Boundary Forces Research Articles

Future intraplate stress and the longevity of carbon storage

Carbon capture and storage (CCS) is regarded as a promising strategy for mitigating global warming. A 19% CCS contribution to CO2 reduction by 2050, as envisaged by the International Energy Agency, would require the construction of thousands of CCS sites by the 2030s and beyond. CO2 storage may need to last for tens of thousands of years to avoid potential global warming and major Earth system changes, and a critical site selection criterion will be the likelihood of future escape of stored CO2 due to fault reactivation. However, future long-term intraplate stress field changes have not been considered in this context. Here we focus on Australia, where 61 potential CCS sites have been proposed, and model the evolving intraplate stress field due to the future growth of tectonic collisional forces north of Australia. Counter intuitively, the largest changes are predicted for some parts of western, central and southeast Australia, all regions far away from plate boundaries, reflecting the non-linear interaction of plate boundary forces with a geologically heterogeneous continent. We suggest that at least ten suggested CCS sites are located in regions where major changes of in situ stress regimes can be expected in the next 100,000years, requiring a careful evaluation of potential future fault reactivation and a breach of reservoir seals. Our results highlight the importance of considering future intraplate stress field changes for selecting CCS sites, particularly within continental regions affected by ongoing mountain building processes including Australia, India, South America, Asia and southern Europe.

Numerical interpretation of molecular surface field in dielectric modeling of solvation.

Continuum solvent models, particularly those based on the Poisson-Boltzmann equation (PBE), are widely used in the studies of biomolecular structures and functions. Existing PBE developments have been mainly focused on how to obtain more accurate and/or more efficient numerical potentials and energies. However to adopt the PBE models for molecular dynamics simulations, a difficulty is how to interpret dielectric boundary forces accurately and efficiently for robust dynamics simulations. This study documents the implementation and analysis of a range of standard fitting schemes, including both one-sided and two-sided methods with both first-order and second-order Taylor expansions, to calculate molecular surface electric fields to facilitate the numerical calculation of dielectric boundary forces. These efforts prompted us to develop an efficient approximated one-dimensional method, which is to fit the surface field one dimension at a time, for biomolecular applications without much compromise in accuracy. We also developed a surface-to-atom force partition scheme given a level set representation of analytical molecular surfaces to facilitate their applications to molecular simulations. Testing of these fitting methods in the dielectric boundary force calculations shows that the second-order methods, including the one-dimensional method, consistently perform among the best in the molecular test cases. Finally, the timing analysis shows the approximated one-dimensional method is far more efficient than standard second-order methods in the PBE force calculations. © 2017 Wiley Periodicals, Inc.

Prediction of the present-day stress field in the Australian continental crust using 3D geomechanical–numerical models

ABSTRACTThe Australian continent has an enigmatic present-day stress pattern with considerable regional variability in maximum horizontal stress (SHmax) orientations. Previous attempts to estimate the Australian SHmax orientation with geomechanical–numerical models indicate that plate boundary forces provide the major controls on the contemporary stress orientations. However, these models do not satisfactorily predict the observed stress orientation in major basins throughout eastern Australia, where the knowledge of the present-day crustal stresses is of vital importance for development and management of different types of geo-reservoirs. In addition, a new comprehensive stress-data compilation in Australia, which contains 2150 data records and is the key dataset for model calibration, provides motivation to construct a new geomechanical–numerical model for Australia. Herein, we present a 3D geomechanical–numerical model that predicts both the SHmax orientation and the relative stress magnitudes throughout the Australian continent. Our best-fit model, with mean absolute deviation of 15°, is in good agreement with observed SHmax orientations and the stress regime in most areas, and shows a much better fit in areas where the stress pattern was unable to be predicted by previous published attempts. Interestingly, the best-fit model requires a significant push from the western boundary of Australian continental model, which is possible supporting evidence for the east–west-oriented mantle drag postulated by state-of-the-art global convection models, or may be generated by the excess of gravitational potential energy from Tibetan Plateau, transferred through the Indo-Australian Plate. Hence, our modelling results provide a good first-order prediction of the stress field for areas where no stress information is currently available and can be used to derive initial and boundary conditions for local and reservoir-scale 3D geomechanical models across Australia.

A simplified three-dimensional shallow landslide susceptibility framework considering topography and seismicity

Shallow landslides are a prevalent concern in mountainous or hilly regions that can result in severe societal, economic, and environmental impacts. The challenge is further compounded as the size and location of a potential slide is often unknown. This study presents a generalized approach for the evaluation of regional shallow landslide susceptibility using an existing shallow landslide inventory, remote sensing data, and various geotechnical scenarios. The three-dimensional limit equilibrium model derived in this study uses a raster-based approach that uniquely integrates tree root reinforcement, earth pressure boundary forces, and pseudo-static seismic accelerations. Contributions of this methodology include the back-calculation of soil strength from a landslide inventory, sensitivity analyses regarding landslide size-pixel size relationships, and the determination of shallow landslide susceptibility for a landscape or infrastructure considering various root, water, and seismic conditions using lidar bare-earth DEMs as a topographic input. Using a distribution of inventoried landslide points and random points in non-landslide locales, the proposed methodology demonstrated reasonable correlation between regions of high landslide susceptibility and observed shallow landslides within a 150-km2 region of the Oregon Coast Range when the water-height ratio was 0.5. The method may be improved by considering spatial hydrologic conditions and geology more explicitly.

Convective Self-Aggregation in Numerical Simulations: A Review

Organized convection in the tropics occurs across a range of spatial and temporal scales and strongly influences cloud cover and humidity. One mode of organization found is ‘‘self-aggregation,’’ in which moist convection spontaneously organizes into one or several isolated clusters despite spatially homogeneous boundary conditions and forcing. Self-aggregation is driven by interactions between clouds, moisture, radiation, surface fluxes, and circulation, and occurs in a wide variety of idealized simulations of radiative–convective equilibrium. Here we provide a review of convective self-aggregation in numerical simulations, including its character, causes, and effects. We describe the evolution of self-aggregation including its time and length scales and the physical mechanisms leading to its triggering and maintenance, and we also discuss possible links to climate and climate change.

Skill of real-time operational forecasts with the APCC multi-model ensemble prediction system during the period 2008–2015

This paper assesses the real-time 1-month lead forecasts of 3-month (seasonal) mean temperature and precipitation on a monthly basis issued by the Asia-Pacific Economic Cooperation Climate Center (APCC) for 2008–2015 (8 years, 96 forecasts). It shows the current level of the APCC operational multi-model prediction system performance. The skill of the APCC forecasts strongly depends on seasons and regions that it is higher for the tropics and boreal winter than for the extratropics and boreal summer due to direct effects and remote teleconnections from boundary forcings. There is a negative relationship between the forecast skill and its interseasonal variability for both variables and the forecast skill for precipitation is more seasonally and regionally dependent than that for temperature. The APCC operational probabilistic forecasts during this period show a cold bias (underforecasting of above-normal temperature and overforecasting of below-normal temperature) underestimating a long-term warming trend. A wet bias is evident for precipitation, particularly in the extratropical regions. The skill of both temperature and precipitation forecasts strongly depends upon the ENSO strength. Particularly, the highest forecast skill noted in 2015/2016 boreal winter is associated with the strong forcing of an extreme El Nino event. Meanwhile, the relatively low skill is associated with the transition and/or continuous ENSO-neutral phases of 2012–2014. As a result the skill of real-time forecast for boreal winter season is higher than that of hindcast. However, on average, the level of forecast skill during the period 2008–2015 is similar to that of hindcast.

Convective wave breaking in the KdV equation

The KdV equation is a model equation for waves at the surface of an inviscid incompressible fluid, and it is well known that the equation describes the evolution of unidirectional waves of small amplitude and long wavelength fairly accurately if the waves fall into the Boussinesq regime. The KdV equation allows a balance of nonlinear steepening effects and dispersive spreading which leads to the formation of steady wave profiles in the form of solitary waves and cnoidal waves. While these wave profiles are solutions of the KdV equation for any amplitude, it is shown here that there for both the solitary and the cnoidal waves, there are critical amplitudes for which the horizontal component of the particle velocity matches the phase velocity of the wave. Solitary or cnoidal solutions of the KdV equation which surpass these amplitudes feature incipient wave breaking as the particle velocity exceeds the phase velocity near the crest of the wave, and the model breaks down due to violation of the kinematic surface boundary condition. The condition for breaking can be conveniently formulated as a convective breaking criterion based on the local Froude number at the wave crest. This breaking criterion can also be applied to time-dependent situations, and one case of interest is the development of an undular bore created by an influx at a lateral boundary. It is shown that this boundary forcing leads to wave breaking in the leading wave behind the bore if a certain threshold is surpassed.

Implicit immersed boundary method for fluid-structure interaction

A novel immersed boundary method is introduced for simulating the fluid-structure interaction problem. Unlike the body-conforming mesh method which imposes the no-slip boundary conditions directly on the immersed interface, the immersed boundary method adopts a boundary force for the presence of the immersed solid. Therefore, the fluid is simply simulated on a fixed Cartesian mesh irrespective the movement of the immersed solid, which circumvents the mesh quality issue that frequently happens in the body-conforming mesh method. To enforce the correct boundary condition, we derive an additional moving force equation. This additional equation is integrated into a second order accurate fractional step method and solved with the conjugate gradient method. The proposed method is validated with several one-way fluid-structure interaction examples.

ERRORS IN QUANTITIES OF INTEREST IN THE LAMINATED PLATE BENDING PROBLEM USING HIERARCHIC SETS OF BASIS FUNCTIONS IN GFEM

Abstract. A formulation for error estimation is developed for the bending problem of composite laminated plates based on the Mindlin-Reissner kinematic model discritized by the Generalized Finite Element Method (GFEM). The error estimation process starts with an upper bound in energy norm, which is obtained following the basic CRE (Constitutive Relation Error) framework of the Ladev`eze formulation, that is, the estimate is obtained from a statically admissible stress field computed at element level in a Neumann problem where the element boundary forces are equilibrated. The authors have previously shown that an accurate description of the in plane stresses in a laminate is essential to obtain an accurate approximation to the transverse shear stresses at the layers interfaces. Since important failure modes in laminated composite plates, like the delamination, are linked to the transverse stresses, it is essential to develop both, accurate post-processing procedures to compute improved transverse stresses, and also estimate techniques for the discretization errors. The first condition is adequately satisfied by GFEM. Therefore, the aim of the present work is to extend the general CRE technology to develop formulations to estimation of errors in Quantity of Interest (QI) identified preferably with the stress field in the laminated plate problem. One of the steps necessary in the CRE procedure is the computation of and admissible stress field in each element, in a Neumann problem where the boundary forces have been previously equilibrated. For a GFEM basis with high order enrichment, adequate procedures have to be sought. Here we use one single higher order finite element, based on displacement FEM, to obtain an approximation to the equilibrated field. The formulation is implemented for arbitrary degree of the basis, which allows an arbitrarily close approximation to the equilibrium condition. The sharpness of the QI’s error bounds is increased with the accuracy of the primal and dual global energy norm of errors. In the present work we investigate the effectiveness of a local GFEM p-enrichment as a tool to improve the approximability of the model in capturing the local gradients which characterizes response of the dual loading. The GFEM p-enrichment is implemented in a simple and straightforward way, as opposed to some other possible forms of enrichment, e.g. local h-refinement or a sub-domain approach. Numerical tests are performed to asses the effect of the different parameters in the modeling over the errors in the quantities of interest. Keywords: Strict error bounds estimation, Generalized Finite Element Method, Admissible stress field, Element Equilibrated Technique, Laminated plate Mindlin model.

Coastal Inundation Research:An overview of the Process

Coastal inundation is the flooding of coastal zone resulting from increased river discharge, spring tides, severe storms, or generation of powerful waves from tectonic activity (tsunami). This article discusses the critical factors that contribute to coastal inundation. Among the probable factors that cause coastal flooding and destruction, storm surge is the most frequent, and hence this article provides a detailed evaluation of the progress made in storm inundation research. Recent advances in coastal inundation modelling include efforts to understand the nonlinear dynamic interaction of near-shore waves, wind and atmospheric pressure with still water sea level and coastal currents, and their combined effects on storm surge along the coast and interaction with coastal morphology. An advanced storm-surge model comprises different modules, viz. an atmospheric component, and two ocean components for surge and wave simulations; these modules are coupled with each other. The nesting of regional coastal model with an ocean-wide model captures the far-field boundary forcing of extreme events that usually originate from the warm open ocean. Even though significant advancements reported on the efficiency and accuracy of storm surge and inundation prediction, further studies are required to understand the nonlinear interaction of storm surge with coastal landforms and their vegetation (land cover). In the context of rising sea level, increased tropical cyclone activity and rapid shoreline change, it is pertinent to evaluate the future flooding risk associated with landfall of tropical cyclones in densely populated coastal cities.

Issues associated with Galilean invariance on a moving solid boundary in the lattice Boltzmann method.

In lattice Boltzmann simulations involving moving solid boundaries, the momentum exchange between the solid and fluid phases was recently found to be not fully consistent with the principle of local Galilean invariance (GI) when the bounce-back schemes (BBS) and the momentum exchange method (MEM) are used. In the past, this inconsistency was resolved by introducing modified MEM schemes so that the overall moving-boundary algorithm could be more consistent with GI. However, in this paper we argue that the true origin of this violation of Galilean invariance (VGI) in the presence of a moving solid-fluid interface is due to the BBS itself, as the VGI error not only exists in the hydrodynamic force acting on the solid phase, but also in the boundary force exerted on the fluid phase, according to Newton's Third Law. The latter, however, has so far gone unnoticed in previously proposed modified MEM schemes. Based on this argument, we conclude that the previous modifications to the momentum exchange method are incomplete solutions to the VGI error in the lattice Boltzmann method (LBM). An implicit remedy to the VGI error in the LBM and its limitation is then revealed. To address the VGI error for a case when this implicit remedy does not exist, a bounce-back scheme based on coordinate transformation is proposed. Numerical tests in both laminar and turbulent flows show that the proposed scheme can effectively eliminate the errors associated with the usual bounce-back implementations on a no-slip solid boundary, and it can maintain an accurate momentum exchange calculation with minimal computational overhead.

Numerical solution of partial differential equations with stochastic Neumann boundary conditions

The aim of this paper is to study the numerical solution of partial differential equations with boundary forcing. For spatial discretization we apply the Galerkin method and for time discretization we will use a method based on the accelerated exponential Euler method. Our purpose is to investigate the convergence of the proposed method, but the main difficulty in carrying out this construction is that at the forced boundary the solution is expected to be unbounded. Therefore the error estimates are performed in the \begin{document}$ L_p $\end{document} spaces.

The cost of controlling weakly degenerate parabolic equations by boundary controls

We consider the one-dimensional degenerate parabolic equation \begin{document}$u_t - (x^α u_x)_x =0 \;\;x∈(0,1), t ∈ (0,T) ,$ \end{document} controlled by a boundary force acting at the degeneracy point \begin{document}$ x=0$\end{document} . We study the reachable targets at some given time \begin{document}$T$\end{document} using \begin{document}$ H^1$\end{document} controls, studying the influence of the degeneracy parameter \begin{document}$ α ∈ [0,1)$\end{document} . First we obtain precise upper and lower bounds for the null controllability cost, proving that the cost blows up rationnally as \begin{document}$ \mathit{\alpha } \to {{\rm{1}}^{\rm{ - }}}$\end{document} and exponentially fast when \begin{document}$ \mathit{T} \to {{\rm{0}}^{\rm{ + }}}$\end{document} . Next, thanks to the special structure of the eigenfunctions of the problem, we investigate and obtain (partial) results concerning the structure of the reachable states. Our approach is based on the moment method developed by Fattorini and Russell [ 19 , 20 ]. To achieve our goals, we extend some of their general results concerning biorthogonal families, using complex analysis techniques developped by Seidman [ 48 ], Guichal [ 26 ], Tenenbaum-Tucsnak [ 49 ] and Lissy [ 35 , 36 ].

A Hyperelastic Two-Scale Optimization Model for Shape Matching

We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations. Deformation boundary conditions that supplement the underlying equations are usually unknown. Given an initial guess, these are optimized such that the mechanical boundary forces that are responsible for the deformation are of a simple nature. We show a heuristic way to approximate the nonlinear optimization problem by a sequence of convex problems using finite elements. The deformation cost, i.e., the forces, is measured on a coarse scale, while ICP-like matching is done on the fine scale. We demonstrate the plausibility of our algorithm through examples taken from different datasets.

Coupling Strategies Investigation of Hybrid Atomistic-Continuum Method Based on State Variable Coupling

Different configurations of coupling strategies influence greatly the accuracy and convergence of the simulation results in the hybrid atomistic-continuum method. This study aims to quantitatively investigate this effect and offer the guidance on how to choose the proper configuration of coupling strategies in the hybrid atomistic-continuum method. We first propose a hybrid molecular dynamics- (MD-) continuum solver in LAMMPS and OpenFOAM that exchanges state variables between the atomistic region and the continuum region and evaluate different configurations of coupling strategies using the sudden start Couette flow, aiming to find the preferable configuration that delivers better accuracy and efficiency. The major findings are as follows:(1)theC→Aregion plays the most important role in the overlap region and the “4-layer-1” combination achieves the best precision with a fixed width of the overlap region;(2)the data exchanging operation only needs a few sampling points closer to the occasions of interactions and decreasing the coupling exchange operations can reduce the computational load with acceptable errors;(3)the nonperiodic boundary force model with a smoothing parameter of 0.1 and a finer parameter of 20 can not only achieve the minimum disturbance near the MD-continuum interface but also keep the simulation precision.

Gravitation-Based 3-D Redeployment Schemes for the Mobile Sensors and Sink in Gas Leakage Monitoring

Gas leakage is one of the most frequent types of accidents in the petrochemical industry. It is imperative to use mobile sensors to monitor such an accident area. The new and effective way is to use drones and helicopters that spray wireless sensors from the air to monitor harmful gases and to locate the gas leaking source. However, the sprayed wireless sensors will be distributed randomly around the accident area, and it is a challenge to obtain effective coverage. This paper proposes a gravitation-based redeployment algorithm for sensors (GRSS) that considers the virtual boundary forces and the gas concentration in a 3-D accident monitoring area. A priority-based redeployment algorithm for sensors (PRSS) is proposed to further improve the coverage and simplify the 3-D redeployment problem. PRSS considers the layer priorities of the monitoring area to control the movements of the mobile sensors. The simulation results show that the GRSS and PRSS methods can achieve better coverage and utilize less distance compared with the random algorithm and 3-D self-deployment.

Granular rheology: measuring boundary forces with laser-cut leaf springs

In granular physics experiments, it is a persistent challenge to obtain the boundary stress measurements necessary to provide full a rheological characterization of the dynamics. Here, we describe a new technique by which the outer boundary of a 2D Couette cell both confines the granular material and provides spatially- and temporally- resolved stress measurements. This key advance is enabled by desktop laser-cutting technology, which allows us to design and cut linearly-deformable walls with a specified spring constant. By tracking the position of each segment of the wall, we measure both the normal and tangential stress throughout the experiment. This permits us to calculate the amount of shear stress provided by basal friction, and thereby determine accurate values of $\mu(I)$.

전자기장과 열하중을 받는 복합재료 평판의압전제어에 따른 동특성변화

본 논문에서 전자기장과 열 하중을 받는 복합재료 평판에 대하여 압전재료를 이용한 압전제어를 수행하였다. 구조물에 가해지는 전자기장과 열 하중, 그리고 구성방정식에서 고려되는 압전효과가 모두 포함된 지배방정식을 FSDT 판 이론에 기초하여 Hamilton 원리에 의하여 유도하였다. 평판의 경계면에서 발생하는 제어력과 제어 모멘트는 비례제어 및 속도제어 로직에 의하여 적용되었다. 전자기장과 열 하중, 그리고 압전효과가 복합재료 평판의 동특성에 미치는 영향에 대하여 고찰하고, 압전효과 및 복합재료의 섬유각 변화를 통하여 복합재 구조물의 동특성을 효과적으로 제어 가능함을 확인하였다. Structural model of laminated composite plate based on the first order shear deformation theory and subjected to a combination of piezoelectric, electromagnetic and thermal fields is established. Coupled equations of motion are derived via Hamilton's principle on the basis of electromagnetic and piezoelectric equations which are involved in constitutive equations. Proportional control and velocity feedback control logics are applied via boundary control moments and forces. Variations of dynamic chasracteristics of composite plate with collocated piezoelectric sensor and actuators, electromagnetic field and temperature gradient are investigated and it reveals that dynamic characteristics of structure can be effectively controlled by utilizing the piezoelectric effect and ply angles of fiber reinforced composites.

Optimal wavy surface to suppress vortex shedding using second-order sensitivity to shape changes

A method to find optimal 2nd-order perturbations is presented, and applied to find the optimal spanwise-wavy surface for the suppression of cylinder wake instability. As shown in recent studies (Hwang et al., 2013, Tammisola et al., 2014, Del Guercio et al., 2014), 2nd-order perturbations are required to capture the stabilizing effect of spanwise waviness, which is ignored by standard adjoint-based sensitivity analyses. Here, previous methods are extended so that (i) 2nd-order sensitivity is formulated for base flow changes satisfying the linearized Navier–Stokes, and (ii) the resulting method is applicable to a 2D global instability problem. This makes it possible to formulate the 2nd-order sensitivity to shape modifications. This formulation is used to find the optimal shape to suppress the cylinder wake instability. The optimal shape is then perturbed by random distributions in full 3D stability analysis to confirm that it is a local optimal at the given amplitude and wavelength. At Re=100, surface waviness of maximum height 1% of the cylinder diameter is sufficient to stabilize the flow. The optimal surface creates streaks passively by extracting energy from the base flow derivatives and altering the tangential velocity component at the wall. This paper extends previous techniques to a fully two-dimensional method to find boundary perturbations which optimize the 2nd-order drift. The method should be applicable to generic flow instability problems, and to different types of control, such as boundary forcing, shape modulation or suction.

Discrete element method investigation on thermally-induced shakedown of granular materials

Temperature change, as a common kind of internal perturbation performed on granular materials, has a significant effect on the bulk properties of granular materials. However, few studies on thermally-induced shakedown under a long-term thermal cycling were reported. In this work, the discrete element method was used to give insight into the thermally-induced shakedown on the fabric and stress states within non-cohesive, frictional granular assemblies. Assemblies were submitted to thermal cycling at a stationary boundary condition after experiencing a one-dimensional compression. Evolution of coordination number, entropy and anisotropy was investigated as well as boundary forces and contact forces. At the same time, effects of the heating rate, the initial vertical load and the magnitude of temperature change were examined. It demonstrates that thermal cycling induces a significant force relaxation within granular materials, while the corresponding granular fabric has a small change. In addition, the entropy and anisotropy decreases with thermal cycling. Moreover, the initial vertical load can constrain the development of thermally-induced fabric change, thereby limiting force relaxation to some degree. Both high heating rate and larger magnitudes of temperature change contribute to more significant force relaxation. However, they cause smaller fabric changes even though they provide larger perturbations.