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: This work is the first dowel in a rather wide research
activity in collaboration with Euro Mediterranean Center for Climate
Changes, aimed at introducing scalable approaches in Ocean
Circulation Models. We discuss designing and implementation of
a parallel algorithm for solving the Variational Data Assimilation
(DA) problem on Graphics Processing Units (GPUs). The algorithm
is based on the fully scalable 3DVar DA model, previously proposed
by the authors, which uses a Domain Decomposition approach
(we refer to this model as the DD-DA model). We proceed with
an incremental porting process consisting of 3 distinct stages:
requirements and source code analysis, incremental development of
CUDA kernels, testing and optimization. Experiments confirm the
theoretic performance analysis based on the so-called scale up factor
demonstrating that the DD-DA model can be suitably mapped on
GPU architectures.
Abstract: This paper addresses the problem of how one can
improve the performance of a non-optimal filter. First the theoretical question on dynamical representation for a given time correlated
random process is studied. It will be demonstrated that for a wide class of random processes, having a canonical form, there exists
a dynamical system equivalent in the sense that its output has the
same covariance function. It is shown that the dynamical approach is more effective for simulating and estimating a Markov and non-
Markovian random processes, computationally is less demanding,
especially with increasing of the dimension of simulated processes.
Numerical examples and estimation problems in low dimensional
systems are given to illustrate the advantages of the approach. A very useful application of the proposed approach is shown for the
problem of state estimation in very high dimensional systems. Here a modified filter for data assimilation in an oceanic numerical model
is presented which is proved to be very efficient due to introducing
a simple Markovian structure for the output prediction error process
and adaptive tuning some parameters of the Markov equation.
Abstract: In this paper we describe the design and implementation of a parallel algorithm for data assimilation with ensemble Kalman filter (EnKF) for oil reservoir history matching problem. The use of large number of observations from time-lapse seismic leads to a large turnaround time for the analysis step, in addition to the time consuming simulations of the realizations. For efficient parallelization it is important to consider parallel computation at the analysis step. Our experiments show that parallelization of the analysis step in addition to the forecast step has good scalability, exploiting the same set of resources with some additional efforts.