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2022 ◽  
Author(s):  
Meiyi Hou ◽  
Youmin Tang ◽  
Wansuo Duan ◽  
Zheqi Shen

Abstract This paper investigates the optimal observational array for improving the prediction of the El Niño-Southern Oscillation (ENSO) by exploring sensitive areas for target observations of two types of El Niño events in the whole Pacific. A target observation method based on the particle filter and pre-industrial control runs from six coupled model outputs in Coupled Model Intercomparison Project Phase 5 (CMIP5) experiments are used to quantify the relative importance of the initial accuracy of sea surface temperature (SST) in different Pacific areas. The initial accuracy of the tropical Pacific, subtropical Pacific, and extratropical Pacific can all exert influences on both types of El Niño predictions. The relative importance of different areas changes along with different lead times of predictions. Tropical Pacific observations are crucial in decreasing the root mean square error of predictions of all lead times. Subtropical and extratropical observations play an important role in decreasing the prediction uncertainty, especially when the prediction is made before and throughout boreal spring. To consider different El Niño types and different start months for predictions, a quantitative frequency method based on frequency distribution is applied to determine the optimal observations of ENSO predictions. The final optimal observational array contains 31 grid points, including 21 grid points in the equatorial Pacific and 10 grid points in the north Pacific, suggesting the importance of the initial SST conditions for ENSO predictions not only in the tropical Pacific but also in the area outside the tropics. Furthermore, the predictions made by assimilating SST in sensitive areas have better prediction skills in the verification experiment, which can indicate the validity of the optimal observational array designed in this study.


Author(s):  
Shin-ichi Sawada

Abstract Track-etched nanoporous membranes prepared by swift heavy ion irradiation are promising for separation processes such as water purification. However, one drawback is that multiple pores are undesirably formed by pore overlapping to reduce separation performance. The techniques for predicting the size and amount of multiple pores in detail are still underdeveloped, which hinders the precise membrane design. In this study, a computer simulation program was developed to predict the size distribution of the track-etched pores. The program generates a number of single pores on the virtual grid plane to simulate random ion bombardment, finds multiple pores containing several single pores, and determines the multiple pore size by counting the inside grid points. All the multiple pores are categorized into different size classes, and the areal percentage occupied by the pores belonging to each size class is estimated. The simulation algorithm and the results of a model case simulation were described.


Author(s):  
Waleed Adel ◽  
Kumbinarasaiah Srinivasa

Abstract This paper generates a novel approach called the clique polynomial method (CPM) using the clique polynomials raised in graph theory and used for solving the fractional order PDE. The fractional derivative is defined in terms of the Caputo fractional sense and the fractional partial differential equations (FPDE) are converted into nonlinear algebraic equations and collocated with suitable grid points in the current approach. The convergence analysis for the proposed scheme is constructed and the technique proved to be uniformly convegant. We applied the method for solving four problems to justify the proposed technique. Tables and graphs reveal that this new approach yield better results. Some theorems are discussed with proof.


Geophysics ◽  
2022 ◽  
pp. 1-71
Author(s):  
Shu-Li Dong ◽  
Jing-Bo Chen

Effective frequency-domain numerical schemes were central for forward modeling and inversion of the elastic wave equation. The rotated optimal nine-point scheme was a highly used finite-difference numerical scheme. This scheme made a weighted average of the derivative terms of the elastic wave equations in the original and the rotated coordinate systems. In comparison with the classical nine-point scheme, it could simulate S-waves better and had higher accuracy at nearly the same computational cost. Nevertheless, this scheme limited the rotation angle to 45°; thus, the grid sampling intervals in the x- and z-directions needed to be equal. Otherwise, the grid points would not lie on the axes, which dramatically complicates the scheme. Affine coordinate systems did not constrain axes to be perpendicular to each other, providing enhanced flexibility. Based on the affine coordinate transformations, we developed a new affine generalized optimal nine-point scheme. At the free surface, we applied the improved free-surface expression with an adaptive parameter-modified strategy. The new optimal scheme had no restriction that the rotation angle must be 45°. Dispersion analysis found that our scheme could effectively reduce the required number of grid points per shear wavelength for equal and unequal sampling intervals compared to the classical nine-point scheme. Moreover, this reduction improved with the increase of Poisson’s ratio. Three numerical examples demonstrated that our scheme could provide more accurate results than the classical nine-point scheme in terms of the internal and the free-surface grid points.


Author(s):  
Toni Schneidereit ◽  
Michael Breuß

AbstractSeveral neural network approaches for solving differential equations employ trial solutions with a feedforward neural network. There are different means to incorporate the trial solution in the construction, for instance, one may include them directly in the cost function. Used within the corresponding neural network, the trial solutions define the so-called neural form. Such neural forms represent general, flexible tools by which one may solve various differential equations. In this article, we consider time-dependent initial value problems, which require to set up the neural form framework adequately. The neural forms presented up to now in the literature for such a setting can be considered as first-order polynomials. In this work, we propose to extend the polynomial order of the neural forms. The novel collocation-type construction includes several feedforward neural networks, one for each order. Additionally, we propose the fragmentation of the computational domain into subdomains. The neural forms are solved on each subdomain, whereas the interfacing grid points overlap in order to provide initial values over the whole fragmentation. We illustrate in experiments that the combination of collocation neural forms of higher order and the domain fragmentation allows to solve initial value problems over large domains with high accuracy and reliability.


2021 ◽  
Author(s):  
Erik Hansen ◽  
Altay Kaçan ◽  
Bettina Frohnapfel ◽  
Andrea Codrignani

Abstract Many engineering applications rely on lubricated gaps where the hydrodynamic pressure distribution is influenced by cavitation phenomena and elastic deformations. To obtain details about the conditions within the lubricated gap, solvers are required that can model cavitation and elastic deformation effects efficiently when a large amount of discretization cells is employed. The presented unsteady EHL-FBNS solver can compute the solution of such large problems that require the consideration of both mass-conserving cavitation and elastic deformation. The execution time of the presented algorithm scales almost with N log(N) where N is the number of computational grid points. A detailed description of the algorithm and the discretized equations is presented. The MATLAB© code is provided in the supplements along with a maintained version on GitHub to encourage its usage and further development. The output of the solver is compared to and validated with simulated and experimental results from the literature to provide a detailed comparison of different discretization schemes of the Couette term in presence of gap height discontinuities. As a final result, the most favourable scheme is identified for the unsteady study of surface textures in ball-on-disc tribometers under severe EHL conditions.


MAUSAM ◽  
2021 ◽  
Vol 48 (2) ◽  
pp. 323-328
Author(s):  
P.S. MUKHOPADHYAY ◽  
G. K. MANDAL ◽  
G. K. SEN ◽  
D. K. SINHA

ABSTRACT. In this paper we have tried to set up a mathematical model that will show the contribution of wind-induced surface waves of the ocean, on surges in shallow basin of Bay of Bengal. For this, the energy balance equation, excluding non-linear forcing term, is considered and solved by Lax-Wendroff integration scheme. Wind is specified over all the grid points following Cardone' s formulation. The hydrodynamic equations in linearised form as used by Jelesnianski have been considered and using Shuman's algorithm, those equations have been solved. In the process of solving these equations, the output of the energy balance equation is included as wave set up term to incorporate energy contribution of wind waves to surges. The estimated surge height is compared with and without considering wave contribution.      


2021 ◽  
Vol 14 (12) ◽  
pp. 7439-7457
Author(s):  
Mohammad Reza Heidari ◽  
Zhaoyang Song ◽  
Enrico Degregori ◽  
Jörg Behrens ◽  
Hendryk Bockelmann

Abstract. ​​​​​​​The scalability of the atmospheric model ECHAM6 at low resolution, as used in palaeoclimate simulations, suffers from the limited number of grid points. As a consequence, the potential of current high-performance computing architectures cannot be used at full scale for such experiments, particularly within the available domain decomposition approach. Radiation calculations are a relatively expensive part of the atmospheric simulations, taking up to approximately 50 % or more of the total runtime. This current level of cost is achieved by calculating the radiative transfer only once in every 2 h of simulation. In response, we propose extending the available concurrency within the model further by running the radiation component in parallel with other atmospheric processes to improve scalability and performance. This paper introduces the concurrent radiation scheme in ECHAM6 and presents a thorough analysis of its impact on the performance of the model. It also evaluates the scientific results from such simulations. Our experiments show that ECHAM6 can achieve a speedup of over 1.9× using the concurrent radiation scheme. By performing a suite of stand-alone atmospheric experiments, we evaluate the influence of the concurrent radiation scheme on the scientific results. The simulated mean climate and internal climate variability by the concurrent radiation generally agree well with the classical radiation scheme, with minor improvements in the mean atmospheric circulation in the Southern Hemisphere and the atmospheric teleconnection to the Southern Annular Mode. This empirical study serves as a successful example that can stimulate research on other concurrent components in atmospheric modelling whenever scalability becomes challenging.


2021 ◽  
Vol 13 (4) ◽  
pp. 25-33
Author(s):  
Ilinca-Laura BURDULEA ◽  
Alina BOGOI

The topic of this paper is the Kelvin-Helmholtz instability, a phenomenon which occurs on the interface of a stratified fluid, in the presence of a parallel shear flow, when there is a velocity and density difference across the interface of two adjacent layers. This paper focuses on a numerical simulation modelled by the Taylor-Goldstein equation, which represents a more realistic case compared to the basic Kelvin-Helmholtz shear flow. The Euler system is solved with new modelled smooth velocity and density profiles at the interface. The flux at cell boundaries is reconstructed by implementing a third order WENO (Weighted Essentially Non-Oscillatory) method. Next, a Riemann solver builds the fluxes at cell interfaces. The use of both Rusanov and HLLC solvers is investigated. Temporal discretization is done by applying the second order TVD (total variation diminishing) Runge-Kutta method on a uniform grid. Numerical simulations are performed comparatively for both Kelvin-Helmholtz and Taylor-Goldstein instabilities, on the same simulation domains. We find that increasing the number of grid points leads to a better accuracy in shear layer vortices visualization. Thus, we can conclude that applying the Taylor-Goldstein equation improves the realism in the general fluid instability modelling.


Abstract Oceanic density fronts can evolve, be advected, or propagate as gravity currents. Frontal evolution studies require methods to temporally track evolving density fronts. We present an automated method to temporally track these fronts from numerical model solutions. First, at all time steps contiguous density fronts are detected using an edge detection algorithm. A front event, defined as a set of sequential-in-time fronts representing a single time-evolving front, is then identified. At time step i, a front is compared to each front at time step i + 1 to determine if the two fronts are matched. An i front grid point is trackable if the minimum distance to the i + 1 front falls within a range. The i front is forward-matched to the i + 1 front when a sufficient number of grid points are trackable and the front moves onshore. A front event is obtained via forward tracking a front for multiple time steps. Within an event, the times that a grid point can be tracked is its connectivity and a pruning algorithm using a connectivity cutoff is applied to extract only the coherently evolving components. This tracking method is applied to a realistic 3-month San Diego Bight model solution yielding 81 front events with duration ≥ 7 hours, allowing analyses of front event properties including occurrence frequency and propagation velocity. Sensitivity tests for the method’s parameters support that this method can be straightforwardly adapted to track evolving fronts of many types in other regions from both models and observations.


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