Data assimilation and bathymetric inversion in a two-dimensional horizontal surf zone model

Abstract The zone method of radiation analysis has been widely used in mathematical models of a range of industrial heating processes. This paper is thus concerned with the use of a two-dimensional, multi-zone model to predict fuel consumptions, heating rates and load temperatures following the “cold start up” of a gas-fired furnace heating steel bars to a nominal discharge temperature of 1250°C. The model takes into account variations in the flows of the combustion products and in particular examines the influence of the re-circulation of these hot gases within the furnace chamber. The predictions of this complex two-dimensional model are compared with those of a one-dimensional so-called “long furnace model” to illustrate the differences resulting from the use of a more sophisticated multi-zone model.

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The Application of a Two-Dimensional Zone Model to the Design and Control of a Continuously Operated, Gas-Fired Furnace

Energy Conversion ◽

10.1115/imece2002-39297 ◽

2002 ◽

Cited By ~ 2

Author(s):

Sara A. C. Correia ◽

John Ward

Keyword(s):

Dynamics Simulation ◽

Relative Mass ◽

Zone Model ◽

Two Dimensional ◽

Furnace Design ◽

Simplified Approach ◽

Flow Models ◽

Discharge Temperature ◽

Wide Range ◽

And Control

This paper describes the development of a two-dimensional zone model to predict the throughput and thermal performance of a continuously operated gas-fired furnace heating steel bars to a nominal discharge temperature of 1250°C. Ultimately the model is intended to be a tool which can be used for the design and control of industrial furnaces. Consequently relatively short computing times are necessary and this was achieved by employing an isothermal computational fluid dynamics simulation to estimate the relative mass flows, and hence enthalpy flows to or from adjacent volume zones in the overall model. This simplified approach, which utilises a single “once off” isothermal computation of the flows, was considered to be adequate since isothermal flow models have been used successfully in the past to study the flow related behaviour of combustion systems. The coupling of a multi-zone model with a single “once off” isothermal computation of the flows enables a wide range of furnace design modifications to be studied quickly and easily. To illustrate the potential use of the model in a furnace design application, it was then used to investigate the effects of inclining the burners downwards towards the load as well as those associated with increasing the length of the furnace.

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Fully discrete numerical schemes of a data assimilation algorithm: uniform-in-time error estimates

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drz043 ◽

2019 ◽

Vol 40 (4) ◽

pp. 2584-2625 ◽

Cited By ~ 2

Author(s):

Hussain A Ibdah ◽

Cecilia F Mondaini ◽

Edriss S Titi

Keyword(s):

Data Assimilation ◽

Error Estimates ◽

Stokes Equations ◽

Time Discretization ◽

Dissipative Systems ◽

Complete Analysis ◽

Two Dimensional ◽

Time Error ◽

Time Step ◽

Fully Discrete

Abstract Our aim is to approximate a reference velocity field solving the two-dimensional Navier–Stokes equations (NSE) in the absence of its initial condition by utilizing spatially discrete measurements of that field, available at a coarse scale, and continuous in time. The approximation is obtained via numerically discretizing a downscaling data assimilation algorithm. Time discretization is based on semiimplicit and fully implicit Euler schemes, while spatial discretization (which can be done at an arbitrary scale regardless of the spatial resolution of the measurements) is based on a spectral Galerkin method. The two fully discrete algorithms are shown to be unconditionally stable, with respect to the size of the time step, the number of time steps and the number of Galerkin modes. Moreover, explicit, uniform-in-time error estimates between the approximation and the reference solution are obtained, in both the $L^2$ and $H^1$ norms. Notably, the two-dimensional NSE, subject to the no-slip Dirichlet or periodic boundary conditions, are used in this work as a paradigm. The complete analysis that is presented here can be extended to other two- and three-dimensional dissipative systems under the assumption of global existence and uniqueness.

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Improvement of the Snow Depth in the Common Land Model by Coupling a Two-Dimensional Deterministic Ensemble Model with a Variational Hybrid Snow Cover Fraction Data Assimilation Scheme and a New Observation Operator

Journal of Hydrometeorology ◽

10.1175/jhm-d-16-0149.1 ◽

2017 ◽

Vol 18 (1) ◽

pp. 119-138 ◽

Cited By ~ 3

Author(s):

Jianhui Xu ◽

Feifei Zhang ◽

Hong Shu ◽

Kaiwen Zhong

Keyword(s):

Data Assimilation ◽

Snow Cover ◽

Snow Depth ◽

Cloud Cover ◽

Two Dimensional ◽

Observation Operator ◽

Snow Cover Fraction ◽

Depletion Curve ◽

Common Land Model ◽

The Common

Abstract During snow cover fraction (SCF) data assimilation (DA), the simplified observation operator and presence of cloud cover cause large errors in the assimilation results. To reduce these errors, a new snow cover depletion curve (SDC), known as an observation operator in the DA system, is statistically fitted to in situ snow depth (SD) observations and Moderate Resolution Imaging Spectroradiometer (MODIS) SCF data from January 2004 to October 2008. Using this new SDC, a two-dimensional deterministic ensemble–variational hybrid DA (2DEnVar) method of integrating the deterministic ensemble Kalman filter (DEnKF) and a two-dimensional variational DA (2DVar) is proposed. The proposed 2DEnVar is then used to assimilate the MODIS SCF into the Common Land Model (CoLM) at five sites in the Altay region of China for data from November 2008 to March 2009. The analysis performance of the 2DEnVar is compared with that of the DEnKF. The results show that the 2DEnVar outperforms the DEnKF as it effectively reduces the bias and root-mean-square error during the snow accumulation and ablation periods at all sites except for the Qinghe site. In addition, the 2DEnVar, with more assimilated MODIS SCF observations, produces more innovations (observation minus forecast) than the DEnKF, with only one assimilated MODIS SCF observation. The problems of cloud cover and overestimation are addressed by the 2DEnVar.

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Analysis of SAGE II observations using data assimilation by the SUNY-SPB two-dimensional model and comparison to TOMS data

Journal of Geophysical Research Atmospheres ◽

10.1029/2001jd000353 ◽

2001 ◽

Vol 106 (D23) ◽

pp. 32327-32335 ◽

Cited By ~ 5

Author(s):

Sergei P. Smyshlyaev ◽

Marvin A. Geller

Keyword(s):

Data Assimilation ◽

Two Dimensional ◽

Dimensional Model ◽

Two Dimensional Model ◽

Using Data

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A Computational Study of a Data Assimilation Algorithm for the Two-dimensional Navier-Stokes Equations

Communications in Computational Physics ◽

10.4208/cicp.060515.161115a ◽

2016 ◽

Vol 19 (4) ◽

pp. 1094-1110 ◽

Cited By ~ 24

Author(s):

Masakazu Gesho ◽

Eric Olson ◽

Edriss S. Titi

Keyword(s):

Data Assimilation ◽

Stokes Equations ◽

Computational Study ◽

Nodal Point ◽

Navier Stokes ◽

Reference Solution ◽

Two Dimensional ◽

Computationally Efficient ◽

Navier Stokes Equations ◽

Feedback Control Theory

AbstractWe study the numerical performance of a continuous data assimilation (downscaling) algorithm, based on ideas from feedback control theory, in the context of the two-dimensional incompressible Navier-Stokes equations. Our model problem is to recover an unknown reference solution, asymptotically in time, by using continuous-in-time coarse-mesh nodal-point observational measurements of the velocity field of this reference solution (subsampling), as might be measured by an array of weather vane anemometers. Our calculations show that the required nodal observation density is remarkably less than what is suggested by the analytical study; and is in fact comparable to the number of numerically determining Fourier modes, which was reported in an earlier computational study by the authors. Thus, this method is computationally efficient and performs far better than the analytical estimates suggest.

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