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  Subjects -> GEOGRAPHY (Total: 493 journals)
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GEM - International Journal on Geomathematics
Journal Prestige (SJR): 0.321
Citation Impact (citeScore): 1
Number of Followers: 1  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1869-2672 - ISSN (Online) 1869-2680
Published by Springer-Verlag Homepage  [2467 journals]
  • Non-hydrostatic unified model of the ocean with application to ice/ocean
           interaction modeling

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      Abstract: Abstract The non-hydrostatic unified model of the ocean (NUMO) has been developed to advance model capability to realistically represent the dynamics and ice/ocean interactions in Greenland fjords, including an accurate representation of complex fjord geometries. To that end, NUMO uses high-order spectral element methods on unstructured grids to solve the incompressible Navier–Stokes equations complemented with heat and salinity transport equations. This paper presents the model’s description and discusses the formulation of ice/ocean Neumann boundary conditions based on the three-equation model. We validate the model on a range of test cases. The convergence study on the classical Kovasznay flow shows exponential convergence with arbitrary basis function polynomial order. The lock-exchange and density current cases show that the model results of buoyancy-driven flows solved with 2D and 3D unstructured meshes agree well with previously published findings. Finally, we show that a high-order simulation of an ice block immersed in saline water produces results that match both direct numerical simulation and laboratory experiments.
      PubDate: 2022-12-05
       
  • Multiscale simulation of colloids ingressing porous layers with evolving
           internal structure

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      Abstract: Abstract We report on a reaction-diffusion model posed on multiple spatial scales that accounts for diffusion, aggregation, fragmentation, and deposition of populations of colloidal particles. The model is able to account for the heterogeneity of the internal porous structure of the layer. For simplicity, we represent the microstructures as discs with prescribed initial random distribution of radii. As microstructures grow due to the deposition of populations of colloidal particles, local clogging becomes possible, that is neighbouring disks may touch each other. We investigate how distributions of evolving microstructures influence the transport and storage properties of porous layers. As working tool, we propose a FD-FEM discretization of the multiscale model. We illustrate numerically local clogging effects on the dispersion tensor and quantify herewith the layer’s performance with respect to both the efficiency of the transport and the storage capacity. The presented model and numerical approach can be extended in a rather straightforward way to handle slightly more complex geometrical settings like thin porous structures with multi-layers in 2D, or single layers in 3D.
      PubDate: 2022-11-18
       
  • Predicting shallow water dynamics using echo-state networks with transfer
           learning

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      Abstract: Abstract In this paper we demonstrate that reservoir computing can be used to learn the dynamics of the shallow-water equations. In particular, while most previous applications of reservoir computing have required training on a particular trajectory to further predict the evolution along that trajectory alone, we show the capability of reservoir computing to predict trajectories of the shallow-water equations with initial conditions not seen in the training process. However, in this setting, we find that the performance of the network deteriorates for initial conditions with ambient conditions (such as total water height and average velocity) that are different from those in the training dataset. To circumvent this deficiency, we introduce a transfer learning approach wherein a small additional training step with the relevant ambient conditions is used to improve the predictions.
      PubDate: 2022-11-04
       
  • Fourier analysis of the local discontinuous Galerkin method for the
           linearized KdV equation

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      Abstract: Abstract A Fourier/stability analysis of the third-order Korteweg–de Vries equation is presented subject to a class of local discontinuous Galerkin discretization using high-degree Lagrange polynomials. The selection of stability parameters involved in the method is made on the basis of the study of the higher frequency eigenmodes and the Fourier analysis. Explicit analytical dispersion relation and group velocity are obtained and the stability study of the discrete frequency is performed. The emergence of gaps in the imaginary part of the computed frequency is observed and studied for the first time to our knowledge. Further, a superconvergent result is demonstrated for the discrete frequency by obtaining an explicit analytical asymptotic formula for the latter.
      PubDate: 2022-10-27
       
  • p-adaptive discontinuous Galerkin method for the shallow water equations
           with a parameter-free error indicator

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      Abstract: Abstract We propose a p-adaptive quadrature-free discontinuous Galerkin method for the shallow water equations based on a computationally efficient adaptivity indicator which works without any problem-dependent parameters. The error and smoothness of the solution are detected using the information collected for slope limiting and, for piecewise constant discretizations, by carrying out a reconstruction procedure. The accuracy and robustness of the new scheme are evaluated using several benchmarks and compared to other adaptivity indicators. Our results indicate that the proposed indicator finds a good balance between solution quality and computational overhead.
      PubDate: 2022-10-11
       
  • Emergence of non-Fickian transport in truncated pluri-Gaussian
           permeability fields

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      Abstract: Abstract We present a numerical simulation study of advective–diffusive scalar transport in three-dimensional high-contrast discontinuous permeability fields, generated with a truncated pluri-Gaussian geostatistical approach. The numerical experiments are run with an Eulerian approach using a novel unified numerical framework based on the finite-volume library OpenFOAM®(Weller et al. in Comput Phys 12(6):620–631, 1998), for (1) generating random pluri-Gaussian porous media, (2) solving the steady state Darcy-scale flow, (3) solving the advection diffusion equation, (4) computing post-processing quantities such as first order statistics, spatial probability density functions and breakthrough curves. A range of permeability contrasts, correlation lengths, and Péclet numbers are tested to assess their relative weight on transport control and for the first time, the deviation of a calibrated macrodispersive model from the Fickian transport is quantified. We identify a hierarchy of non-Fickian transport triggering factors. From the tested scenarios, permeability contrast is the main controlling parameter for the anomalous transport behaviour as it enhances the generation of preferential flow paths which are characterised by high advective flow velocities. The Péclet number and the characteristic length at which facies transitions are observed as secondary factors.
      PubDate: 2022-10-01
       
  • A comparative study of integral and coupled approaches for modeling
           hydraulic exchange processes across a rippled streambed

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      Abstract: Abstract Although both are crucial parts of the hydrological cycle, groundwater and surface water had traditionally been addressed separately. In recent decades, considering them as a single hydrological continuum in light of their continuous interaction has become well established in the scientific community through the development of numerous measurement and experimental techniques. Nevertheless, numerical models, as necessary tools to study a wide range of scenarios and future event predictions, are still based on outdated concepts that consider groundwater and surface water separately. This study compares these “coupled models”, which result from the successive execution of a surface water model and a groundwater model, to a recently developed “integral model”. The integral model uses a single set of equations to model both groundwater and surface water simultaneously, and can account for the continuous interaction at their interface. For comparison, we investigated small-scale flow across a rippled porous streambed. Although we applied identical model domain details and flow conditions, which resulted in very similar water tables and pressure distributions, comparing the integral and coupled models yielded very dissimilar velocity values across the groundwater–surface water interface. These differences highlight the impact of continuous exchange across the interface in the integral model, which imitates such flow processes more realistically than the coupled model. A few decimeters away from the interface, modeled velocity fields are very similar. Since the integral model and the surface water component of the coupled model are both CFD-based (computational fluid dynamics), they require very similar computational resources, namely access to cluster computers. Unfortunately, replacing the surface water component of the coupled model with the widely used shallow water equations model, which indeed would reduce the computational resources required, produces inaccuracy.
      PubDate: 2022-09-13
      DOI: 10.1007/s13137-022-00206-5
       
  • A self-similar solution for transient Darcy–Forchheimer flow in an
           aquifer

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      Abstract: Abstract In this study we examine the classical problem of fluid flow in an aquifer, obeying the transient Darcy–Forchheimer law. This problem is solved by using the symmetry properties of the governing equations (e.g. the mass balance equation and the transient Darcy–Forchheimer momentum equation) which enable us to transform the time and the space coordinates into one independent coordinate. According to our study the flow in the aquifer may be divided into two main components. One component is the steady part of the flow discharge and the other one is the transient part of the flow discharge. The obtained solution shows that the reduction in the above-mentioned transient part leads to the creation of three zones: (1) the “near zone” located near the inlet face to the aquifer and is characterized by a positive flow; (2) the “far zone” in the aquifer lying at an infinite distance from the inlet face where the flow is also positive and (3) the “intermediate backflow zone”, which is lying among the above-mentioned zones and is characterized by reverse flow. The results obtained in this study may be useful for understanding the transient flow process in the aquifer, stemming from the Darcy–Forchheimer flow, and for the prediction of the discharge and head distribution in the aquifer.
      PubDate: 2022-08-19
      DOI: 10.1007/s13137-022-00205-6
       
  • Generation of SH-wave in a medium of welded two-quarter spaces with a
           uniform layer on one quarter space

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      Abstract: Abstract This paper examines the generation of elastic SH-waves in a medium of two-quarter spaces in welded contact with a layer of uniform thickness overlying one of the quarter spaces. Impulsive surface tractions on the surface generate the waves. Transform methods are employed to obtain the functional integral equation in the general case. Approximations are made when a layer overlies a halfspace to obtain the solution. The displacement at the surface of the layer is obtained as a series of definite integrals representing the different pulses reflected at the interface between the layer and the halfspace.
      PubDate: 2022-08-02
      DOI: 10.1007/s13137-022-00201-w
       
  • A forecasting model for the porosity variation during the carbonation
           process

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      Abstract: Abstract In this paper we introduce a mathematical model of concrete carbonation Portland cement specimens. The main novelty of this work is to describe the intermediate chemical reactions, occurring in the carbonation process of concrete, involving the interplay of carbon dioxide with the water present into the pores. Indeed, the model here proposed, besides describing transport and diffusion processes inside the porous medium, takes into account both fast and slow phenomena as intermediate reactions of the carbonation process. As a model validation, by using the mathematical based simulation algorithm we are able to describe the effects of the interaction between concrete and CO \(_2\) on the porosity of material as shown by the numerical results in substantial accordance with experimental results of accelerated carbonation taken from literature. We also considered a further reaction: the dissolution of calcium carbonate under an acid environment. As a result, a trend inversion in the evolution of porosity can be observed for long exposure times. Such an increase in porosity results in the accessibility of solutions and pollutants within the concrete leading to an higher permeability and diffusivity thus significantly affecting its durability.
      PubDate: 2022-07-25
      DOI: 10.1007/s13137-022-00204-7
       
  • The geophysical KdV equation: its solitons, complexiton, and conservation
           laws

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      Abstract: Abstract The main goal of the current paper is to analyze the impact of the Coriolis parameter on nonlinear waves by studying the geophysical KdV equation. More precisely, specific transformations are first adopted to derive one-dimensional and operator forms of the governing model. Solitons and complexiton of the geophysical KdV equation are then retrieved with the help of several well-established approaches such as the Kudryashov and Hirota methods. In the end, the new conservation theorem given by Ibragimov is formally employed to extract conservation laws of the governing model. It is shown that by increasing the Coriolis parameter, based on the selected parameter regimes, less time is needed for tending the free surface elevation to zero.
      PubDate: 2022-07-24
      DOI: 10.1007/s13137-022-00203-8
       
  • Propagation of hydropeaking waves in heterogeneous aquifers: effects on
           flow topology and uncertainty quantification

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      Abstract: Topological flow properties are proxies for mixing processes in aquifers and allow us to better understand the mechanisms controlling transport of solutes in the subsurface. However, topological descriptors, such as the Okubo–Weiss metric, are affected by the uncertainty in the solution of the flow problem. While the uncertainty related to the heterogeneous properties of the aquifer has been widely investigated in the past, less attention has been given to the one related to highly transient boundary conditions. We study the effect of different transient boundary conditions associated with hydropeaking events (i.e., artificial river stage fluctuations due to hydropower production) on groundwater flow and the Okubo–Weiss metric. We define deterministic and stochastic modeling scenarios applying four typical settings to describe river stage fluctuations during hydropeaking events: a triangular wave, a sine wave, a complex wave that results of the superposition of two sine waves, and a trapezoidal wave. We use polynomial chaos expansions to quantify the spatiotemporal uncertainty that propagates into the hydraulic head in the aquifer and the Okubo–Weiss. The wave-shaped highly transient boundary conditions influence not only the magnitude of the deformation and rotational forces of the flow field but also the temporal dynamics of dominance between local strain and rotation properties. Larger uncertainties are found in the scenario where the trapezoidal wave was imposed due to sharp fluctuation in the stage. The statistical moments that describe the propagation of the uncertainty highly vary depending on the applied boundary condition. Highlights Deterministic and stochastic scenarios to describe the groundwater flow field under river stage fluctuations during hydropeaking. Propagation of uncertainty of highly transient boundary conditions in the Okubo–Weiss metric. Highly transient boundary conditions can significantly affect mixing potential.
      PubDate: 2022-07-22
      DOI: 10.1007/s13137-022-00202-9
       
  • Permeability extraction from multiple well logs using particle swarm
           optimization based factor analysis

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      Abstract: Abstract In this paper, we present an innovative factor analysis algorithm for hydrocarbon exploration to estimate the intrinsic permeability of reservoir rocks from well logs. Unlike conventional evaluation methods that employ a single or a limited number of data types, we process simultaneously all available data to derive the first statistical factor and relate it to permeability by regression analysis. For solving the problem of factor analysis, we introduce an improved particle swarm optimization method, which searches for the global minimum of the distance between the observed and calculated data and gives a quick estimation for the factor scores. The learning factors of the intelligent computational technique such as the cognitive and social constants are specified as hyperparameters and calculated by using simulated annealing algorithm as heuristic hyperparameter estimator. Instead of the arbitrary fixation of these hyperparameters, we refine them in an iterative process to give reliable estimation both for the statistical factors and formation permeability. The estimated learning parameters are consistent with literature recommendations. We demonstrate the feasibility of the proposed well-log analysis method by a Hungarian oilfield study involving open-hole wireline logs and core data. We determine the spatial distribution of permeability both along a borehole and between more wells using the factor analysis approach, which serves as efficient and reliable multivariate statistical tool for advanced formation evaluation and reservoir modeling.
      PubDate: 2022-06-25
      DOI: 10.1007/s13137-022-00200-x
       
  • Recovery of wave speeds and density of mass across a heterogeneous smooth
           interface from acoustic and elastic wave reflection operators

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      Abstract: Abstract We revisit the problem of recovering wave speeds and density across a curved interface from reflected wave amplitudes. Such amplitudes have been exploited for decades in (exploration) seismology in this context. However, the analysis in seismology has been based on linearization and mostly flat interfaces. Here, we present an analysis without linearization and allow curved interfaces, establish uniqueness and provide a reconstruction, while making the notion of amplitude precise through a procedure rooted in microlocal analysis.
      PubDate: 2022-05-13
      DOI: 10.1007/s13137-022-00199-1
       
  • On the existence of Parker’s ideal bodies

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      Abstract: Abstract After a short introduction on the historical context, the paper deals with the existence of the solution of Parker’s ideal body problem, namely the body of minimum constant density generating a given external potential. A crucial element of the proof is the use of a recently introduced topological space of closed sets, closed and compact with the distance defined as the Lebesgue measure of the symmetric difference of a couple of sets. Such a space is indeed smaller than that of all closed sets of a given B, but larger than that of star-shaped Lipschitz domains, where previous studies of the inverse gravimetric problem (with constant density) have been conducted. However, with the present knowledge, it is only in this class that a uniqueness theorem holds.
      PubDate: 2022-05-11
      DOI: 10.1007/s13137-022-00198-2
       
  • Optimal experiment design for a bottom friction parameter estimation
           problem

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      Abstract: Abstract Calibration with respect to a bottom friction parameter is standard practice within numerical coastal ocean modelling. However, when this parameter is assumed to vary spatially, any calibration approach must address the issue of overfitting. In this work, we derive calibration problems in which the control parameters can be directly constrained by available observations, without overfitting. This is achieved by carefully selecting the ‘experiment design’, which in general encompasses both the observation strategy, and the choice of control parameters (i.e. the spatial variation of the friction field). In this work we focus on the latter, utilising existing observations available within our case study regions. We adapt a technique from the optimal experiment design (OED) literature, utilising model sensitivities computed via an adjoint-capable numerical shallow water model, Thetis. The OED method uses the model sensitivity to estimate the covariance of the estimated parameters corresponding to a given experiment design, without solving the corresponding parameter estimation problem. This facilitates the exploration of a large number of such experiment designs, to find the design producing the tightest parameter constraints. We take the Bristol Channel as a primary case study, using tide gauge data to estimate friction parameters corresponding to a piecewise-constant field. We first demonstrate that the OED framework produces reliable estimates of the parameter covariance, by comparison with results from a Bayesian inference algorithm. We subsequently demonstrate that solving an ‘optimal’ calibration problem leads to good model performance against both calibration and validation data, thus avoiding overfitting.
      PubDate: 2022-04-30
      DOI: 10.1007/s13137-022-00196-4
       
  • Semi-analytical solutions for the problem of the electric potential set in
           a borehole with a highly conductive casing

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      Abstract: Abstract Highly conductive thin casings pose a great challenge in the numerical simulation of well-logging instruments. Witty asymptotic models may replace the presence of casings by impedance transmission conditions in those numerical simulations. The accuracy of such numerical schemes can be tested against benchmark solutions computed semi-analytically in simple geometrical configurations. This paper provides a general approach to construct those benchmark solutions for three different models: one reference model that indeed considers the presence of the casing; one asymptotic model that avoids computations in the casing domain; and one asymptotic model that reduces the presence of the casing to an interface. Our technique uses a Fourier representation of the solutions, where special care has been taken in the analytical integration of singularities to avoid numerical instabilities.
      PubDate: 2022-04-29
      DOI: 10.1007/s13137-022-00197-3
       
  • Rayleigh wave propagation in a nonlocal isotropic magneto-thermoelastic
           solid with multi-dual-phase lag heat transfer

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      Abstract: Abstract The present paper deals with Rayleigh wave propagation in a homogeneous isotropic nonlocal magneto-thermoelastic solid with hall current and rotation. The considered thermoelastic solid is subjected to multi-dual-phase lag heat transfer. The Secular equations of Rayleigh waves are derived mathematically at the stress-free and thermally insulated boundaries. The values of stress components, temperature change, phase velocity, attenuation coefficient, penetration depth and specific loss have been computed numerically and depicted graphically. The effects of hall current and nonlocal parameter have been depicted on the various wave quantities. Some particular cases have also been deduced from the present investigation.
      PubDate: 2022-04-01
      DOI: 10.1007/s13137-022-00195-5
       
  • Variational principle for some nonlinear problems

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      Abstract: Abstract A variational principle is established by the semi-inverse method and used to solve approximately a nonlinear problem by the Ritz method. In this process,it may be difficult to solve a large system of algebraic equations,the Groebner bases theory (Buchberger’s algorithm) is applied to solve this problem. The results show that the variational approach is much simpler and more efficient.
      PubDate: 2022-02-04
      DOI: 10.1007/s13137-022-00194-6
       
  • A study of moisture content in unsaturated porous medium by using homotopy
           perturbation method (HPM) and variational iteration method (VIM)

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      Abstract: Abstract Vertical infiltration of water plays an important role in the recharged of contaminated water and enhanced moisture content in the unsaturated porous media. The mathematical model used for such type of phenomenon is Burger's equation. Unsaturated porous media are analyzed by solving Burger's equation using the variational iterative modeling and homotopy perturbation method. When considering all moisture contents, it appears that the cumulative coefficient is unchanged. It is also shown that the soil's moisture content decreases with depth (y) and time (t). The results indicate that this method is very efficient and can be useful to solve large-scale problems that arise in civil engineering, geology, material science, and fossil fuel problems.
      PubDate: 2022-01-06
      DOI: 10.1007/s13137-021-00193-z
       
 
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