Non-structured Meshes Research Articles

TLM Local Mesh-Refinement Scheme Based on N-Port Network Representation and Conference-Matrix Connection Topology

This article presents an optimal connection topology to model the voltage-exchange at the interface between different sub-grids in nonstructured TLM meshes. As a first step, the derivation—using Kirchhoff’s circuit laws—of these voltage-exchange equations between two subdomains with an arbitrary meshing ratio and a specific connection topology is presented. It was then generalized as an S-matrix of an N-port network that processes all desired properties in an ideal interface. In contrast to previous approaches, these S-matrix elements are derived directly for their properties and no concrete physical representation is required. Moreover, stability in this novel connection topology is ensured since all eigenvalues of the optimal S-matrix are located on the unit circle.

Random Walk Particle Tracking for Convection-diffusion Dominated Problems in Shallow Water Flows

This paper deals with a Lagrangian stochastic approach to solve the advection-diffusion equation of a scalar tracer inflow based on random walk particle tracking (RWPT) of a fine number of particles that describe the tracer. The water flow is governed by the shallow water equations that are solved using a finite volume upwinding scheme on a non-structured triangular mesh. Results are presented for two problems, pure advection in a square cavity and pollutant advection in the strait of Gibraltar, that demonstrate the performance, accuracy, and the flexibility of the RWPT method to examine the process of pollutant convection by comparing predictions with those from the Eulerian approach. The Lagrangian approach is shown to have advantages in terms of the high level of simplicity and stability relative to the Eulerian approach.

A focused and constrained 2D inversion of potential field geophysical data through Delaunay triangulation, a case study for iron-bearing targeting at the Shavaz deposit in Iran

This work illustrates the performance of a focused algorithm for 2D inversion of potential field geophysics (gravity and magnetic) in regions with rugged topography. A non-structured model discretization mesh is performed through Delaunay triangular cells to accurately represent the rugged observation surface and recover complex-shaped sources. Several synthetic single and multi-source targets are simulated to evaluate the applicability of the focused algorithm for simultaneously preserving the edges, correct depth estimation and body distribution of the inverted models. The algorithm is written in such a way that it is able to improve the modeling result per iteration by imposing physical properties constraining (magnetic susceptibility or density contrast), depth weighting and focused term in the central system of linear equation. Whereby a preconditioned conjugate gradient scheme is used iteratively to solve efficiently the L2-norm cost function comprising of a data misfit norm and a model stabilizer. Potential field data pertaining to a real case study for iron-bearing targeting are also inverted along two profiles to investigate the geometry of the sought targets at the Shavaz deposit in Iran. Iron-oxide ore occurrence was approved by exploratory drilling indicating a shallow hematite target with minor compounds of magnetite. Of note is that the significant point of this study lies in accurate recovering of causative sources responsible for potential field anomaly when a severe undulating topography occurs.

Using the Maximum Pressure Principle for Verification of Calculation of Stationary Subsonic Flow

The principle of maximum pressure for subsonic stationary three-dimensional vortex flows of an ideal gas (author Sizykh G.B., 2018) is applied to verify the calculation method and its implementation on a specific computer technology. The four criteria for solution's verification are proposed. The method for obtaining flow parameters is based on solving of discrete analogs of the Navier --- Stokes system of equations on three-dimensional non-structured computational meshes. For example, there was consider the vortex tear-off flow around the fuselage of a helicopter with an empennage and landing gear at obviously insufficient computing resources. Conclusions of the feasibility of applying the author's criteria for evaluation of a particular calculation and for estimation of reliability of the results have been made.

Simulation of a Bubble-Column Reactor by Three-Dimensional CFD: Multidimension- and Function-Adaptive Network-Based Fuzzy Inference System

Recently, novel approaches have been developed for simulating bubbly flow as well as distributed and constant phase evolution by means of a two-phase reactor. Among these approaches, the Eulerian–Eulerian method and soft computing approaches can be mentioned. Since complex numerical methods (for example, multidimensional Eulerian–Eulerian method) require several runs for fluid conditions optimization, a method which can decrease these runs can be very useful and practical. This method is provided by joining computational fluid dynamic (CFD) to the adaptive neuro-fuzzy inference system (ANFIS). In this technique, valuable information is provided for a careful analysis of fluid conditions. Also, it can facilitate a vast amount of data categorization in synthetic neural network nodes, which eliminates the need for a complex nonstructured CFD mesh. Moreover, a neural geometry can be provided, in which no limitation of mesh numbers in the fluid domain would exist. The key CFD parameters in the scale-up of the reactorstaken into consideration in the current research are gas and liquid circulations. These factors are applied as output factors for prediction tool in various dimensions in the ANFIS method. The results obtained in this study show appropriate conformity concerning ANFIS and CFD results depending on multiple dimensions. In this study, the grouping of CFD and multifunction the ANFIS method delivers the nondiscrete domain in different dimensions and presents an intelligent instrument for the local prediction of multiphase flow. The result shows that three inputs, which represent the dimension of the reactor, and learning stage of the ANFIS method provide a better understanding of flow characteristics in the two-phase reactor, while the two-dimensional ANFIS method even with multistructured functions cannot predict well the multiphase flow in the reactor.

A 2.5D micromagnetic solver for randomly distributed magnetic thin objects

Abstract This paper presents a GPU-parallelized 2.5D micromagnetic solver for the efficient calculation of the magnetization configuration and hysteresis loop of 3D random distributions of magnetic thin-film objects, strongly interacting in the space. To well-reproduce complex shapes, the exchange field is calculated with a finite difference approach able to handle non-structured meshes. To enable the treatment of many objects, the magnetostatic field is locally separated into two contributions: an internal and an external one. The first term includes the magnetostatic interactions internal to each object and is obtained by numerically solving the Green’s integral equation. The second term describes the inter-object magnetostatic interactions and it is determined by approximating each object as a collection of magnetic dipoles, associated with mesh elements. The accuracy and computational efficiency of the solver are analysed by comparison to a standard 3D-FFT code and to a reference code, where all the magnetostatic field terms are evaluated by numerically solving the Green’s integral equation.

A magnetic-field independent approach for strongly anisotropic equations arising plasma-edge transport simulations

Abstract [Summary] The control of the power exhaust in tokamaks is still an open issue for the future fusion operations. The heat loads on divertor and limiter PFCs is largely determined by the physics of the Scrape-Off Layer (SOL), and therefore it depends mainly on the geometry of the magnetic surfaces and on the geometry of wall components. A better characterization of the heat exhaust mechanisms requires therefore to improve the capabilities of the transport codes in terms of geometrical description of the wall components and in terms of the description of the magnetic geometry. The possibility of dealing with evolving magnetic configurations becomes also critical: during start-up or control operations, for example, the evolution of particles and heat fluxes is little known, although being critical for the safety of the machine. Hence, among the new capabilities of future transport codes will be the possibility of accurately describe the reactor chamber, and the flexibility with respect the magnetic configuration. In particular, avoiding expensive re-meshing of the computational domain in case of evolving equilibrium is mandatory. In order to fulfill these requirements, in this work a fluid solver based on non-aligned discretization is used to solve the plasma-edge transport equations for density, momentum and energies. Preliminary tests on non-structured meshes and realistic geometries/physical parameters show the pertinency of this novel approach.

How to adapt numerical simulation of wave propagation and ultrasonic laboratory experiments to be comparable — A case study for a complex topographic model

Numerical methods are widely used in seismic exploration to simulate wave propagation; however, the algorithms are based on various assumptions. The accuracy of numerical simulations is of particular interest in the case of realistic geologic setups. The direct comparison of numerical results can have limitations, and an alternative approach can be the comparison of synthetic results with experimental data, obtained for a small-scale physical model in laboratory conditions. Laboratory experiments are repeatable and provide high-quality data for a known configuration. We have developed a possible workflow to adapt the numerical simulations and the laboratory experiments to each other, such that the two can be easily compared with high accuracy. The model is immersed in a water tank, and a conventional pulse-echo technique is used to collect the reflection data in zero-offset and offset configurations. We use a spectral-element method for the numerical modeling. The model geometry is implemented using a nonstructured mesh, and the computational cost can be optimized using larger elements and higher-order basis functions. The real source transducer characteristics are implemented based on a new approach: laboratory characterization of the impulse response, followed by an inversion step to obtain a numerically equivalent source. The comparison of the zero-offset synthetic and laboratory results reveals an excellent fit in terms of arrival time, phase, and amplitude. Minor amplitude mismatches may be attributed to the noise recorded in the laboratory data and to the possible inaccuracy of the proposed source implementation. Comparison of the simulated and laboratory offset traces also exhibits a good fit in general, but with significantly less accuracy for some arrivals than in the zero-offset case. This can be mainly attributed to the inaccuracies of the transducer positions during the laboratory measurements combined with the strong topography of the model.

Numerical simulation of two-phase filtration in the near well bore zone

Abstract On the basis of the fundamental laws of energy conservation, nonstationary processes of filtration of two-phase liquids in multilayered reservoirs in the near well bore zone are considered. Number of reservoirs, fluid pressure in the given reservoirs, reservoir permeability, oil viscosity, etc. are taken into account upon that. Plane-parallel flow and axisymmetric cases have been studied. In the numerical solution, non-structured meshes are used. Closer to the well, the meshes thicken. The integration step over time is defined by the generalized Courant inequality. As a result, there are no large oscillations in the numerical solutions obtained. Oil production rates, Poisson’s ratios, D-diameters of the well, filter height, filter permeability, and cumulative thickness of the filter cake and the area have been taken as the main inputs in numerical simulation of non-stationary processes of two-phase filtration.

Numerical modeling with high performance computing of seismic waves for complex marine environments: Benchmarking with laboratory experiments

Numerical simulations are widely used for forward and inverse problems in seismic exploration to investigate different wave propagation phenomena. However, the numerical results are hard to be compared to real seismic measurements as the subsurface is never exactly known. Using laboratory measurements for small-scale physical models can provide a valuable link between purely numerical and real seismic datasets. We present a case study for comparing ultrasonic data for a complex model with spectral-element and finite-difference synthetic results. The small-scale model was immersed in a water tank. Reflection data was recorded with piezoelectric transducers using a conventional pulse-echo technique. We paid special attention to the implementation of the real source signal—and radiation pattern—in the numerical domain. It involved a laboratory calibration measurement, followed by an inversion process. The model geometry was implemented using a non-structured mesh for the spectral-element simulations. The comparisons show a very good fit between synthetic and laboratory traces in general, and the small discrepancies can be assigned mostly to the noise present in the laboratory data.

Water Injection for Oil Recovery by using Reservoir Simulation via CFD

Waterflooding process involves the water injection into the reservoir to increase the oil recovery by oil displacement and pressure maintenance mechanisms. This article is based on three-dimensional numerical simulation of a homogeneous reservoir saturated by oil, 22.1°API, with water injection using a non-structured mesh. In order to analyze the behavior of formation and prediction of the fluid production, it was used the ANSYS CFX 12.0 ® commercial software. The model consists in a reservoir with the dimensions, 270x180x15 m³, and two in parallel five-spot meshes, considering the internal injection, and in the top of the reservoir, and variations of water rate injected, during a total time of 72,000 hours of project. Results of recovery factor, water production, saturation advance front and pressure are presented and analyzed. Was observed that increasing the water rate injected caused an increment in the oil recovery, and consequently the water production, however better results were obtained with injection on the top. This study allowed identifying best practices to water injection optimization.

A Lagrangian finite element method for 3D compressible flow applications

We discuss a Lagrangian approach for the simulation of 3D compressible flows on non-structured tetrahedral meshes. The formulation is nodal-based, in the sense that kinematic and thermodynamic variables are all interpolated with continuous P1 polynomials. The equations are solved with an explicit time-marching scheme without stabilizing terms and with the inclusion only of a shock-capturing viscosity. Several examples featuring shock propagations and mixing of fluids are addressed, with particular emphasis on the stability of the approach and on possible strategies for mesh update.

3-D IC Interconnect Capacitance Extraction Using Dual Discrete Geometric Methods With Prism Elements

The dual discrete geometry methods (DGMs) in terms of scalar potential using prism elements are employed in 3-D interconnect capacitance extraction of integral circuits. The energy complementarity property of the dual methods is explored to speed up the extraction. The dual DGMs work on the mutually orthogonal primal-dual mesh doublets, i.e., dual Delaunay–Voronoi mesh complex. As the orthogonal dual mesh is built based on the circumcenter of the primal mesh, the stability of the dual DGM heavily depends on the quality of the mesh. Elements with circumcenter dropping outside of the elements inevitably appear in the nonstructured prismatic meshes, due to the complicated structures in practical problems. The impact of these elements on the stability of the DGM is discussed. Comprehensive comparison between dual DGMs and dual finite-element methods (FEMs) and other golden references is performed. The dual DGM in terms of scalar potential has a reduced number of unknowns and simpler forms and works without extra links as required in the dual FEM in terms of vector potential. Capacitance extraction examples, such as a CMOS inverter and multilayer crossover parallel wires, are studied. The results demonstrate the energy bounds of dual DGMs and the improvement of accuracy with reduced cost.

Consistent formulation for the Discrete-Continuous Model: Improving complex dislocation dynamics simulations

A new and efficient formulation of the Discrete-Continuous Model (DCM) for the simulation of 3D dislocation dynamics in complex finite or periodic volumes is presented. As in previous versions, the improved model is based on a coupling between a Dislocation Dynamics (DD) code and a Finite Element (FE) code through eigenstrain theory. Short-range interactions are now handled more properly. Specifically, in the continuous limit the stress field driving the dislocation dynamics is now reconstructed consistently. Furthermore, the DCM can now handle nonstructured meshes, and free surface and interface handling does not depend on having a structured mesh anymore. Also numerical experiments shed some light on the influence of the choice of the FE quadrature. Some approximations are proposed and justified, and the use of advanced algorithmic techniques are used for time integration and the homogeneisation procedure to reach a high computational efficiency. Basic tests demonstrate the validity and the efficiency of the proposed strategy. Remarkably, it is demonstrated that for a periodic domain the DCM with a very fine FE mesh is actually faster than a corresponding classical DD simulation.

Erratum to: Simulation of Supersonic Flow in a Channel with a Step on Nonstructured Meshes with the Use of the Weno Scheme

Erratum to: Simulation of Supersonic Flow in a Channel with a Step on Nonstructured Meshes with the Use of the Weno Scheme

Simulation of Supersonic Flow in a Channel with a Step on Nonstructured Meshes with the Use of the Weno Scheme

Results of modeling of the temperature and stressed-strained states of the reflector of a mirror space antenna installed on a spacecraft that conducts a flight on geostationary and low near-earth orbits have been presented.

High Order Boundary Extrapolation Technique for Finite Difference Methods on Complex Domains with Cartesian Meshes

The application of suitable numerical boundary conditions for hyperbolic conservation laws on domains with complex geometry has become a problem with certain difficulty that has been tackled in different ways according to the nature of the numerical methods and mesh type. In this paper we present a technique for the extrapolation of information from the interior of the computational domain to ghost cells designed for structured Cartesian meshes (which, as opposed to non-structured meshes, cannot be adapted to the morphology of the domain boundary). This technique is based on the application of Lagrange interpolation with a filter for the detection of discontinuities that permits a data dependent extrapolation, with higher order at smooth regions and essentially non oscillatory properties near discontinuities.

Monitoring the state of the moving train by use of high performance systems and modern computation methods

The objective of this work has been to study the propagation of elastic waves in rails. It presents the comparison of calculations obtained by the grid-characteristic and discontinuous Galerkin methods. The propagation of elastic waves in the presence and absence of the karst inclusion in the ground under the embankment, diagnosed in these cases from the rails, are compared. The wave pictures and diagnosed signals for four types of defects of a fractured character: vertical and horizontal head layering, cross fracture in the head and cracks in the rail web are given. The grid-characteristic method on the curvilinear structural meshes and the discontinuous Galerkin method on the nonstructured triangular meshes make it possible to solve efficiently the tasks on monitoring the state of the moving train and rail, including a great number of integrity violations, dynamic interactions in the train-rail system, and obtain the full wave picture.

Parallelized micromagnetic solver for the efficient simulation of large patterned magnetic nanostructures

The paper presents a novel parallelized micromagnetic solver, engineered to run on massively parallel architectures based on graphical processing units and thus suitable for the efficient simulation of large magnetic nanostructures. The code adopts a multipole expansion technique for the evaluation of long-range magnetostatic interactions and enables the calculation of the exchange field also on non-structured meshes. Its computational performances are here tested in the simulation of the hysteresis loops of dot array films with maximum size in the order of 5 μm.

2D hybrid meshes for direct simulation Monte Carlo solvers

The efficiency of the direct simulation Monte Carlo (DSMC) method decreases considerably if gas is not rarefied. In order to extend the application range of the DSMC method towards non-rarefied gas regimes, the computational efficiency of the DSMC method should be increased further. One of the most time consuming parts of the DSMC method is to determine which DSMC molecules are in close proximity. If this information is calculated quickly, the efficiency of the DSMC method will be increased. Although some meshless methods are proposed, mostly structured or non-structured meshes are used to obtain this information. The simplest DSMC solvers are limited with the structured meshes. In these types of solvers, molecule indexing according to the positions can be handled very fast using simple arithmetic operations. But structured meshes are geometry dependent. Complicated geometries require the use of unstructured meshes. In this case, DSMC molecules are traced cell-by-cell. Different cell-by-cell tracing techniques exist. But, these techniques require complicated trigonometric operations or search algorithms. Both techniques are computationally expensive. In this study, a hybrid mesh structure is proposed. Hybrid meshes are both less dependent on the geometry like unstructured meshes and computationally efficient like structured meshes.