Grid Arrangement Research Articles

Three-dimensional numerical study for laminar natural convection within a rectangular solar chimney

A numerical study of three – dimensional, steady, laminar and incompressible natural convection of air (Pr=0.72) within a rectangular solar chimney is presented. Partial differential equations for conservation of mass, momentum and energy equations are solved by finite volume method with staggered grid arrangement. SIMPLE algorithm is applied to solve the set of discretization equations. The numerical results are compared with those of previous published work under the same conditions and gives a good agreement. The influence of changing in chimney dimension (thickness and height) and the inlet air temperature on the amount of induced flow rate is studied. From the presented results the optimal design for the chimney can be achieved

Research on Effects of Obstacles on Heat Transfer and Fluid Flow in Backward Facing Step Flow

An extensive research has been done on heat transfer and pressure drop characteristics in micro-channel using liquid water. A baffle has been introduced downstream the sudden expansion zone to enhance the rate of heat transfer. The height and the location of the baffle were varied for the Reynolds number range 50≤ Re ≤ 200, which is a laminar flow. Twodimensional flow domain with non-staggered grid arrangement was taken and the two-dimensional mass, momentum and energy equation was solved using finite volume method in ANSYS 16.2. This study reports that the presence of baffle in the microchannel increased the rate of heat transfer. The skin friction coefficient has been calculated and the parameters influencing the heat transfer augmentation have been optimized

Using Simpler Algorithm for Cavity Flow Problem

Selecting compute nodes and solution grid generation are the first steps of numerical solutions. The most distinct manner is storing the values of dependent variables in the same set of nodes and using the identical control volumes for all variables. Such a grid is called Collocated. Collocated grid arrangement has many positive results in problems with complex solving range, especially with discontinuous boundary conditions. But this arrangement was not used for a long time for incompressible flow due to pressure and velocity isolation problems and creation of fluctuations in pressure. So the researchers in the mid-60s, have developed a new arrangement to reduce this isolation and increase the coupling between pressure and velocity. This new arrangement called staggered grid, provided the field of a new method for solving fluid flow problems called SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm [1]. This report presents the solution to the continuity, Navier-Stokes equations. Standard fundamental methods like SIMPLER and primary variable formulation have been utilized. The results were analyzed for standard CFD test case- cavity flow. Different Reynold number (1000, 3000) and grid sizes with the finest meshes ie. (100×100), (1000×1000) have been studied.

NUMERICAL STUDY OF MATCHING STRUCTURE FOR INFINITE WAVEGUIDE PHASED ANTENNA ARRAY BY FINITE ELEMENTS METHOD

In this paper a numerical study of an infinite plane rectangular waveguides PAA with the proposed matching structure has been performed in the form of a modified matching structure with an extra layer of dielectric (foam) by the finite element method.To analyze the antenna array mode l by the finite element method, a program package of HFSS 14 has been used. An infinite waveguide PAA analyzed by the HFSS program, is approximated by an infinite number of emitters placed periodically with geometry identical to the real antenna array. When constructing a triangular grid arrangement of emitters for the correct description of a central single cell, one must determine the shift between the boundary conditions of the Master and the Slave, which determines the ratio of the breakdown of the Master and Slave boundary conditions along the coordinate meshes. This procedure should take into account the grid angle and the transverse geometric dimensions of the "Flock channel" and the waveguide.The purpose of the modification of the matching structure (MS) consisting of the dielectric layer, which is located above the antenna aperture, is to remove the defect in the form of a air layer between the aperture and the dielectric layer, which may lead to the bending of the dielectric layer, which, in turn, can cause heterogeneity of the dielectric value permeability along the MS. To remove this air layer, it has been suggested to use an extra layer that will not allow bending the upper dielectric layer. The foam was chosen as an dielectric, which, firstly, has a small density that essentially does not change the mass of the MS, and secondly, it is cheap and well-treated, and its relative permittivity is close to the air (ε = 1.1). The results of the theoretical study of the use of foam in the CS were carried out in a wide range of values of the thickness of dielectric layers.The numerical results of the calculations allow us to conclude that the model of the MS, which is being investigated, allows to improve the mechanical properties of the PAA while maintaining the operating parameters: reflection coefficient, frequency range and range of angles of scanning.

Bento Box: An Interactive and Zoomable Small Multiples Technique for Visualizing 4D Simulation Ensembles in Virtual Reality.

We present Bento Box, a virtual reality data visualization technique and bimanual 3D user interface for exploratory analysis of 4D data ensembles. Bento Box helps scientists and engineers make detailed comparative judgments about multiple time-varying data instances that make up a data ensemble (e.g., a group of 10 parameterized simulation runs). The approach is to present an organized set of complementary volume visualizations juxtaposed in a grid arrangement, where each column visualizes a single data instance and each row provides a new view of the volume from a different perspective and/or scale. A novel bimanual interface enables users to select a sub-volume of interest to create a new row on-the-fly, scrub through time, and quickly navigate through the resulting virtual “bento box.” The technique is evaluated through a real-world case study, supporting a team of medical device engineers and computational scientists using in-silico testing (supercomputer simulations) to redesign cardiac leads. The engineers confirmed hypotheses and developed new insights using a Bento Box visualization. An evaluation of the technical performance demonstrates that the proposed combination of data sampling strategies and clipped volume rendering is successful in displaying a juxtaposed visualization of fluid-structure-interaction simulation data (39 GB of raw data) at interactive VR frame rates.

Nanofluid flow and heat transfer from heated square cylinder in the presence of upstream rectangular cylinder under Couette-Poiseuille flow

A heated square cylinder (with height A*) is kept parallel to the cold wall at a fixed gap height 0.5A* from the wall. Another adiabatic rectangular cylinder (of same height A* and width 0.5A*) is placed upstream in an inline tandem arrangement. The spacing between the two cylinders is fixed at 3.0A*. The inlet flow is taken as Couette-Poiseuille flow based non-linear velocity profile. The conventional fluid (also known as base fluid) is chosen as water (W) whereas the nanoparticle material is selected as Al2O3. Numerical simulations are performed by using SIMPLE algorithm based Finite Volume approach with staggered grid arrangement. The dependencies of hydrodynamic and heat transfer characteristics of the cylinder on non-dimensional parameters governing the nanofluids and the fluid flow are explored here. A critical discussion is made on the mechanism of improvement/reduction (due to the presence of the upstream cylinder) of heat transfer and drag coefficient, in comparison to those of an isolated cylinder. It is observed that the heat transfer increases with the increase in the non-linearity in the incident velocity profile at the inlet. For the present range studied, particle concentration has a negligible effect on heat transfer.

Impact of nanoparticles migration on mixed convection and entropy generation of a $$\hbox {Al}_{2}\hbox {O}_{3}$$–water nanofluid inside an inclined enclosure with wavy side wall

A numerical study based on the non-homogeneous model of the mixed convection of $$\hbox {Al}_{2}\hbox {O}_{3}$$–water nanofluid in an inclined enclosure is made. The heated side wall of the enclosure is considered to be wavy while the top wall is made to translate horizontally. The wavy physical domain is transformed to a square computational domain through a suitable coordinate transformation. The transformed governing equations are integrated based on the control volume approach in a staggered grid arrangement. A third-order accurate upwind scheme QUICK is used to discretize the convective terms while a central difference type scheme is used to approximate the diffusive terms. The discretized equations along with the specified boundary conditions are solved through a pressure correction-based SIMPLE algorithm. The impact of the inclination angle of the enclosure and surface waviness on the nanofluid mixed convection is elucidated. The parameters governing the Brownian motion, thermophoresis, Lewis number and buoyancy ratio parameter are determined based on the nanofluid thermophysical properties. The effect of the nanoparticle bulk volume fraction and nanoparticle diameter on the mixed convection is analyzed for different choices of nanofluid-to-base fluid thermal buoyancy ratio in the buoyancy-dominated regime as well as shear-dominated regime. A comparison of the non-homogeneous model for the nanofluid with the homogeneous model is also made in this study. The inclination angle of the enclosure is found to have an impact on the mixed convection when buoyancy force is dominant. Heat transfer augmentation occurs as the wave number, and/or wave amplitude of the wavy side wall is increased. The thermodynamic optimization is studied by analyzing the average Nusselt number and the total entropy generation.

Bingham fluid flow simulation in a lid-driven skewed cavity using the finite-volume method

ABSTRACTIn this paper, laminar flow of non-Newtonian (Bingham) fluid is studied numerically in a two-dimensional lid-driven skewed cavity that incorporates Papanastasiou exponential regularization approach of Bingham constitutive model [Papanastasiou, Flows of materials with yield, J. Rheol. 31 (1987), pp. 385–404]. Numerical simulation has been done using the finite-volume method with collocated grid arrangement. The governing equations including continuity and momentum are initially non-dimensionalized using appropriate transformation. To simulate irregular shape cavity flow problem, body-fitted non-orthogonal grids are used, and governing equations have been transformed to generalized curvilinear co-ordinates. In this study, two dimensionless parameters namely, Reynolds number and Bingham number are considered. A wide range of skew angles are considered which comprises both acute and obtuse angles. The obtained results are presented in terms of velocity and streamlines with yielded/unyielded region for different values of Bingham number and Reynolds number having different angles of the skewed cavity. The present results may be serve as benchmark results for comparison purpose in the case of non-Newtonian (Bingham) fluid flow.

Hexagonal and Square Patterned Silver Nanowires/PEDOT:PSS Composite Grids by Screen Printing for Uniformly Transparent Heaters.

Transparent conductive films with hexagonal and square patterns were fabricated on poly(ethylene terephthalate) (PET) substrates by screen printing technology utilizing a poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate) (PEDOT:PSS) and silver nanowire (Ag NWs) composite ink. The printing parameters—mesh number, printing layer, mass ratio of PEDOT:PSS to Ag NWs and pattern shape—have a significant influence on the photoelectric properties of the composite films. The screen mesh with a mesh number of 200 possesses a suitable mesh size of 74 µm for printing clear and integrated grids with high transparency. With an increase in the printing layer and a decrease in the mass ratio of PEDOT:PSS to Ag NWs, the transmittance and resistance of the printed grids both decreased. When the printing layer is 1, the transmittance and resistance are 85.6% and 2.23 kΩ for the hexagonal grid and 77.3% and 8.78 kΩ for the square grid, indicating that the more compact arrangement of square grids reduces the transmittance, and the greater number of connections of the square grid increases the resistance. Therefore, it is believed that improved photoelectric properties of transparent electrodes could be obtained by designing a printing pattern with optimized printing parameters. Additionally, the Ag NWs/PEDOT:PSS composite films with hexagonal and square patterns exhibit high transparency and good uniformity, suggesting promising applications in large-area and uniform heaters.

Numerical Simulation of Non-Newtonian Power-Law Fluid Flow in a Lid-Driven Skewed Cavity

Non-Newtonian laminar fluid flow in a lid-driven skewed cavity has been studied numerically using power-law viscosity model. The governing two-dimensional unsteady incompressible Navier–Stokes equations were initially non-dimensionalized using appropriate transformation, and then the dimensionless form is transformed to generalized curvilinear coordinates to simulate complex geometry. The transformed equations are discretized using finite volume method with the collocated grid arrangement. The code is first validated against the existing benchmark results for two-dimensional lid-driven square cavity problem considering both Newtonian and non-Newtonian fluids. The validation has also been carried out for a lid-driven skewed cavity in the case of a Newtonian fluid. Then the code is applied to the skewed cavity problem involving non-Newtonian fluid flow which can be described by the power-law viscosity model. Moreover, grid independence test has been performed for a skewed cavity for different values of power-law index. In the present case, the skewness of the geometry has been changed by changing the skew angle for both shear-thinning and shear-thickening fluids. The consequent numerical results are presented in terms of the velocity as well as streamlines for the different values of the power-law index $$n=0.5$$ , 1 and 1.5, Reynolds number $$Re = 100, 200, 300$$ and 500 as well as for the different angles of the skewed cavity ( $$\alpha =15^{\circ }$$ to $$165^{\circ }$$ ).

NUMERICAL INVESTIGATION OF THE HYDRODYNAMICS OF A LID-DRIVEN NON-DARCY ANISOTROPIC POROUS CAVITY

The present study investigates the hydrodynamics of a lid-driven flow saturated with non-Darcy anisotropic porous media. The Reynolds numbers considered for the study are 10, 100, and 1000. The effect of the Darcy number (10-5 ≤ Da ≤ 10-2) and porosity (ε = 0.3 and 0.6) have been varied to analyze the permeability ratio (K* = 0.1, 1, and 10), Forchheimer constants ratio (F* = 1, 10, and 100), and principal axes inclination (θ = 0°, 45°, and 90°) on the flow behavior. A semi-implicit method for pressure-linked equations algorithm–based finite-volume method has been employed to solve the governing equations. Quadrilateral cells in a collocated grid arrangement have been considered. The flow physics has been interpreted by plotting the results in terms of streamlines and maximum stream function values. The study reveals that with an increase in the Reynolds number the influence of nonlinear drag forces becomes significant. Also, it is observed that the anisotropic parameters of the non-Darcy porous media profoundly modulate the flow.

Voronoi-Like Grid Systems for Tall Buildings

In the context of innovative patterns for tall buildings, Voronoi tessellation is certainly worthy of interest. It is an irregular biomimetic pattern based on the Voronoi diagram, which derives from the direct observation of natural structures. The paper is mainly focused on the application of this nature-inspired typology to load-resisting systems for tall buildings, investigating the potential of non-regular grids on the global mechanical response of the structure. In particular, the study concentrates on the periodic and non-periodic Voronoi tessellation, describing the procedure for generating irregular patterns through parametric modelling and illustrates the homogenization-based approach proposed in the literature for dealing with unconventional patterns. To appreciate the consistency of preliminary design equations, numerical and analytical results are compared. Moreover, since the mechanical response of the building strongly depends on the parameters of the microstructure, the paper focuses on the influence of the grid arrangement on the global lateral stiffness, therefore on the displacement constraint, which is an essential requirement in the design of tall buildings. To this end, five case studies, accounting for different levels of irregularity and relative density, are generated and analyzed through static and modal analysis in the elastic field. In addition, the paper focuses on the mechanical response of a pattern with gradual rarefying density to evaluate its applicability to tall buildings. Displacement‐based optimizations are carried out to assess the adequate member cross sections that provide the maximum contribution in restraining deflection with the minimum material weight. The results obtained for all the models generated are compared and discussed to outline a final evaluation of the Voronoi structures. In addition to the wind loading scenario, the efficiency of the building model with varying density Voronoi pattern, is tested for seismic ground motion through a response spectrum analysis. The potential applications of Voronoi tessellation for tall buildings is demonstrated for both regions with high wind load conditions and areas of high seismicity.

Numerical model of two-dimensional flow dynamic of explicit splitting method

A solution of partial differential equations has been examined in the 2D Navier-Stokes Hydrodynamic equation by applying a numerical solution. This study aims to discuss the preparation of the circulation model by using a two-dimensional numerical model explicit splitting method. The solution can only be applied if it has fulfilled a stability requirement in determining the time and space steps. In modeling this method, the effects that cause instability such as boundary conditions and initial values of numerical equations was analyzed. Theresults of the rectangular discretization grid arrangement model shows a flow distribution value similar to the SUTRENCH model, which models the linear grid curve. The difference occurred only at the open boundary value in the east, however, the value is not significant to conclude the incompatibility with the verified model. In this study, it is also found that the velocity distribution in front of the jetty is greater than the current distribution in other areas, this is caused by narrowing area passed by the water mass, causing the discharge out of water larger.

Advancing Dynamical Cores of Oceanic Models across All Scales

Oceanic numerical models are used to understand and predict a wide range of processes from global paleoclimate scales to short-term prediction in estuaries and shallow coastal areas. One of the overarching challenges, and the main topic of the COMMODORE workshop, is the appropriate design of the dynamical cores given the wide variety of scales of interest and their interactions with atmosphere, sea-ice, biogeochemistry, and even societal processes. The construction of a dynamical core is a very long effort which takes years and decades of research and development and which requires a collaborative mixture of scientific disciplines. This work involves a significant number of fundamental choices, such as which equations to solve, which horizontal and vertical grid arrangement is adequate, which discrete algorithms allows jointly computational efficiency and sufficient accuracy, etc. Nowadays, a broad range of numerical methods are implemented in models used for realistic ocean simulations, and, owed to the advances in computational power, a meeting point has been reached between global circulation models and regional local models such that there can be mutual benefits of a cross-fertilization between communities. This report outlines an initiative to bring together the world-wide leading researchers actively contributing to the development of oceanic model dynamical cores, such that participants could network together and focus on next challenges irrespective of target applications (regional, coastal, or global). The first community for the numerical modeling of the global, regional and coastal ocean (COMMODORE) workshop (https://commodore2018.sciencesconf.org/) has been organized in Paris in September 2018. In total, the participants represented 15 oceanic dynamical cores among the most widely used by the research and operational community. The motivations, topics of discussion sessions, and outcomes of the workshop are summarized below.

Optimization of a table-top x-ray fluorescence computed tomography (XFCT) system

Pencil beam x-ray fluorescence computed tomography (XFCT) has typically used a single spectrometer and prohibitively long scan times. However, detecting backscattered fluorescent x-rays from gold nanoparticles (AuNPs) using multiple spectrometers greatly reduces image noise and scan time. The arrangement of eight spectrometers for combined K-shell and L-shell XFCT was investigated along with a variety of conditions. A 2.5 cm-diameter cylindrical water phantom containing 4 mm-diameter vials with 0.1%–2% AuNP concentrations by weight was modeled by TOPAS, a GEANT4-based Monte Carlo software. The phantom was irradiated to 30 mGy by a 0.5 mm Pb-filtered 120 kVp and 1 mm Al-filtered 30 kVp 1 mm2 x-ray pencil beam to yield respective Au K-shell and L-shell fluorescent x-rays, with 50 0.5 mm translation and 2-degree rotation steps. Eight CdTe and silicon drift detector (SDD) spectrometers were placed 2.25 cm away from the isocentre. The respective energy resolution was applied to the detected energy spectra and the spectra were corrected for detector response before extracting the fluorescence signal. Three CdTe and SDD spectrometer configurations (isotropic/backscattered grid/backscattered row arrangements), two CdTe crystal sizes (9 mm2/25 mm2), two scanning techniques (moving/stationary spectrometers) and five vial-edge depths (0–4 mm) were considered in optimizing the contrast-to-noise ratio (CNR) for each XFCT image reconstructed with a maximum-likelihood expectation maximization (MLEM) algorithm. The isotropic spectrometer arrangement had AuNP detection sensitivities of 0.106% for K-shell and 0.132% for L-shell XFCT at 4 mm depth. Comparatively, the backscattered grid arrangement had the best AuNP sensitivity of 0.055% and 0.095%. The highest K-shell (0.044%) and L-shell (0.004%) AuNP sensitivities were found for vials at 0 mm depth. Using stationary spectrometers or the 9 mm2 CdTe crystal compromised the CNR. For the best-case arrangement, L-shell XFCT is superior at vial-edge depths less than 3.0 mm. This work demonstrated the importance of spectrometer arrangement and vial depth for improving AuNP sensitivity and will guide the design for our table-top XFCT system.

Magnetic field modelling and analysis of uncertainty in archaeological geophysics

AbstractOne of the major problems in the forward modelling of magnetic anomalies is the assessment of a minimum level of acceptable accuracy in the fit between observed and theoretical anomalies. We present a new approach to the analysis and interpretation of archaeological magnetic anomalies, based on classical algorithms of forward modelling and a new technique of error assessment. This approach allows us to determine geometry, physical properties, and location of buried archaeological features, as well as the occurrence of fires or other historical events that may have affected the observed magnetic signal. Our method starts from the acquisition of total field data, usually in a regular grid arrangement, and proceeds through their reduction to archaeological magnetic anomalies. This reduction is performed subtracting from the observed total field data a polynomial representation of the regional field, on the basis of a rigorous criterion that tries to separate archaeological anomalies from geological (crustal) contributions. At the next step, a map of the maximum allowed misfit is built, which depends from the estimated uncertainty at each point of the magnetic anomaly field. This map specifies the maximum allowed deviation of theoretical anomalies from the observed values. The last step is the analysis of these anomalies through a new forward modelling tool, with the objective to reconstruct the three‐dimensional arrangement of buried features and possibly obtain some information about the history.

Combined effects of thermal jump and momentum slip on heat transfer phenomena of unbounded spherical particles

Combined effects of momentum slip and thermal jump on the forced convective heat transfer from spherical particles to Newtonian fluids are reported based on a numerical study. The governing dimensionless conservation equations of the mass, momentum, and energy are solved using in-house computational fluid dynamics-based solver, namely simplified marker and cell algorithm implemented on a staggered grid arrangement in spherical coordinates. The range of parameters considered herein is Reynolds number ( $$1 \le Re \le 200$$ ), dimensionless momentum slip parameter ( $$0.01 \le \lambda _\mathrm{v}\le 100$$ ), dimensionless thermal jump parameter ( $$0.01 \le \lambda _\mathrm{T}\le 10$$ ), and Prandtl number ( $$1 \le Pr \le 100$$ ). The isotherm contours along with the local and surface-mean Nusselt numbers are presented for better understanding of heat transfer phenomena around the spherical particles under the influence of momentum and thermal jump at the interface. The main conclusion of this study is that the effects of the momentum slip parameter and temperature jump on heat transfer act in opposite manner; i.e., large momentum slip (small $$\lambda _\mathrm{v}$$ values) on a solid surface increases the convection while a large thermal jump decreases the rate of heat transfer due to the reduction in the magnitude of the temperature gradient at the solid–fluid interface. Finally, the effect of a thermal jump on the rate of heat transfer is more severe than that of velocity slip condition, especially when $$\lambda _\mathrm{T} > 1$$ for any combination of the Reynolds and Prandtl numbers.

CFD modelling of pump-around jet mixing tanks: a discrepancy in concentration profiles

ABSTRACTJet mixing tanks are important in chemical processes. Over the past two decades or so, computational fluid dynamics (CFD) has been employed to study jet mixers. The shortfalls of the previous CFD models were the discrepancy in concentration profiles between simulation and experiment and the absence of exact inlet turbulence conditions. So, in our present work, the CFD model was developed to investigate the proper conditions for jet mixing tank simulation and improve the accuracy of concentration profile prediction by using an appropriate grid arrangement, a realizable k-epsilon model, and a second-order upwind discretization scheme. The results revealed that the CFD model with proper inlet conditions predicted the overall mixing time well and somewhat improved the predicted concentration profiles. Further, the reasons for discrepancies in concentration profiles were inappropriate inlet turbulence conditions and overprediction in total momentum available for mixing due to the flat top liquid surface assumption. In addition, this discrepancy may be caused by the dynamic response of concentration measuring device.

Dynamic Heat Transfer Study of a Triangular-Shaped Latent Heat Storage Unit for the Attic Space of a Domestic Dwelling

Abstract A two-dimensional (2D) numerical study is carried out to investigate the thermal performance of an impure phase-change material (PCM) in an equilateral triangular-shaped double pipe heat exchanger. To tackle the irregular boundaries, a nonorthogonal body-fitted coordinate (BFC) transformation technique is employed. The nondimensional transformed curvilinear conservation equations for mass, momentum, and energy are written in terms of physical variables and they are solved using a control-volume based finite difference method on a staggered grid arrangement. The developed model is then used to study the effects of the inner tube wall temperature, the initial temperature of the solid PCM, and the shape, as well as the position of the inner tube in the annulus on the melting characteristics, and cumulatively stored energy. Various quantities such as average Nusselt numbers over the inner tube surface, the total and complete melt fractions, and the latent and total stored energies all as a function of the melting time are reported. A correlation for the average Nusselt number on the inner tube wall is also provided. The numerical results show that the shape and the placement of the inner tube are crucial for the efficient design of a latent heat thermal energy storage (LHTES) system. The storage of energy is greatly influenced by the change of the inner tube wall temperature compared to the change of initial solid PCM temperature.

Inverse Source Problem for a Host Medium Having Pointlike Inhomogeneities

The reconstruction of a source embedded within a multipath environment, which is created by inserting a grid of point scatterers in the scene, is addressed. In particular, the source Fourier spectrum is assumed known so that the focus here is on the reconstruction of the spatial support. As well documented, multipath can allow for resolution improvement. However, it also gives rise to artifacts when a backpropagation-like imaging is adopted. In this paper, we study in detail how resolution improvement and artifacts depend on the grid layout by employing a weighted backpropagation algorithm. More in detail, stationary phase arguments are used to predict the reconstruction leading order terms to which resolution improvement is linked. Moreover, it is shown that artifacts are mainly due to high-order terms and are dependent on the point scatterers’ arrangement. The nature of such artifacts is studied, and a simple way to mitigate their role (without resolution loss) is introduced; it consists in a suitable nonuniform grid arrangement with a “hole in the center.” Backpropagation is then compared with an inverse filtering imaging based on the truncated singular value decomposition (TSVD) of the radiation operator. It is shown that the TSVD is less prone to artifacts and can, in principle, allow for a higher resolution improvement. However, when model error (due to multiple scattering between the elements of the grid) and/or noise corrupt data, backpropagation performs definitely better. The theoretical findings are supported by an extensive numerical analysis. In particular, to keep the figures simple, we consider only 2-D cases.