Two-phase flow of CO2-brine in a heterogeneous sandstone: Characterization of the rock and comparison of the lattice-Boltzmann, pore-network, and direct numerical simulation methods
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defects, mechanical behavior, carbon sequestration↗
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Asymptotic solution for heat convection-radiation equation
In this paper, we employ a new approximate analytical method called the optimal homotopy asymptotic method (OHAM) to solve steady state heat transfer problem in slabs. The heat transfer problem is modeled using nonlinear two-point boundary value problem. Using OHAM, we obtained the approximate analytical solution for dimensionless temperature with different values of a parameter ε. Further, the OHAM results for dimensionless temperature have been presented graphically and in tabular form. Comparison has been provided with existing results from the use of homotopy perturbation method, perturbation method and numerical method. For numerical results, we used Runge-Kutta Fehlberg fourth-fifth order method. It was found that OHAM produces better approximate analytical solutions than those which are obtained by homotopy perturbation and perturbation methods, in the sense of closer agreement with results obtained from the use of Runge-Kutta Fehlberg fourth-fifth order method.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A practical model for fluid flow in discrete-fracture porous media by using the numerical manifold method
Here in this study, a numerical manifold method (NMM) model is developed to analyze flow in porous media with discrete fractures in a non-conforming mesh. This new model is based on a two-cover-mesh system with a uniform triangular mathematical mesh and boundary/fracture-divided physical covers, where local independent cover functions are defined. The overlapping parts of the physical covers are elements where the global approximation is defined by the weighted average of the physical cover functions. The mesh is generated by a tree-cutting algorithm. A new model that does not introduce additional degrees of freedom (DOF) for fractures was developed for fluid flow in fractures. The fracture surfaces that belong to different physical covers are used to represent fracture flow in the direction of the fractures. In the direction normal to the fractures, the fracture surfaces are regarded as Dirichlet boundaries to exchange fluxes with the rock matrix. Furthermore, fractures that intersect with Dirichlet or Neumann boundaries are considered. Simulation examples are designed to verify the efficiency of the tree-cutting algorithm, the calculation's independency from the mesh orientation, and accuracy when modeling porous media that contain fractures with multiple intersections and different orientations. The simulation results show good agreement with available analytical solutions. Finally, the model is applied to cases that involve nine intersecting fractures and a complex network of 100 fractures, both of which achieve reasonable results. The new model is very practical for modeling flow in fractured porous media, even for a geometrically complex fracture network with large hydraulic conductivity contrasts between fractures and the matrix.
58 GEOSCIENCES↗
Accurate numerical, integral methods for computing drift-kinetic Trubnikov-Rosenbluth potentials
A novel numerical method is employed to compute the integral form of the axi-symmetric Trubnikov-Rosenbluth potentials. Two methods for quadrature in pitch-angle are described and their convergence properties are studied. Careful attention is given to quadrature over a singular Green's function. Here it is shown that an infinite series representation of the Green's function can be used more efficiently than its closed form involving complete elliptic integrals. Then a collocation method in speed, with its associated quadrature scheme, is laid out and its convergence properties are studied. Using the proposed scheme, accurate low-order moments of the field collision operator are obtained using relatively few velocity space degrees of freedom. The scheme is showcased by solving for the equilibrium, axi-symmetric bootstrap current in tokamaks. A C 0 Gauss-Lobatto-Legendre finite element pitch-angle basis with vertex nodes at the trapped/passing boundary is shown, in the context of the integral methods used, to be much more efficient than the more common Legendre polynomial expansion.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Fatigue Crack Propagation of Nickel-Based Superalloy: Experiments and Simulations with Extended Finite Element Method
Numerical simulation based on extended finite element method was employed to investigate the fatigue crack propagation of nickel-based superalloy at room temperature. Experimental tests on compact tension specimens have performed to obtain fatigue crack propagation parameters in Paris region. The extended finite element method has presented a new approach to solve the stress intensity factors and can effectively predict crack propagation without re-meshing at crack tip. The simulation results are in good accordance with experimental data in real 3D cases.
36 MATERIALS SCIENCE↗
Coupled Mooring Analyses for the WEC-Sim Wave Energy Converter Design Tool: Preprint
A wave-energy-converter-specific time-domain modeling method (WEC-Sim) was coupled with a lumped-mass-based mooring model (MoorDyn) to improve its mooring dynamics modeling capability. This paper presents a verification and validation study on the coupled numerical method. First, a coupled model was built to simulate a 1/25 model scale floating power system connected to a traditional three-point catenary mooring with an angle of 120 between the lines. The body response and the tension force on the mooring lines at the fairlead in decay tests and under regular and irregular waves were examined. To validate and verify the coupled numerical method, the simulation results were compared to the measurements from a wave tank test and a commercial code (OrcaFlex). Second, a coupled model was built to simulate a two-body point absorber system with a chain-connected catenary system. The influence of the mooring connection on the point absorber was investigated. Overall, the study showed that the coupling of WEC-Sim and the MoorDyn model works reasonably well for simulating a floating system with practical mooring designs and predicting the corresponding dynamic loads on the mooring lines. Further analyses on improving coupling efficiency and the feasibility of applying the numerical method to simulate WEC systems with more complex mooring configuration are still needed.
16 TIDAL AND WAVE POWER↗
Interfacial gauge methods for incompressible fluid dynamics
Designing numerical methods for incompressible fluid flow involving moving interfaces, for example, in the computational modeling of bubble dynamics, swimming organisms, or surface waves, presents challenges due to the coupling of interfacial forces with incompressibility constraints. A class of methods, denoted interfacial gauge methods, is introduced for computing solutions to the corresponding incompressible Navier-Stokes equations. These methods use a type of "gauge freedom" to reduce the numerical coupling between fluid velocity, pressure, and interface position, allowing high-order accurate numerical methods to be developed more easily. Making use of an implicit mesh discontinuous Galerkin framework, developed in tandem with this work, high-order results are demonstrated, including surface tension dynamics in which fluid velocity, pressure, and interface geometry are computed with fourth-order spatial accuracy in the maximum norm. Applications are demonstrated with two-phase fluid flow displaying fine-scaled capillary wave dynamics, rigid body fluid-structure interaction, and a fluid-jet free surface flow problem exhibiting vortex shedding induced by a type of Plateau-Rayleigh instability. The developed methods can be generalized to other types of interfacial flow and facilitate precise computation of complex fluid interface phenomena.
42 ENGINEERING↗
Solving Seismic Wave Equations on Variable Velocity Models With Fourier Neural Operator
Here, in the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning (DL) enables solving partial differential equations (PDEs), including wave equations, by applying neural networks to identify the mapping between the inputs and the solution. This approach can be faster than traditional numerical methods when numerous instances are to be solved. Previous works that concentrate on solving the wave equation by neural networks consider either a single velocity model or multiple simple velocity models, which is restricted in practice. Instead, inspired by the idea of operator learning, this work leverages the Fourier neural operator (FNO) to effectively learn the frequency domain seismic wavefields under the context of variable velocity models. We also propose a new framework paralleled FNO (PFNO) for efficiently training the FNO-based solver given multiple source locations and frequencies. Numerical experiments demonstrate the high accuracy of both FNO and PFNO with complicated velocity models in the OpenFWI datasets. Furthermore, the cross-dataset generalization test verifies that PFNO adapts to out-of-distribution velocity models. Finally, PFNO admits higher computational efficiency on large-scale testing datasets than the traditional finite-difference method. The aforementioned advantages endow the FNO-based solver with the potential to build powerful models for research on seismic waves.
58 GEOSCIENCES↗
Porous Media Characterization Using Minkowski Functionals: Theories, Applications and Future Directions
Porous materials are ubiquitous, from biological tissues (skin, cartilage, bones, heart tissue), to manufactured materials (paper, functional porous materials, batteries, drug delivery systems, diapers), to environmental materials (rocks, soils, plants). Because these materials are composed of multiple phases, the effects of flow, heat transfer, chemical reactions, and deformations including swelling and shrinking are more complex than that for a single phase such as a gas, liquid, or solid. The realization that porous materials, regardless of the application, have commonalities in modeling approaches, experimental methods, and numerical methods was the impetus of this journal, Transport in Porous Media (founded by Jacob Bear in 1986) and of the International Society for Porous Media (InterPore, interpore.org), which at its roots, originated in 2006. The growth of TIPM and of InterPore mirrors the explosive interest in porous media research that is now recognized as a field of research in and of itself. It is in the honor of InterPore’s 10th anniversary, celebrated at the InterPore 10th Annual Meeting and Jubilee in 2018 in New Orleans, USA, that this special issue was conceived.
Armstrong, Ryan T. (ORCID:0000000164317902)↗
A continuum meshfree method for sandbox-style numerical modeling of accretionary and doubly vergent wedges
Here, in this study, we introduce and utilize GEOSPH, a Lagrangian particle-based continuum Smoothed Particle Hydrodynamics (SPH) code to simulate the deformation of geologic materials in sandbox-style experiments using an elastoplastic constitutive model. Due to the meshfree nature of SPH, our proposed framework is capable of handling the large deformations characteristic of sandbox-style experiments. SPH is also able to capture strain localization and discontinuities, allowing us to resolve faulting patterns emerging in the sandbox experiments. We successfully validate our SPH implementation against the benchmark experiments of Buiter and co-workers, and then apply SPH to understand the deformational processes occurring in doubly vergent orogens resultant from the S-point experimental setup and from finitely high wedge-like indenter backstops of different inclinations. We find that the topographic slope of the prowedge results from the competing processes of vertical uplift due to the indenter and forward thrusting, while the topographic slope of the retrowedge is a product of repeated shallow slope failure. Our findings show that SPH is a promising numerical method which should be added to the current palette of computational tools used by structural geologists for solving problems relating to tectonics and crustal deformation.
58 GEOSCIENCES↗
DT-HYDRO
The software solves the time dependent, one dimensional (1D) coupled mass and momentum balance equations governing the elastic flow of water through the penstock, turbine and draft tube in a hydroelectric facility using a high order finite volume based method. The numerical method is based on the Kurganov-Tadmor central method paired with the Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL). This solution method accurately resolves the fast transient behavior of the flow, including water hammer. Additionally, the software estimates the full 3D flow field within the turbine chamber in real time, a feat that is made possible by leveraging pre-computed CFD results by utilizing a reduced order modeling method based on an efficient randomized singular value decomposition (SVD) driven proper orthogonal decomposition (POD) with POD-mode weight regression. The reduced order model of the 3D flow is directly coupled to the 1D elastic flow model so the entire flow field through the penstock and turbine system is resolved quickly and with high fidelity.
Gurecky, William [Oak Ridge National Laboratory (O↗
Assessment of Lost Circulation Material Particle-Size Distribution on Fracture Sealing: A Numerical Study
Summary Lost circulation materials (LCMs) are essential to combat fluid loss while drilling and may put the whole operation at risk if a proper LCM design is not used. The focus of this research is understanding the function of LCMs in sealing fractures to reduce fluid loss. One important consideration in the success of fracture sealing is the particle-size distribution (PSD) of LCMs. Various studies have suggested different guidelines for obtaining the best size distribution of LCMs for effective fracture sealing based on limited laboratory experiments or field observations. Hence, there is a need for sophisticated numerical methods to improve the LCM design by providing some predictive capabilities. In this study, computational fluid dynamics (CFD) and discrete element methods (DEM) numerical simulations are coupled to investigate the influence of PSD of granular LCMs on fracture sealing. Dimensionless variables were introduced to compare cases with different PSDs. We validated the CFD-DEM model in reproducing specific laboratory observations of fracture-sealing experiments within the model boundary parameters. Our simulations suggested that a bimodally distributed blend would be the most effective design in comparison to other PSDs tested here.
Engineering↗
Generation of Turbulence in Colliding Reconnection Jets
The collision of magnetic reconnection jets is reported on by means of a three-dimensional numerical simulation at the kinetic scale, in the presence of a strong guide field. We demonstrate that turbulence develops due to the collision of jets, producing several current sheets in reconnection outflows, aligned with the guide field direction. The turbulence is mainly two-dimensional, with stronger gradients in the plane perpendicular to the guide field and low wave-like activity in the parallel direction. First, we provide a numerical method to isolate the central turbulent region. Second, we analyze the spatial second-order structure function and prove that turbulence is confined in this region. Lastly, we compute local magnetic and electric frequency spectra, finding a trend in the subion range that differs from typical cases for which the Taylor hypothesis is valid, as well as wave activity in the range between ion and electron cyclotron frequencies. Our findings are relevant to understand observed collisions of reconnection jets in space plasmas.
79 ASTRONOMY AND ASTROPHYSICS↗
General-relativistic Resistive Magnetohydrodynamics with Robust Primitive-variable Recovery for Accretion Disk Simulations
Recent advances in black hole astrophysics, particularly the first visual evidence of a supermassive black holeat the center of the galaxy M87 by the Event Horizon Telescope (EHT), and the detection of an orbiting “hot spot”nearby the event horizon of Sgr A* in the Galactic center by the Gravity Collaboration, require the developmentof novel numerical methods to understand the underlying plasma microphysics. Non-thermal emission related tosuch hot spots is conjectured to originate from plasmoids that form due to magnetic reconnection in thin currentlayers in the innermost accretion zone. Resistivity plays a crucial role in current sheet formation, magneticreconnection, and plasmoid growth in black hole accretion disks and jets. We included resistivity in the three-dimensional general-relativistic magnetohydrodynamics (GRMHD) codeBHACand present the implementationof an Implicit-Explicit scheme to treat the stiff resistive source terms of the GRMHD equations. The algorithmis tested in combination with adaptive mesh refinement to resolve the resistive scales and a constrained transportmethod to keep the magnetic field solenoidal. Several novel methods for primitive variable recovery, a key part inrelativistic magnetohydrodynamics codes, are presented and compared for accuracy, robustness, and efficiency.We propose a new inversion strategy that allows for resistive-GRMHD simulations of low gas-to-magneticpressure ratio and highly magnetized regimes as applicable for black hole accretion disks, jets, and neutron starmagnetospheres. We apply the new scheme to study the effect of resistivity on accreting black holes, accountingfor dissipative effects as reconnection
(magnetohydrodynamics:) MHD↗
A Coarse-Mesh Nonlinear Diffusion Acceleration Scheme with Local Refinement for Neutron Transport Calculations
The coarse-mesh nonlinear diffusion acceleration (CM-NDA) technique, or commonly known as coarse-mesh finite difference (CMFD), is one of the most widely used acceleration methods for numerical transport calculations. Although CM-NDA is very effective to reduce the iteration number of neutron transport sweep, it can sometimes become unstable, in particularly when the coarse mesh size becomes large. Over the last two decades a number of ad hoc techniques have been developed to stabilize the CM-NDA scheme. In this paper, we present a new scheme, LR-NDA, which is based on CM-NDA with local refinement. Within the CM-NDA framework, the LR-NDA scheme incorporates solving an additional local boundary-value problem (BVP) of the neutron flux on each individual coarse mesh cell, yielding a finer flux profile than CMNDA. Our assessments show that this new scheme can significantly improve the effectiveness of CM-NDA, and more importantly it is very stable even for extremely high optical thickness. A great feature of LR-NDA is that it is fully adaptive, which means that it can be easily applied to any local region of the problem domain, and local refinement can be performed using any numerical method (e.g., finite difference, finite element, or spectral element, etc.). (authors)
42 ENGINEERING↗
Mean Field Type Control with Congestion (II): An Augmented Lagrangian Method
This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential equations arising from the model were discussed and existence and uniqueness were proved. Here, the focus is put on numerical methods: a monotone finite difference scheme is proposed and shown to have a variational interpretation. Then an Alternating Direction Method of Multipliers for solving the variational problem is addressed. It is based on an augmented Lagrangian. Two kinds of boundary conditions are considered: periodic conditions and more realistic boundary conditions associated to state constrained problems. Various test cases and numerical results are presented.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A numerical manifold method model for analyzing fully coupled hydro-mechanical processes in porous rock masses with discrete fractures
A numerical manifold method (NMM) model was developed for fully coupled analysis of hydro-mechanical (HM) processes in porous rock masses with discrete fractures. Using an NMM two-cover-mesh system of mathematical and physical covers, fractures are conveniently discretized by dividing the mathematical cover along fracture traces to physical cover, resulting in a discontinuous model on a non-conforming mesh. In this model, discrete fracture deformation (e.g. open and slip) and fracture fluid flow within a permeable and deformable porous rock matrix are rigorously considered. For porous rock, direct pore-volume coupling was modeled based on an energy-work scheme. For mechanical analysis of fractures, a fracture constitutive model for mechanically open states was introduced. For fluid flow in fractures, both along-fracture and normal-to-fracture fluid flow are modeled without introducing additional degrees of freedom. When the mechanical aperture of a fracture is changing, its hydraulic aperture and hydraulic conductivity is updated. At the same time, under the effect of coupled deformation and fluid flow, the contact state may dynamically change, and the corresponding contact constraint is updated each time step. Therefore, indirect coupling is realized under stringent considerations of coupled HM effects and fracture constitutive behavior transfer dynamically. To verify the new model, examples involving deformable porous media containing a single and two sets of fractures were designed, showing good accuracy. Finally, the model was applied to analyze coupled HM behavior of fractured porous rock domains with complex fracture networks under effects of loading and injection.
58 GEOSCIENCES↗
Numerical Continuation Methods for Intrusive Uncertainty Quantification Studies
Rigorous modeling of engineering systems relies on efficient propagation of uncertainty from input parameters to model outputs. In recent years, there has been substantial development of probabilistic polynomial chaos (PC) Uncertainty Quantification (UQ) methods, enabling studies in expensive computational models. One approach, termed ”intrusive”, involving reformulation of the governing equations, has been found to have superior computational performance compared to non-intrusive sampling-based methods in relevant large-scale problems, particularly in the context of emerging architectures. However, the utility of intrusive methods has been severely limited due to detrimental numerical instabilities associated with strong nonlinear physics. Previous methods for stabilizing these constructions tend to add unacceptably high computational costs, particularly in problems with many uncertain parameters. In order to address these challenges, we propose to adapt and improve numerical continuation methods for the robust time integration of intrusive PC system dynamics. We propose adaptive methods, starting with a small uncertainty for which the model has stable behavior and gradually moving to larger uncertainty where the instabilities are rampant, in a manner that provides a suitable solution.
97 MATHEMATICS AND COMPUTING↗