| Fluid flow phenomena,especially some complex flow characteristics which exist extensively and have special properties,are key and difficult points of hydromechanics in the past a few decades.Subject to the lack of measuring methods and numerical calculation capabilities,tra-ditional research interests focus on the establishment of the dynamic mechanism models.Re-searches formulate the model by applying laws including conservation of mass and momentum and most of the models are nonlinear partial differential equations(PDEs).Although the mecha-nism models can cover the characters of a certain kind of flows,some specific parameters of the model describing a particular flow usually cannot be obtained through direct measurement.Thus,this method is more suitable to qualitatively describe the shared characteristics of a whole family of flow phenomena.With the development of the ability of calculations and the appearance of new measuring methods such as optical method and particle image velocimetry(PIV)in recent years,now we can measure some new physical quantities related to the flow field.However,the measurements can only supply the partial and instantaneous information by which one cannot be able to recover the whole fluid field evolutionary process.One can overcome such difficulties by taking advantages of the accuracy of the measurement information and the prediction ability of the mechanism models.The main work of this thesis is to eliminate the uncertain factors of the mechanism model.We mainly study two distinctive types of flow:the vortex shedding phenomena when flow past a cylinder and the free-surface flow.We adopt the nonlinear Ginzburg-Landau(G-L)equation whose parameters cannot be measured directly to describe the former one.Therefore,we try to estimate the parameters by measuring the velocities at some fixed points along the centerline.We first formulate it as a dynamical optimization problem for which we introduce the costate vector and deduce the gradient of the given cost function and solve it using gradient-based optimization method.Since this method can only supply the most likely parameters without information about the uncertainty of the parameters.When the measurements contain large noises,we formulate the problem in a Bayesian framework to estimate the whole distribution of the unknown parameters.In addition,we introduce the implicit sampling method which is used to construct a good importance function to accelerate the sampling procedure.We adopt the shallow-water equations(SWEs)which contain three PDEs of velocities and height to describe the free-surface flow.Since there are several uncertain time-varying parameter depending on the particular environment,we use ensemble Kalman filter(EnKF)to achieve the data assimilation(DA)procedure.For this 2D model,a very good choice of the measurement method is PIV which estimate the velocities by calculating the displacement of the particles in two adjacent images obtained by camera.In this thesis,we propose two scenarios:one is to add the image sequences into the DA procedure directly as the observation information while the other one is to use the stochastic optical flow constraint equation(OFCE)alone to estimate the flow field in the first step and then add the resulting flow field into the DA framework.The simulation results show that both of this two scenarios have good effects.The main innovative spots of this thesis are:ˇUsing the implicit sampling method to solve the parameter estimation problem of the parabolic nonlinear G-L equations and combining the gradient-based optimization method and the im-plicit sampling method to solve such problems.ˇUsing the image information and the SWEs to achieve the DA procedure to recover the free-surface flow.ˇApplying the gradient-based optimization method to obtain more accurate velocities by solv-ing the stochastic OFCE along with the mechanism model. |
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