Numerical Calculation Scheme Research Articles

Numerical Simulation and Stress Testing Research on Elliptical Bipolar Linear Shaped Charge

Based on shaped charge technology, the method of linear cracks of directional fracture in rocks controlled blasting by shaped charge and the elliptical bipolar linear shaped charge with low detonation velocity explosive was presented in this paper. The stress testing experiment was carried on by the stress sensor for analyzing the characters of cumulative pre-splitting of the shaped charge. A numerical calculation scheme for simulating the formation and movement of jet was developed based on the ansys/ls-dyna. The damage of the concrete target penetrated by the jet was showed in the numerical simulation. The results of experiment and the simulation indicted that the shaped charge can form good effect on cumulative energy and produce good pre-splitting blasting effect. At the same time, the safe, economic and environmental benefits had been clearly made.

A New Simple Equation Governing Distortion of Compression Wave Propagating Through Shinkansen Tunnel with Slab Tracks

A high-speed train entering a tunnel generates a compression wave that propagates through the tunnel toward its exit. When the compression wave reaches the tunnel exit, a pressure pulse causing environmental problems (the micro-pressure wave) is radiated from the exit portal. The magnitude of the micro-pressure wave is approximately proportional to the maximum pressure gradient of the compression wave arriving at the tunnel exit. In a long Shinkansen tunnel with concrete slab tracks the compression wavefront steepens due to the nonlinear effect during its propagation because the whole surfaces of the tunnel being smooth. Hence, it is necessary to investigate the distortion of the compression wave in a tunnel and clarify the characteristics of compression wave propagation for estimating and reducing the micro-pressure wave. In this paper, we introduce a new simple equation governing the distortion of the compression wave propagating through a Shinkansen tunnel with concrete slab-tracks and propose a new simple scheme for a numerical calculation. A space evolution type equation with one variable is derived from the three conservation equations (mass, momentum, and energy including the wall friction and heat transfer terms) of the 1D CFD by assuming small disturbances excited by the compression wave. The numerical calculation scheme based on the simple equation remarkably reduces the computing time because its CFL condition is relaxed. The calculation results by the present scheme agree well with those by a conventional scheme based on the 1D CFD and the accuracy of the simple equation is verified.

Bayesian Focusing for Coherent Wideband Beamforming

In this paper, we present and study a Bayesian focusing transformation (BFT) for coherent wideband array processing, which takes into account the uncertainty of the direction of arrivals (DOAs). The Bayesian focusing method minimizes the mean-square error of the transformation over the probability density functions (pdfs) of the DOAs, thus achieving improved focusing accuracy over the entire bandwidth. In order to solve the Bayesian focusing problem, we derive and utilize a weighted extension of the wavefield interpolated narrowband generated subspace (WINGS) focusing transformation. We provide a closed-form expression for the optimal BFT and extend it to the case of directional sensors. We then consider a numerical computation scheme of the BFT in the angular domain. We show that if an angular sampling condition is satisfied then the angle domain approximation yields the optimal BFT. We also treat the important issue of robust focused minimum variance distortionless response (MVDR) beamformer. We analyze the sensitivity of the focused MVDR to the focusing errors and show that the array gain (AG) is inversely proportional to the square of the signal-to-noise ratio (SNR) for large values of the SNR, and highly sensitive to the focusing errors. In order to reduce this sensitivity we generalize the popular narrowband diagonal loaded MVDR to the focused wideband case, referred to as the Q-loaded focused MVDR wideband beamformer. We derive a closed-form analytic expression for the AG of the Q-loaded focused MVDR beamformer which depends on the focusing transformations. A numerical performance evaluation and simulations demonstrate the advantage of the BFT over that of other focusing transformations, for multiple source scenarios.

A New Simple Equation Governing Distortion of Compression Wave Propagating Through Shinkansen Tunnel with Slab Tracks

A high-speed train entering a tunnel generates a compression wave that propagates through the tunnel toward its exit. When the compression wave reaches the tunnel exit, a pressure pulse causing environmental problems (the micro-pressure wave) is radiated from the exit portal. The magnitude of the micro-pressure wave is approximately proportional to the maximum pressure gradient of the compression wave arriving at the tunnel exit. In a long Shinkansen tunnel with concrete slab tracks the compression wavefront steepens due to the nonlinear effect during its propagation because the whole surfaces of the tunnel being smooth. Hence, it is necessary to investigate the distortion of the compression wave in a tunnel and clarify the characteristics of compression wave propagation for estimating and reducing the micro-pressure wave. In this paper, we introduce a new simple equation governing the distortion of the compression wave propagating through a Shinkansen tunnel with concrete slab-tracks and propose a new simple scheme for a numerical calculation. A space evolution type equation with one variable is derived from the three conservation equations (mass, momentum, and energy including the wall friction and heat transfer terms) of the 1D CFD by assuming small disturbances excited by the compression wave. The numerical calculation scheme based on the simple equation remarkably reduces the computing time because its CFL condition is relaxed. The calculation results by the present scheme agree well with those by a conventional scheme based on the 1D CFD and the accuracy of the simple equation is verified.

Numerical scheme for riser motion calculation during 3-D VIV simulation

This paper presents a numerical scheme for riser motion calculation and its application to riser VIV simulations. The discretisation of the governing differential equation is studied first. The top tensioned risers are simplified as tensioned beams. A centered space and forward time finite difference scheme is derived from the governing equations of motion. Then an implicit method is adopted for better numerical stability. The method meets von Neumann criteria and is shown to be unconditionally stable. The discretized linear algebraic equations are solved using a LU decomposition method. This approach is then applied to a series of benchmark cases with known solutions. The comparisons show good agreement. Finally the method is applied to practical riser VIV simulations. The studied cases cover a wide range of riser VIV problems, i.e. different riser outer diameter, length, tensioning conditions, and current profiles. Reasonable agreement is obtained between the numerical simulations and experimental data on riser motions and cross-flow VIV a/D. These validations and comparisons confirm that the present numerical scheme for riser motion calculation is valid and effective for long riser VIV simulation.

Flux-Based Wave Decomposition Scheme for an Isentropic Hyperbolic Two-Fluid Model

We present a flux-based wave decomposition (FBWD) scheme for numerical computation of isentropic two-fluid two-phase flows. We use Tait's equation of state for both the gas and the liquid phases. Extension of the scheme to the second order is made by the MUSCL-Hancock approach. The solutions of several two-phase shock tube problems resulting from the present scheme are compared with the solutions obtained by the earlier HLL scheme. Investigation of the effect of the interfacial pressure models and the drag coefficient are also included. It is concluded that the present FBWD scheme is robust and accurate for computation of isentropic two-fluid models.

High order numerical differentiation and approximation of Laplace fields using regular grid data

Specialized numerical schemes for calculation of high order field derivatives are considered. The input data are a regular rectangular mesh with potential values at its nodes, the output data are high order derivative values at grid nodes and associated expressions which enable the calculation of potentials, field values or high order derivatives inside a grid cell with high accuracy. An important feature is that differentiation and approximation techniques are based on a priori knowledge about the Laplace equation which allow the production of numerical schemes with higher order properties.

Upscaling Saturation-Height Technology for Arab Carbonates for Improved Transition-Zone Characterization

SummaryMuch of the oil in Saudi Arabia is stored in giant and supergiant multireservoir fields. The Arab-D limestone is the most important of these and the most prolific. The large volumes, excellent porosity, and high productivity of these reservoirs do not mask the fact that these carbonates have complex pore systems. The problems associated with heterogeneous carbonate reservoirs pose significant and longstanding modeling complications that are not yet fully addressed by the industry. One important difficulty is the accurate modeling of the substantial transition zones present above the freewater levels (FWLs). In these giant fields, these transition zones hold large amounts of oil and are important commercial objectives. Commerciality requires accurate assessment of saturations and rock properties. Standard J-function methods are inadequate to model the well-log observed saturation-height behavior in the transition zones. It is necessary to characterize and account for the pore system variations and scale when modeling the saturation behavior of large rock volumes. The reservoir properties of geocells and wellbores must be reconciled with the measurements on core plugs. The measurements performed on these tiny pieces of rock need to be upscaled to represent the reservoir bulk properties.Upscaling of core-plug-scale, laboratory measured porosimetry data and transport properties has been a general and persistent problem since the beginning of reservoir simulation. This critical step has been handled, over the years, using a wide variety of numerical computational schemes, approximations, and empirical methods. In this paper, we take the different and very specific approach of upscaling the capillary pressure data for the Arab-D limestone. We base the approach on the availability of a large amount of mercury (Hg) -injection data and statistical analysis thereof, obtained by fitting hundreds of individual core plugs to Thomeer functions.For the Arab-D limestone, and similar carbonates, we derive a closed-form analytic expression for the upscaled capillary pressure function, which has significant implications for improving transitionzone hydrocarbon-volume estimates for this important petroleum system. The analytic expression also offers major efficiencies compared with other methods used by petroleum engineers, provided that the pore systems are adequately investigated and statistically characterized. A key result of the upscaled formalism is that reservoir cells, consisting of a large variation of pore systems, will start to fill with hydrocarbons much closer to the FWL than when using saturation-height functions based on simple averaged pore system parameter values. Therefore, transition zones for upscaled reservoir elements (and well-log volumes) are thicker than simple calculations based on data from single core plugs would indicate. The accurate upscaling of pore-system architecture is a major step toward the full understanding of the fluid-rock interactions of giant-field transition zones in the Middle East and is an industry technical milestone.

Bertrand-Edgeworth Auction with Multiple Asymmetric Bidders

Motivated by supply competitions in the service sector, we consider a version of the Bertrand-Edgeworth game where capacitated suppliers compete in prices to serve a deterministic demand and a price cap is imposed exogenously. We characterize the equilibrium structure for games with multiple suppliers that are asymmetric in cost and capacity. A pure-strategy equilibrium exists only in special cases, otherwise a mixed-strategy equilibrium prevails. For a mixed-strategy equilibrium, we show there exists an anchoring supplier whose pricing range covers those of the other suppliers, and we pin down the lower and upper bounds of that price range. We derive a canonical closed-form solution for a set of games, and for other more general cases, we demonstrate a numerical scheme for equilibrium calculation. In contrast to a well-known intuition established in the existing literature, we identify a new equilibrium pricing structure in games with N >= 3 suppliers who have similar costs but different capacities: A low-capacity supplier's price distribution is more concentrated than those of its high-capacity competitors, by spanning a smaller interval. We demonstrate an interesting strategy for a buyer with a competitive supply base: Subsidizing a cost-competitive incumbent may reduce the total procurement cost.

Discussion of “Application of a Nonstandard Explicit Integration to Solve Green and Ampt Infiltration Equation” by D. R. Mailapalli, W. W. Wallender, R. Singh, and N. S. Raghuwanshi

Mailapalli et al. (2009) presented an explicit numerical scheme for calculation of solutions to the 1D Green and Ampt (1911) infiltration equation. They compared their numerical solution to a numerical solution obtained using the Newton-Raphson method (e.g., Rao et al., 2006) and the “approximate explicit solutions” of Salvucci and Entekhabi (1994) and (iii) Barry et al. (1995d). It is shown that (i) that the Green-Ampt model can be approximated very accurately using a simple formula, (ii) that the effective hydraulic conductivity mentioned by the authors is consistent with another infiltration model and (iii) that their numerical scheme becomes more accurate if the short-time expansion of the Green and Ampt model is used to provide that starting value of the infiltration.

Advanced simulation tool for the design of sensors and actuators

Sensors, actuators, and sensor-actuator systems are often based on the mutual interaction of physical fields, e.g., the mechanical field with the electromagnetic field. The accurate modeling of such transducers leads to so-called multi-field problems, which are described by a system of non-linear partial differential equations. These systems cannot be solved analytically and thus numerical calculation schemes have to be applied. Therewith, we have developed the simulation tool CFS++(Coupled Field Simulation in C++) based on the Finite Element (FE) method, which is capable of efficiently solving the arising partial differential equations. The program is applicable for simulating capacitive micromachined transducers, piezoelectric transducers, electromagnetic and magnetomechanical sensors and actuators. It also contains models for (aero-)acoustics and ultrasound transducers. Furthermore, we offer advanced material models including hysteretic behaviors.

Stable computation of the functional variation of the Dirichlet–Neumann operator

This paper presents an accurate and stable numerical scheme for computation of the first variation of the Dirichlet–Neumann operator in the context of Euler’s equations for ideal free-surface fluid flows. The Transformed Field Expansion methodology we use is not only numerically stable, but also employs a spectrally accurate Fourier/Chebyshev collocation method which delivers high-fidelity solutions. This implementation follows directly from the authors’ previous theoretical work on analyticity properties of functional variations of Dirichlet–Neumann operators. These variations can be computed in a number of ways, but we establish, via a variety of computational experiments, the superior effectiveness of our new approach as compared with another popular Boundary Perturbation algorithm (the method of Operator Expansions).

Model Calculations With a Fast Field Programme and Comparison With Selected Procedures to Calculate Road Traffic Noise Propagation Under Defined Meteorological Conditions

National guidelines for calculating noise propagation are still in use though progress was made to develop a unified scheme for sound propagation outdoors by taking more physical parameters of the propagation path into account. Besides comprehensive models simpler and faster calculations are under development in order to be used as an engineering model. Widespread classical engineering models from different European countries are compared in this study with physical wave propagation from a defined line source representing traffic noise. The numerical model is based on a fast-field programme. This scheme allows for a very fast calculation of wave propagation in a layered medium including complex boundary conditions. Source properties are carefully adjusted for comparison and the respective meteorological conditions of national guidelines are taken into account. It turns out that the different guidelines are in good agreement with exact calculations up to distances about 1000 m. The so-called downwind condition gives an excellent estimate for the conditions most favourable for sound propagation. The fast numerical calculation scheme enables easy systematic variation of e.g. source properties, meteorological conditions and ground impedances for any sensitivity analysis.

Physical modeling and numerical computation of magnetostriction

PurposeMagnetostrictive alloys are widely used in actuator and sensor applications. The purpose of this paper is to developed a realistic physical model and a numerical computational scheme for their precise computation.Design/methodology/approachThe main step in the physical modeling is the decomposition of the mechanical strain and the magnetic induction into a reversible and an irreversible part. For the efficient solution of the arising coupled nonlinear partial differential equations the authors apply the finite element method.FindingsIt can be demonstrated, that the hysteresis operators can be fitted by appropriate measurements. Therewith, the developed physical model and numerical simulation scheme is applicable for the design of magnetostrictive actuators and sensors.Originality/valueThe decomposition of the mechanical strain and the magnetic induction into a reversible and an irreversible part. The reversible part is described by the linear magnetostrictive constitutive equations, where the entries of the coupling tensor depend on the magnetization. The irreversible part of the magnetic induction is modeled by a Preisach hysteresis operator, and the irreversible part of the mechanical strain by a polynomial function depending on the magnetization.

Mesh refinement algorithms in an unstructured solver for multiphase flow simulation using discrete particles

This study developed spray-adaptive mesh refinement algorithms with directional sensitivity in an unstructured solver to improve spray simulation for internal combustion engine application. Inadequate spatial resolution is often found to cause inaccuracies in spray simulation using the Lagrangian–Eulerian approach due to the over-estimated diffusion and inappropriate liquid–gas phase coupling. Dynamic mesh refinement algorithms adaptive to fuel sprays and vapor gradients were developed in order to increase the grid resolution in the spray region to improve simulation accuracy. The local refinement introduced the coarse-fine face interface that requires advanced numerical schemes for flux calculation and grid rezoning with moving boundaries. To resolve the issue in flux calculation, this work implemented the refinement/coarsening algorithms into a collocated solver to avoid tedious interpolations in solving the momentum equations. A pressure correction method was applied to address unphysical pressure oscillations due to the collocation of pressure and velocity. An edge-based algorithm was used to evaluate the edge-centered quantities in order to account for the contributions from all the cells around an edge at the coarse-fine interface. A quasi-second-order upwind scheme with strong monotonicity was also modified to accommodate the coarse-fine interface for convective fluxes. To resolve the issue related to grid rezoning, rezoning was applied to the initial baseline mesh only and the new locations of the refined grids were obtained by interpolating the updated baseline mesh. The time step constraints were also re-evaluated to account for the change resulting from mesh refinement. The present refinement algorithm was used in simulating fuel sprays in an engine combustion chamber. It was found that the present approach could produce the same level of results as those using the uniformly fine mesh with substantially reduced computer time. Results also showed that this approach could alleviate the artifacts related to the Lagrangian discrete modeling of spray drops due to insufficient spatial resolution.

Multi-scale calculation of settling speed of coarse particles by accelerated Stokesian dynamics without adjustable parameter

The calculation of settling speed of coarse particles is firstly addressed, with accelerated Stokesian dynamics without adjustable parameters, in which far field force acting on the particle instead of particle velocity is chosen as dependent variables to consider inter-particle hydrodynamic interactions. The sedimentation of a simple cubic array of spherical particles is simulated and compared to the results available to verify and validate the numerical code and computational scheme. The improved method keeps the same computational cost of the order O(N log N) as usual accelerated Stokesian dynamics does. Then, more realistic random suspension sedimentation is investigated with the help of Mont Carlo method. The computational results agree well with experimental fitting. Finally, the sedimentation of finer cohesive particle, which is often observed in estuary environment, is presented as a further application in coastal engineering.

Internal waves in a two‐layer system using fully nonlinear internal‐wave equations

AbstractIn order to understand the nonlinear effect in a two‐layer system, fully nonlinear strongly dispersive internal‐wave equations, based on a variational principle, were proposed in this study. A simple iteration method was used to solve the internal‐wave equations in order to solve the equations stably. The applicability of the proposed numerical computation scheme was confirmed to agree with linear dispersion relation theoretically obtained from variational principle. The proposed computational scheme was also shown to reproduce internal waves including higher‐order nonlinear effect from the analysis of internal solitary waves in a two‐layer system. Furthermore, for the second‐order numerical analysis, the balance of nonlinearity and dispersion was found to be similar to the balance assumed in the KdV theory and the Boussinesq‐type equations. Copyright © 2009 John Wiley & Sons, Ltd.

Simulation of primary atomization with an octree adaptive mesh refinement and VOF method

We present different simulations of primary atomization using an adaptive Volume-of-Fluid method based on octree meshes. The use of accurate numerical schemes for mesh adaptation, Volume-of-Fluid advection and balanced force surface tension calculation implemented in Gerris, the code used to perform the simulations included in this work, has made possible to carry out accurate simulations with characteristic scales spreading over several orders of magnitude. The code is validated by comparisons with the temporal linear theory for moderate density and viscosity ratios, which basically corresponds to atomization processes in high pressure chambers. In order to show the potential of the code in different scenarios related to atomization, preliminary results are shown in relation with the study of the two-dimensional and 3D temporal and spatial problem, the influence of the injector and the vortex generated inside the chamber, and the effect of swirling at high Reynolds numbers.

On a numerical scheme for solving differential equations of fractional order

In this work, on the basis of a modified expansion formula obtained in Atanackovic and Stankovic [Atanackovic, T.M., Stankovic, B., 2004. An Expansion formula for fractional derivatives and its applications. Fractional Calculus and Applied Analysis 7(3), 365–378], we propose a numerical procedure for solving differential equations with fractional derivative by transforming the original system into a system of ordinary differential equations of the first order. Our method is different from the widely used method of Yuan and Agarwal [Yuan, L., Agrawal, O. P., 2002. A numerical scheme for dynamic systems containing fractional derivatives. Journal of Vibration and Acoustics 124, 321–324] and overcomes difficulties in satisfying the initial conditions that where noted by Schmidt and Gaul [Schmidt, A., Gaul, L., 2006. On a critique of a numerical scheme for calculation of fractionally damped dynamical systems. Mechanics Research Communications 33, 99–107]. We tested our procedure on several examples. The results show good agreement with the results obtained by other methods.

Efficient Symmetric FEM-BEM Coupled Simulations of Electro-Quasistatic Fields

Electro-quasistatic as well as electrostatic simulations of 3D high-voltage (HV) technical devices are presented using a symmetric coupled formulation of both the finite-element-method (FEM) and the boundary-element-method (BEM). This formulation allows for the specification of Dirichlet boundary conditions on the coupling interface. Accurate solutions can be achieved without the need of large spatial discretization domains. The use of the adaptive-cross-approximation (ACA) and a block Jacobi preconditioner for the linear system solver results in an efficient simulation scheme for numerical computations of electric field distributions of realistic 3D high-voltage devices.