Estimate of uncertain cohesive suspended sediment deposition rate from uncertain floc size in Meghna estuary, Bangladesh

Suspended sediment in the Meghna estuary, Bangladesh, typically consists of fine to medium silt near the water surface, silty sand at increasing depth, and sandy silt close to the bed. The behavior of fine, cohesive sediment in a complex environment with multiple drivers, such as river and tidal flows, is comparatively little understood because the deposition and erosion processes depend on many chemical, biological, and physical factors. This article examines the propagation of uncertainty from input floc size to output sedimentation rate in the Meghna estuary, Bangladesh, using a fine-sediment hydro-morphodynamic model that utilizes the cohesive sediment transport module in Delft3D. We assume that sediment particles and flocs are both single-sized throughout the solution domain. The effect of uncertainty in floc size on output sediment transport statistics is examined at three sites of interest located in the Meghna estuary using a novel numerical derived distribution approach. After deriving the probability distribution of suspended cohesive sediment, we find the coefficient of variation to range from 20% to 38% across the three locations. Planners therefore need to consider substantial uncertainty in cohesive sediment transport estimates for the coastal zone of Bangladesh, especially given the increased risk of flooding in deposition-prone areas as they become shallower. The methodology may be readily extended to the estimation of uncertainty in land reclamation and erosion control planning studies

Stochastic modeling of flows behind a square cylinder with uncertain Reynolds numbers

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 72-73).In this thesis, we explore the use of stochastic Navier-Stokes equations through the Dynamically Orthogonal (DO) methodology developed at MIT in the Multidisciplinary Simulation, Estimation, and Assimilation Systems Group. Specifically, we examine the effects of the Reynolds number on stochastic fluid flows behind a square cylinder and evaluate computational schemes to do so. We review existing literature, examine our simulation results and validate the numerical solution. The thesis uses a novel open boundary condition formulation for DO stochastic Navier-Stokes equations, which allows the modeling of a wide range of random inlet boundary conditions with a single DO simulation of low stochastic dimensions, reducing computational costs by orders of magnitude. We first test the numerical convergence and validating the numerics. We then study the sensitivity of the results to several parameters, focusing for the dynamics on the sensitivity to the Reynolds number. For the method, we focus on the sensitivity to the: resolution of in the stochastic subspace, resolution in the physical space and number of open boundary conditions DO modes. Finally, we evaluate and study how key dynamical characteristics of the flow such as the recirculation length and the vortex shedding period vary with the Reynolds number.by Jacob Kasozi Wamala.S.B

Numerical Methods for Hyperbolic Partial Differential Equations

Department of Mathematical SciencesIn this dissertation, new numerical methods are proposed for different types of hyperbolic partial differential equations (PDEs). The objectives of these developments aim for the improvements in accuracy, robustness, efficiency, and reduction of the computational cost. The dissertation consists of two parts. The first half discusses shock-capturing methods for nonlinear hyperbolic conservation laws, and proposes a new adaptive weighted essentially non-oscillatory WENO-?? scheme in the context of finite difference. Depending on the smoothness of the large stencils used in the reconstruction of the numerical flux, a parameter ?? is set adaptively to switch the scheme between a 5th-order upwind or 6th-order central discretization. A new indicator depending on parameter ?? measures the smoothness of the large stencils in order to choose a smoother one for the reconstruction procedure. ?? is devised based on the possible highest-order variations of the reconstructing polynomials in an L2 sense. In addition, a new set of smoothness indicators ??_k???s of the sub-stencils is introduced. These are constructed in a central sense with respect to the Taylor expansions around point x_j . Numerical results show that the new scheme combines good properties of both 5th-order upwind and 6th-order central schemes. In particular, the new scheme captures discontinuities and resolves small-scaled structures much better than other 5th-order schemes; overcomes the loss of resolution near some critical regions; and is able to maintain symmetry which are drawbacks detected in other 6th-order central WENO schemes. The second part extends the scope to hyperbolic PDEs with uncertainty, and semi-analytical methods using singular perturbation analysis for dispersive PDEs. For the former, a hybrid operator splitting method is developed for computation of the two-dimensional transverse magnetic Maxwell equations in media with multiple random interfaces. By projecting the solutions into random space using the Polynomial Chaos (PC) expansions, the deterministic and random parts of the solution are solved separately. The deterministic parts are then numerically approximated by the FDTD method with domain decomposition implemented on a staggered grid. Statistic quantities are obtained by the Monte Carlo sampling in the post-processing stage. Parallel computing is proposed for which the computational cost grows linearly with the number of random interfaces. The last section deals with spectral methods for dispersive PDEs. The Kortewegde Vries (KdV) equation is chosen as a prototype. By Fourier series, the PDE is transformed into a system of ODEs which is stiff, that is, there are rapid oscillatory modes for large wavenumbers. A new semi-analytical method is proposed to tackle the difficulty. The new method is based on the classical integrating factor (IF) and exponential time differencing (ETD) schemes. The idea is to approximate analytically the stiff parts by the so-called correctors and numerically the non-stiff parts by the IF and ETD methods. It turns out that rapid oscillations are well absorbed by our corrector method, yielding better accuracy in the numerical results. Due to the nonlinearity, all Fourier modes interact with each other, causing the computation of the correctors to be very costly. In order to overcome this, the correctors are recursively constructed to accurately capture the stiffness of the mode interactions.ope

Estimation of uncertainty in the hydro-morphodynamic characteristics of the Meghna Estuary, Bangladesh

The coastal zone of Bangladesh is a part of the Ganga–Brahmaputra–Meghna basin, and is home to about 38.5 million people. This coastal community is particularly vulnerable to natural disasters, such as catastrophic floods from extreme river flows, cyclones, land erosion, and sea level rise. Although advances in computational hydraulics facilitate the numerical simulation of extreme events in the coastal zone, informing risk assessment, the numerical models themselves propagate uncertainty from input to output parameters. This thesis presents a numerical derived distribution approach for uncertainty propagation through a computational model of tidal and fluvial processes in Meghna estuary of Bangladesh. The approach involves discretization of an estimated probability distribution function of a key input variable, the computation of a response function linking a single input parameter to a single output variable of interest, and the use of conservation of probability to determine the probability distribution of the output variable. The method requires only a few simulations to be conducted, and so it is very efficient to implement. In the thesis, Delft3D, a well-established computational tool, is verified for a series of standard tests. Then, Delft3D model is set up for the Meghna estuary and Bay of Bengal. Uncertainty propagation is then examined by studying the effect of uncertain bed roughness on the estimate of maximum water level, the effect of uncertain sea level rise on the maximum water level, and the effect of uncertain floc size on the sediment deposition rate at selected sites around the Meghna estuary of Bangladesh. It is found that with a 50% increase of mean Manning’s n, the maximum water level can increase from 24% to 80% at various locations. For several IPCC scenarios of sea level rise, the standard deviation of maximum water level increases about 33-40% at the same locations. For a mean floc size of 227 micron and standard deviation of 171 micron, the coefficient of variation of cohesive sediment deposition rate is estimated to range from 19.8% to 37.6% at three locations in the Meghna estuary