欧美大片| 亚洲国产最新在线播放| 2021天堂中文幕一二区在线观| 久久久精品大字幕| 国产免费视频播放在线视频 | 国产成年人精品一区二区| 亚洲无线观看免费| 亚洲最大成人手机在线| 久久久久精品久久久久真实原创| 中文字幕av在线有码专区| 午夜免费激情av| av国产免费在线观看| 午夜视频国产福利| 午夜免费激情av| 欧美日韩精品成人综合77777| 欧美变态另类bdsm刘玥| 春色校园在线视频观看| 91aial.com中文字幕在线观看| 真实男女啪啪啪动态图| 国产精品爽爽va在线观看网站| av天堂中文字幕网| 国产亚洲一区二区精品| 美女黄网站色视频| 亚洲人成网站在线观看播放| 午夜福利视频1000在线观看| 少妇丰满av| 国产亚洲精品av在线| 欧美色视频一区免费| 菩萨蛮人人尽说江南好唐韦庄 | 看非洲黑人一级黄片| 成人午夜精彩视频在线观看| 春色校园在线视频观看| 最新中文字幕久久久久| 尾随美女入室| 亚洲欧美中文字幕日韩二区| 亚洲av.av天堂| 岛国毛片在线播放| 麻豆精品久久久久久蜜桃| 天堂√8在线中文|