Browsing by Subject "Shallow water equations"
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Item Adaptive measure-theoretic parameter estimation for coastal ocean modeling(2015-08) Graham, Lindley Christin; Dawson, Clinton N.; Butler, Troy; Gamba, Irene; Ghattas, Omar; Moser, RobertSince Hurricane Katrina (2005), there has been a marked increase in the quantity of field observations gathered during and after hurricanes. There has also been an increased effort to improve our ability to model hurricanes and other coastal ocean phenomena. The majority of death and destruction due to a hurricane is from storm surge. The primary controlling factor in storm surge is the balance between the surface stress due to the wind and bottom stress. Manning's formula can be used to model the bottom stress; the formula includes the Manning's n coefficient which accounts for momentum loss due to bottom roughness and is a spatially dependent field. It is impractical to measure Manning's n over large physical domains. Instead, given a computational storm surge model and a set of model observations, one may formulate and solve an inverse problem to determine probable Manning's n fields using observational data, which in turn can be used for predictive simulations. On land, Manning's n may be inferred from land cover classification maps. We leverage existing land cover classification data to determine the spatial distribution of land cover classifications which we consider certain. These classifications can be used to obtain a parameterized mesoscale representation of the Manning's n field. We seek to estimate the Manning's n coefficients for this parameterized field. The inverse problem we solve is formulated using a measure-theoretic approach; using the ADvanced CIRCulation model for coastal and estuarine waters as the forward model of storm surge. The uncertainty in observational data is described as a probability measure on the data space. The solution to the inverse problem is a non-parametric probability measure on the parameter space. The goal is to use this solution in order to measure the probability of arbitrary events in the parameter space. In the cases studied here the dimension of the data space is smaller than the dimension of the parameter space. Thus, the inverse of a fixed datum is generally a set of values in parameter space. The advantage of using the measure-theoretic approach is that it preserves the geometric relation between the data space and the parameter space within the probability measure. Solving an inverse problem often involves the exploration of a high-dimensional parameter space requiring numerous expensive forward model solves. We use adaptive algorithms for solving the stochastic inverse problem to reduce error in the estimated probability of implicitly defined parameter events while minimizing the number of forward model solves.Item Advances towards a multi-dimensional discontinuous Galerkin method for modeling hurricane storm surge induced flooding in coastal watersheds(2016-08) Neupane, Prapti; Dawson, Clinton N.; Gamba, Irene M; Engquist, Bjorn; Bui-Thanh, Tan; Moser, Robert DCoastal areas are regions of high population density and urbanization. These areas are highly vulnerable to inundation and flooding not only because of hurricane storm surge, but also because of the torrential rainfall that often accompanies hurricanes. In order to accurately predict the extent of damage such an event might cause, any model that is used to simulate this process needs to couple rainfall with storm surge. The works that have tried to address this issue have mostly used a unidirectional coupling technique, where one of the following two approaches is taken. In the first approach, a hydrology model is used in the domain of interest and storm surge is incorporated in the domain as a boundary condition. In the second approach, a storm surge model is used in the domain of interest and rainfall is incorporated in the domain as a river inflow boundary condition. Neither of these approaches allows the rainwater and the surge water to interact bidirectionally. In order to improve on those efforts, in this dissertation, we develop a comprehensive framework for modeling flooding in coastal watersheds. We present an approach to decompose a watershed into multiple sub-domains depending on the dynamics of flow in the region. We use different simplifications of the shallow water equations on different sub-domains to gain computational efficiency without compromising on physical accuracy. The different sub-domains are coupled with each other through numerical fluxes in a discontinuous Galerkin framework. This technique allows for a tight coupling of storm surge with rainfall runoff, so that the flooding that occurs is truly influenced by the nonlinear interaction of these two processes. We present numerical tests to validate and verify the methods used for modeling flow in different sub-domains as well as the techniques used for coupling different sub-domains with each other.Item Analysis, implementation, and verification of a discontinuous galerkin method for prediction of storm surges and coastal deformation(2011-08) Mirabito, Christopher Michael; Dawson, Clinton N.; Demkowicz, Leszek F.; Gamba, Irene M.; Ghattas, Omar; Kim, WonsuckStorm surge, the pileup of seawater occurring as a result of high surface stresses and strong currents generated by extreme storm events such as hurricanes, is known to cause greater loss of life than these storms' associated winds. For example, inland flooding from the storm surge along the Gulf Coast during Hurricane Katrina killed hundreds of people. Previous storms produced even larger death tolls. Simultaneously, dune, barrier island, and channel erosion taking place during a hurricane leads to the removal of major flow controls, which significantly affects inland inundation. Also, excessive sea bed scouring around pilings can compromise the structural integrity of bridges, levees, piers, and buildings. Modeling these processes requires tightly coupling a bed morphology equation to the shallow water equations (SWE). Discontinuous Galerkin finite element methods (DGFEMs) are a natural choice for modeling this coupled system, given the need to solve these problems on large, complicated, unstructured computational meshes, as well as the desire to implement hp-adaptivity for capturing the dynamic features of the solution. Comprehensive modeling of these processes in the coastal zone presents several challenges and open questions. Most existing hydrodynamic models use a fixed-bed approach; the bottom is not allowed to evolve in response to the fluid motion. With respect to movable-bed models, there is no single, generally accepted mathematical model in use. Numerical challenges include coupling models of processes that exhibit disparate time scales during fair weather, but possibly similar time scales during intense storms. The main goals of this dissertation include implementing a robust, efficient, tightly-coupled morphological model using the local discontinuous Galerkin (LDG) method within the existing Advanced Circulation (ADCIRC) modeling framework, performing systematic code and model verification (using test cases with known solutions, proven convergence rates, or well-documented physical behavior), analyzing the stability and accuracy of the implemented numerical scheme by way of a priori error estimates, and ultimately laying some of the necessary groundwork needed to simultaneously model storm surges and bed morphodynamics during extreme storm events.Item Discontinuous Galerkin methods for spectral wave/circulation modeling(2013-08) Meixner, Jessica Delaney; Dawson, Clinton N.Waves and circulation processes interact in daily wind and tide driven flows as well as in more extreme events such as hurricanes. Currents and water levels affect wave propagation and the location of wave-breaking zones, while wave forces induce setup and currents. Despite this interaction, waves and circulation processes are modeled separately using different approaches. Circulation processes are represented by the shallow water equations, which conserve mass and momentum. This approach for wind-generated waves is impractical for large geographic scales due to the fine resolution that would be required. Therefore, wind-waves are instead represented in a spectral sense, governed by the action balance equation, which propagates action density through both geographic and spectral space. Even though wind-waves and circulation are modeled separately, it is important to account for their interactions by coupling their respective models. In this dissertation we use discontinuous-Galerkin (DG) methods to couple spectral wave and circulation models to model wave-current interactions. We first develop, implement, verify and validate a DG spectral wave model, which allows for the implementation of unstructured meshes in geographic space and the utility of adaptive, higher-order approximations in both geographic and spectral space. We then couple the DG spectral wave model to an existing DG circulation model, which is run on the same geographic mesh and allows for higher order information to be passed between the two models. We verify and validate coupled wave/circulation model as well as analyzing the error of the coupled wave/circulation model.