Interest In Numerical Simulation Research Articles

Accurate modeling and simulation of seepage in 3D heterogeneous fractured porous media with complex structures

The past decades have witnessed an increasing interest in numerical simulation for flow in fractured porous media. To date, most studies have focused on 2D or pseudo-3D computational models, where the impact of 3D complex structures on seepage has not been fully addressed. This work presents a method for modeling seepage in 3D heterogeneous porous media. The complex structures, typically the stochastic discrete fractures and inclusions, are able to be simulated. A mesh strategy is proposed to discretize the complex domain. In particular, a treatment on the intersected elements is developed to ensure a conforming mesh. Then, numerical discretization is provided, in which the flux interactions of fractures, inclusions and surrounding rock matrix are included. Numerical tests are performed to analyze the hydraulic characteristics of 3D fractured media. First, the developed framework is validated by comparing numerical solutions with the results of embedded discrete fracture model. Next, the effects of orientation, aperture and radius of fractures on fluid flow and equivalent permeability tensor are analyzed. The variations of pressure distribution are studied in heterogeneous and homogeneous media. Finally, the hydraulic properties of a medium with complex structures are investigated to show the difference of hydraulic feature between fractures and inclusions.

Chebyshev polynomial method to Landauer–Büttiker formula of quantum transport in nanostructures

The Landauer–Büttiker formula describes the electronic quantum transport in nanostructures and molecules. It will be numerically demanding for simulations of complex or large size systems due to, for example, matrix inversion calculations. Recently, the Chebyshev polynomial method has attracted intense interest in numerical simulations of quantum systems due to the high efficiency in parallelization because the only matrix operation it involves is just the product of sparse matrices and vectors. Much progress has been made on the Chebyshev polynomial representations of physical quantities for isolated or bulk quantum structures. Here, we present the Chebyshev polynomial method to the typical electronic scattering problem, the Landauer–Büttiker formula for the conductance of quantum transport in nanostructures. We first describe the full algorithm based on the standard bath kernel polynomial method (KPM). Then, we present two simple but efficient improvements. One of them has time consumption remarkably less than that of the direct matrix calculation without KPM. Some typical examples are also presented to illustrate the numerical effectiveness.

High order derivatives of Boltzmann microcanonical entropy with an additional conserved quantity

In this article, using a known method [1], a computation is performed of the derivatives of the microcanonical entropy, with respect to the energy up to the 4-th order, using a Laplace transform technique, and adapted it to the case where the total momentum is conserved. The outcome of this computation answers a theoretical question concerning the description of thermodynamics associated with a Hamiltonian flow in presence of an additional conserved quantity besides energy. This is also of practical interest in numerical simulations of the microcanonical thermodynamics associated to classical Hamiltonian flows.

Numerical simulation of fluid‐structure interaction problems by a coupled SPH‐FEM approach

AbstractIn scientific computing there is a great interest in numerical simulation of fluid‐structure interaction (FSI) problems. Within this work a numerical approach to simulate fluid‐structure interactions between elastic structures and weakly incompressible fluids is developed. For the fluid part and the solid part the Smoothed Particle Hydrodynamics method (SPH) and the Finite Element Method (FEM) are used, respectively. To transfer the resulting reaction forces from the fluid particles onto the structure's surface two methods are implemented, investigated and compared. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Computing forces on interface elements exerted by dislocations in an elastically anisotropic crystalline material

Driven by the growing interest in numerical simulations of dislocation–interface interactions in general crystalline materials with elastic anisotropy, we develop algorithms for the integration of interface tractions needed to couple dislocation dynamics with a finite element or boundary element solver. The dislocation stress fields in elastically anisotropic media are made analytically accessible through the spherical harmonics expansion of the derivative of Green’s function, and analytical expressions for the forces on interface elements are derived by analytically integrating the spherical harmonics series recursively. Compared with numerical integration by Gaussian quadrature, the newly developed analytical algorithm for interface traction integration is highly beneficial in terms of both computation precision and speed.

Ice-avalanche scenario elaboration and uncertainty propagation in numerical simulation of rock-/ice-avalanche-induced impact waves at Mount Hualcán and Lake 513, Peru

The interest in numerical simulation of cascading processes involving mass movements and lakes has recently risen strongly, especially as the formation of new lakes in high-mountain areas as a consequence of glacier recession can be observed all over the world. These lakes are often located close to potentially unstable slopes and therewith prone to impacts from mass movements, which may cause the lake to burst out and endanger settlements further downvalley. The need for hazard assessment of such cascading processes is continuously rising, which demands methodological development of coupled numerical simulations. Our study takes up on the need for systematic analysis of the effect of assumptions taken in the simulation of the process chain and the propagation of the corresponding uncertainties on the simulation results. We complemented the research of Adv Geosci 35:145-155, 2014 carried out at Lake 513 in the Cordillera Blanca, Peru, by focusing on the aspects of (a) ice-avalanche scenario development and of (b) analysis of uncertainty propagation in the coupled numerical simulation of the process chain of an impact wave triggered by a rock/ice avalanche. The analysis of variance of the dimension of the overtopping wave was based on 54 coupled simulation runs, applying RAMMS and IBER for simulation of the ice avalanche and the impact wave, respectively. The results indicate (a) location and magnitude of potential ice-avalanche events, and further showed (b) that the momentum transfer between an avalanche and the impact wave seems to be reliably representable in coupled numerical simulations. The assessed parameters—initial avalanche volume, friction calibration, mass entrainment and transformation of the data between the models—was decisive of whether the wave overtopped or not. The overtopping time and height directly characterize the overtopping wave, while the overtopping volume and the discharge describe the overtopping hydrograph as a consequence of the run-up rather than the wave. The largest uncertainties inherent in the simulation of the impact wave emerge from avalanche-scenario definition rather than from coupling of the models. These findings are of relevance also to subsequent outburst flow simulation and contribute to advance numerical simulation of the entire process chain, which might also be applied to mass movements other than rock/ice avalanches.

On thermodynamic consistency of a Scharfetter–Gummel scheme based on a modified thermal voltage for drift-diffusion equations with diffusion enhancement

Driven by applications like organic semiconductors there is an increased interest in numerical simulations based on drift-diffusion models with arbitrary statistical distribution functions. This requires numerical schemes that preserve qualitative properties of the solutions, such as positivity of densities, dissipativity and consistency with thermodynamic equilibrium. An extension of the Scharfetter–Gummel scheme guaranteeing consistency with thermodynamic equilibrium is studied. It is derived by replacing the thermal voltage with an averaged diffusion enhancement for which we provide a new explicit formula. This approach avoids solving the costly local nonlinear equations defining the current for generalized Scharfetter–Gummel schemes.

Experimental and numerical study of the fragmentation of expanding warhead casings by using different numerical codes and solution techniques

Abstract There has been increasing interest in numerical simulations of fragmentation of expanding warheads in 3D. Accordingly there is a pressure on developers of leading commercial codes, such as LS-DYNA, AUTODYN and IMPETUS Afea, to implement the reliable fracture models and the efficient solution techniques. The applicability of the Johnson–Cook strength and fracture model is evaluated by comparing the fracture behaviour of an expanding steel casing of a warhead with experiments. The numerical codes and different numerical solution techniques, such as Eulerian, Lagrangian, Smooth particle hydrodynamics (SPH), and the corpuscular models recently implemented in IMPETUS Afea are compared. For the same solution techniques and material models we find that the codes give similar results. The SPH technique and the corpuscular technique are superior to the Eulerian technique and the Lagrangian technique (with erosion) when it is applied to materials that have fluid like behaviour such as the explosive and the tracer. The Eulerian technique gives much larger calculation time and both the Lagrangian and Eulerian techniques seem to give less agreement with our measurements. To more correctly simulate the fracture behaviours of the expanding steel casing, we applied that ductility decreases with strain rate. The phenomena may be explained by the realization of adiabatic shear bands. An implemented node splitting algorithm in IMPETUS Afea seems very promising.

Stanley Flatté

Physicist Stanley Flatté, whose work in particle physics and wave propagation led to important contributions in hadron spectroscopy and the fields of atmospheric optics, ocean acoustics, and seismology, died on 4 November 2007 at his home in Santa Cruz, California. Flatté, a professor emeritus of physics at the University of California, Santa Cruz (UCSC), had battled illness for many years. Drawing on his technical expertise in physics, he helped to design innovative radiation treatments for his sinus cancer. Throughout that struggle, he maintained an active research program, even after his retirement in 2004.Born in Los Angeles on 2 December 1940, Flatté earned a BS in physics at Caltech in 1962 and a PhD in physics at UC Berkeley in 1966. He worked as a research physicist at Lawrence Berkeley Laboratory for five years before joining the UCSC faculty in 1971. At UCSC he was affiliated with the Santa Cruz Institute for Particle Physics, the Institute of Marine Sciences, and the Institute of Geophysics and Planetary Physics. Starting in 1970 Flatté also served as a member of JASON, a national scientific advisory group to many government agencies.Flatté was unique on the Santa Cruz campus, not only for the number of areas in which he was involved, including ocean sciences and Earth sciences in recent years, but also for the level of recognition he received—namely, election to fellowship in several professional societies—for his contributions in different areas. His work with collaborators in various disciplines grew out of his interest in numerical simulation of waves propagating through random media. In the area of particle physics, Flatté contributed to elucidating the nature of several recently discovered mesons while he was a research physicist at the Berkeley lab in the 1960s. His work in spectroscopy was one of the important pieces of information that led to the discovery of quarks as the underlying constituents of strongly interacting particles. The Flatté parameterization he developed in 1975–76 while on a Guggenheim fellowship at CERN is still used to describe the decay of scalar mesons produced with masses near decay thresholds.Flatté’s work on ocean acoustics began in the mid-1970s and continued for more than two decades. He helped develop a new paradigm for understanding sound transmission in the ocean. Using supercomputer calculations and acoustic data processing, he determined small-scale structures associated with oceanic thermal and salinity heterogeneity that had not been previously measured. In the 1990s he took part in the experiment in acoustic thermometry of ocean climate that aimed to track the ocean’s average temperature using repeated long-range recording of sound waves.In seismology, Flatté contributed to research on the scattering of seismic waves in the deep Earth and the formulation of mathematical methods to determine the distribution and properties of small-scale structures in the lithosphere and near the core–mantle boundary. Geophysicist Ru-Shan Wu came to UCSC in 1986 to work with Flatté on scattering theory; that work led to the development of important techniques, such as using one-way acoustic and elastic propagators for seismic modeling and migration, now widely common in the oil exploration industry.In the area of atmospheric optics, Flatté studied the propagation of light waves through atmospheric turbulence. That led to work on adaptive optics for telescopes, where his contributions paralleled those for wave propagation in the ocean as he developed techniques for handling statistical small-scale heterogeneities. Around 2000, he explored forward modeling, inverse modeling, and adaptive optics procedures for statistical heterogeneities.Flatté’s broad interests led him to scientific interactions with an unusually wide-ranging community, and his insightful comments during seminars and discussions will be keenly missed by physicists, oceanographers, atmospheric scientists, and seismologists. We will also miss Flatté’s talents as a pianist and classical and flamenco guitarist.Stanley FlattéPPT|High resolution© 2008 American Institute of Physics.

On curl-preserving finite volume discretizations for shallow water equations

The preservation of intrinsic or inherent constraints, like divergence-conditions, has gained increasing interest in numerical simulations of various physical evolution equations. In Torrilhon and Fey, SIAM J. Numer. Anal. (42/4) 2004, a general framework is presented how to incorporate the preservation of a discrete constraint into upwind finite volume methods. This paper applies this framework to the wave equation system and the system of shallow water equations. For the wave equation a curl-preservation for the momentum variable is present and easily identified. The preservation in case of the shallow water system is more involved due to the presence of convection. It leads to the vorticity evolution as generalized curl-constraint. The mechanisms of vorticity generation are discussed. For the numerical discretization special curl-preserving flux distributions are discussed and their incorporation into a finite volume scheme described. This leads to numerical discretizations which are exactly curl-preserving for a specific class of discrete curl-operators. The numerical experiments for the wave equation show a significant improvement of the new method against classical schemes. The extension of the curl-free numerical discretization to the shallow water case is possible after isolating the pressure flux. Simulation examples demonstrate the influence of the modification. The vortex structure is more clearly resolved.

Volume visualization on sparse grids

Volume rendering is an important technique of displaying volumetric three-dimensional scalar data sets resulting from measurement or simulation. Additionally, sparse grids are of increasing interest in numerical simulations. Based upon hierarchical tensor product bases, the sparse grid approach is a very efficient one improving the ratio of invested storage and computing time to the achieved accuracy for many problems in the area of numerical solution of partial differential equations, for instance in numerical fluid mechanics. The volume visualization algorithms that are available so far cannot cope with sparse grids. We present an approach that directly works on these grids. As a second aspect in this paper, we suggest to use sparse grids as a data compression method in order to visualize huge data sets even on workstations with low main memory. Since the size of data sets used in numerical simulations is still growing, this feature makes it possible that workstations can continue to handle these data sets. In addition to the standard sparse grid interpolation algorithm and the so-called combination technique, we have developed a new sparse grid interpolation method, which harnesses the texture-mapping hardware of graphics workstations for acceleration purposes. Therefore, hardware based volume rendering becomes possible on compressed data sets at interactive frame rates. This is not possible if other compression methods like wavelet or fractal compression are used.

An efficient implementation of flux formulae in multidimensional relativistic hydrodynamical codes

We derive and analyze a simplified formulation of the numerical viscosity terms appearing in the expression of the numerical fluxes associated to several High-Resolution Shock-Capturing schemes. After some algebraic preprocessing, we give explicit expressions for the numerical viscosity terms of two of the most widely used flux formulae, which implementation saves computational time in multidimensional simulations of relativistic flows. Additionally, such treatment explicitely cancels and factorizes a number of terms helping to damp the growing of round-off errors. We have checked the performance of our formulation running a 3D relativistic hydrodynamical code to solve a standard test-bed problem and found that the improvement in efficiency is of high practical interest in numerical simulations of relativistic flows in Astrophysics.

Flow Behavior Around Stayvanes and Guidevanes of a Francis Turbine

The three-dimensional computation of steady and incompressible internal flows is of interest in numerical simulations of turbomachinery, and such simulations are currently under investigation, from inviscid to viscous flow analyses. First, surface pressure distributions have been measured for the stayvanes and the guidevanes of a Francis turbine. They are presented to verify the numerical results. Second, both inviscid and viscous three-dimensional flow analyses have been made, so as to predict the flow behavior in the same domain. Comparison of the measured pressure distributions to the predicted pressure distributions has been made to study the usefulness of the present simulations. It can be pointed out that a global analysis which includes a runner flow passage, except runner blades, is necessary to predict the three-dimensional flow characteristics and that inviscid flow analysis has the capability of good prediction for flow without separation. Viscous flow analysis gives similar results, though it is necessary to investigate further the improvement of prediction accuracy. Flow characteristics around the stayvanes and the guidevanes are also discussed.

CHARACTERISTICS-BASED, HIGH-ORDER ACCURATE AND NONOSCILLATORY NUMERICAL METHOD FOR HYPERBOLIC HEAT CONDUCTION

For extremely short durations oral very low temperatures (near absolute zero), the classical Fourier heat conduction equation fails and has to be replaced by a hyperbolic equation to account for finite thermal wave propagation. During the last few years, there has been a growing interest in numerical simulation of the hyperbolic heal conduction problem. The schemes used in previous studies were either the classical upwind and central difference or the MacCormack's predictor-corrector schemes. As a result, spurious oscillations or excessive diffusion appeared near the discontinuities. This paper presents a method that makes use of the characteristics to suppress these oscillations or diffusions. The equations governing the hyperbolic heat conduction problem are first transformed into characteristic equations, and the first-order upwind, second-order upwind (Beam-Warming)and second-order central (Lax-Wendroff)schemes are applied based on the direction of the characteristic velocity. It is shown that simple ...