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: A coupled two-layer finite volume/finite element
method was proposed for solving dam-break flow problem
over deformable beds. The governing equations consist of the
well-balanced two-layer shallow water equations for the water flow
and a linear elastic model for the bed deformations. Deformations
in the topography can be caused by a brutal localized force or
simply by a class of sliding displacements on the bathymetry.
This deformation in the bed is a source of perturbations, on
the water surface generating water waves which propagate with
different amplitudes and frequencies. Coupling conditions at the
interface are also investigated in the current study and two mesh
procedure is proposed for the transfer of information through the
interface. In the present work a new procedure is implemented at
the soil-water interface using the finite element and two-layer finite
volume meshes with a conservative distribution of the forces at
their intersections. The finite element method employs quadratic
elements in an unstructured triangular mesh and the finite volume
method uses the Rusanove to reconstruct the numerical fluxes. The
numerical coupled method is highly efficient, accurate, well balanced,
and it can handle complex geometries as well as rapidly varying
flows. Numerical results are presented for several test examples of
dam-break flows over deformable beds. Mesh convergence study is
performed for both methods, the overall model provides new insight
into the problems at minimal computational cost.