Abstract: Modeling dam-break flows over non-flat beds requires
an accurate representation of the topography which is the main
source of uncertainty in the model. Therefore, developing robust
and accurate techniques for reconstructing topography in this class
of problems would reduce the uncertainty in the flow system. In
many hydraulic applications, experimental techniques have been
widely used to measure the bed topography. In practice, experimental
work in hydraulics may be very demanding in both time and cost.
Meanwhile, computational hydraulics have served as an alternative
for laboratory and field experiments. Unlike the forward problem,
the inverse problem is used to identify the bed parameters from the
given experimental data. In this case, the shallow water equations
used for modeling the hydraulics need to be rearranged in a way
that the model parameters can be evaluated from measured data.
However, this approach is not always possible and it suffers from
stability restrictions. In the present work, we propose an adaptive
optimal control technique to numerically identify the underlying bed
topography from a given set of free-surface observation data. In this
approach, a minimization function is defined to iteratively determine
the model parameters. The proposed technique can be interpreted
as a fractional-stage scheme. In the first stage, the forward problem
is solved to determine the measurable parameters from known data.
In the second stage, the adaptive control Ensemble Kalman Filter is
implemented to combine the optimality of observation data in order to
obtain the accurate estimation of the topography. The main features
of this method are on one hand, the ability to solve for different
complex geometries with no need for any rearrangements in the
original model to rewrite it in an explicit form. On the other hand, its
achievement of strong stability for simulations of flows in different
regimes containing shocks or discontinuities over any geometry.
Numerical results are presented for a dam-break flow problem over
non-flat bed using different solvers for the shallow water equations.
The robustness of the proposed method is investigated using different
numbers of loops, sensitivity parameters, initial samples and location
of observations. The obtained results demonstrate high reliability and
accuracy of the proposed techniques.
Abstract: We present a new class of numerical techniques to
solve shallow water flows over dry areas including run-up. Many
recent investigations on wave run-up in coastal areas are based on
the well-known shallow water equations. Numerical simulations have
also performed to understand the effects of several factors on tsunami
wave impact and run-up in the presence of coastal areas. In all these
simulations the shallow water equations are solved in entire domain
including dry areas and special treatments are used for numerical
solution of singularities at these dry regions. In the present study we
propose a new method to deal with these difficulties by reformulating
the shallow water equations into a new system to be solved only in the
wetted domain. The system is obtained by a change in the coordinates
leading to a set of equations in a moving domain for which the
wet/dry interface is the reconstructed using the wave speed. To solve
the new system we present a finite volume method of Lax-Friedrich
type along with a modified method of characteristics. The method is
well-balanced and accurately resolves dam-break problems over dry
areas.
Abstract: Modeling sediment transport processes by means of numerical approach often poses severe challenges. In this way, a number of techniques have been suggested to solve flow and sediment equations in decoupled, semi-coupled or fully coupled forms. Furthermore, in order to capture flow discontinuities, a number of techniques, like artificial viscosity and shock fitting, have been proposed for solving these equations which are mostly required careful calibration processes. In this research, a numerical scheme for solving shallow water and Exner equations in fully coupled form is presented. First-Order Centered scheme is applied for producing required numerical fluxes and the reconstruction process is carried out toward using Monotonic Upstream Scheme for Conservation Laws to achieve a high order scheme. In order to satisfy C-property of the scheme in presence of bed topography, Surface Gradient Method is proposed. Combining the presented scheme with fourth order Runge-Kutta algorithm for time integration yields a competent numerical scheme. In addition, to handle non-prismatic channels problems, Cartesian Cut Cell Method is employed. A trained Multi-Layer Perceptron Artificial Neural Network which is of Feed Forward Back Propagation (FFBP) type estimates sediment flow discharge in the model rather than usual empirical formulas. Hydrodynamic part of the model is tested for showing its capability in simulation of flow discontinuities, transcritical flows, wetting/drying conditions and non-prismatic channel flows. In this end, dam-break flow onto a locally non-prismatic converging-diverging channel with initially dry bed conditions is modeled. The morphodynamic part of the model is verified simulating dam break on a dry movable bed and bed level variations in an alluvial junction. The results show that the model is capable in capturing the flow discontinuities, solving wetting/drying problems even in non-prismatic channels and presenting proper results for movable bed situations. It can also be deducted that applying Artificial Neural Network, instead of common empirical formulas for estimating sediment flow discharge, leads to more accurate results.
Abstract: A fast finite volume solver for multi-layered shallow
water flows with mass exchange and an erodible bed is developed.
This enables the user to solve a number of complex sediment-based
problems including (but not limited to), dam-break over an erodible
bed, recirculation currents and bed evolution as well as levy and
dyke failure. This research develops methodologies crucial to the
under-standing of multi-sediment fluvial mechanics and waterway
design. In this model mass exchange between the layers is allowed
and, in contrast to previous models, sediment and fluid are able
to transfer between layers. In the current study we use a two-step
finite volume method to avoid the solution of the Riemann problem.
Entrainment and deposition rates are calculated for the first time in
a model of this nature. In the first step the governing equations are
rewritten in a non-conservative form and the intermediate solutions
are calculated using the method of characteristics. In the second stage,
the numerical fluxes are reconstructed in conservative form and are
used to calculate a solution that satisfies the conservation property.
This method is found to be considerably faster than other comparative
finite volume methods, it also exhibits good shock capturing. For most
entrainment and deposition equations a bed level concentration factor
is used. This leads to inaccuracies in both near bed level concentration
and total scour. To account for diffusion, as no vertical velocities
are calculated, a capacity limited diffusion coefficient is used. The
additional advantage of this multilayer approach is that there is a
variation (from single layer models) in bottom layer fluid velocity:
this dramatically reduces erosion, which is often overestimated in
simulations of this nature using single layer flows. The model is
used to simulate a standard dam break. In the dam break simulation,
as expected, the number of fluid layers utilised creates variation in
the resultant bed profile, with more layers offering a higher deviation
in fluid velocity . These results showed a marked variation in erosion
profiles from standard models. The overall the model provides new
insight into the problems presented at minimal computational cost.
Abstract: A water surface slope limiting scheme is tested and
compared with the water depth slope limiter for the solution of one
dimensional shallow water equations with bottom slope source term.
Numerical schemes based on the total variation diminishing Runge-
Kutta discontinuous Galerkin finite element method with slope
limiter schemes based on water surface slope and water depth are
used to solve one-dimensional shallow water equations. For each
slope limiter, three different Riemann solvers based on HLL, LF, and
Roe flux functions are used. The proposed water surface based slope
limiter scheme is easy to implement and shows better conservation
property compared to the slope limiter based on water depth. Of the
three flux functions, the Roe approximation provides the best results
while the LF function proves to be least suitable when used with
either slope limiter scheme.
Abstract: Linear stability of wake-shear layers in two-phase
shallow flows is analyzed in the present paper. Stability analysis is
based on two-dimensional shallow water equations. It is assumed that
the fluid contains uniformly distributed solid particles. No dynamic
interaction between the carrier fluid and particles is expected in the
initial moment. Linear stability curves are obtained for different
values of the particle loading parameter, the velocity ratio and the
velocity deficit. It is shown that the increase in the velocity ratio
destabilizes the flow. The particle loading parameter has a stabilizing
effect on the flow. The role of the velocity deficit is also
destabilizing: the increase of the velocity deficit leads to less stable
flow.