Message-Passing-Interface MPI Parallelization of Iteratively Coupled Fluid Flow and Geomechanics Codes for the Simulation of System Behavior in Hydrate-Bearing Geologic Media

The Reservoir GeoMechanics Simulator (RGMS), a geomechanics simulator based on the finite element method and parallelized using the Message Passing Interface (MPI), is developed in this work to model the stresses and deformations in subsurface systems. RGMS can be used stand-alone, or coupled with flow and transport models. pT+H V1.5, a parallel MPI-based version of the serial T+H V1.5 code that describes mass and heat flow in hydrate-bearing porous media, is also developed. Using the fixed-stress split iterative scheme, RGMS is coupled with the pT+H V1.5 to investigate the geomechanical responses associated with gas production from hydrate accumulations. The code development and testing process involve evaluation of the parallelization and of the coupling method, as well as verification and validation of the results. The parallel performance of the codes is tested on the Ada Linux cluster of the Texas A&M High Performance Research Computing using up to 512 processors, and on a Mac Pro computer with 12 processors. The investigated problems are: Group 1: Geomechanical problems solved by RGMS in 2D Cartesian and cylindrical domains and a 3D problem, involving 4x106 and 3.375 x106 elements, respectively; Group 2: Realistic problems of gas production from hydrates using pT+H V1.5 in 2D and 3D systems with 2.45x105 and 3.6 x106 elements, respectively; Group 3: The 3D problem in Group 2 solved with the coupled RGMS-pT+H V1.5 simulator, fully accounting for geomechanics. Two domain partitioning options are investigated on the Ada Linux cluster and the Mac Pro, and the code parallel performance is monitored. On the Ada Linux cluster using 512 processors, the simulation speedups (a) of RGMS are 218.89, 188.13, and 284.70 in the Group 1 problems, (b) of pT+H V1.5 are 174.25 and 341.67 in the Group 2 cases, and (c) of the coupled simulators is 331.80 in Group 3. The results produced in this work show the necessity of using full geomechanics simulators in marine hydrate-related studies because of the associated pronounced geomechanical effects on production and displacements and (b) the effectiveness of the parallel simulators developed in this study, which can be the only realistic option in these complex simulations of large multi-dimensional domains.

Proper Generalized Decomposition Based Model Order Reduction Applied to Problems Defined in Degenerated Domains

Nowadays, the use of simulation in industrial applications is a routine practice. However, the need of considering high fidelity models and their associated solutions is demanding for more efficient solvers. Despite the remarkable progress accomplished in hardware and software in the last decades, the ability to simulate high fidelity 3D models, taking into consideration all their richness is still challenging. For example, if we wish to simulate a 3D problem including 10 parameters, each of them taking 10 different values we should solve 1010 3D problems. This issue is known as the curse of dimensionality, and compromises the solution of models defined in high dimensional spaces.

Axial Flux PM In-Wheel Motor for Electric Vehicles: 3D Multiphysics Analysis

The Axial Flux Permanent Magnet (AFPM) motor represents a valid alternative to the traditional radial flux motor due to its compact structure; it is suitable for in-wheel applications so that the transmission gear can be suppressed. The modeling of the motor is a purely Three-Dimensional (3D) problem and the use of 3D finite element tools allows the attainment of accurate results taking also into account the effects of the end-windings. Moreover, a 3D multiphysics analysis is essential to evaluate not only the motor performance and its thermal behavior, but also the electromagnetic forces acting on the surfaces of the stator teeth and of the magnets that face the air gap. Moreover, as the vehicle’s motors often work in variable-speed conditions, the prediction of vibrations and noise for electric motors over a wide speed range is usually necessary. The paper presents a double-sided AFPM motor for a small pure electric vehicle; the basic drive architecture includes four axial flux motors installed directly inside the vehicle’s wheels. The aim is to propose advanced and integrated electromagnetic, vibroacoustic and thermal analyses that allow the investigation of the axial flux motor behavior in a detailed and exhaustive way.

A SIMPLIFIED TWO-NODE COARSE-MESH FINITE DIFFERENCE METHOD FOR PIN-WISE CALCULATION WITH SP3

For accurate and efficient pin-by-pin core calculation of SP3 equations, a simplified two-node Coarse Mesh Finite Difference (CMFD) method with the nonlinear iterative strategy is proposed. In this study, the two-node method is only used for discretization of Laplace operator of the 0th moment in the first equation, while the fine mesh finite difference (FMFD) is used for the 2nd moment flux and the second equation. In the two-node problem, transverse flux is expanded to second-order Legendre polynomials. In addition, the associated transverse leakage is approximated with flat distribution. Then the current coupling coefficients are updated in nonlinear iterations. The generalized eigenvalue problem from CMFD is solved using Jacobi-Davidson method. A protype code CORCA-PIN is developed. FMFD scheme is implemented in CORCA-PIN as well. The 2D KAIST 3A benchmark problem and extended 3D problem, which are cell homogenized problems with strong absorber, are tested. Numerical results show that the solution of the simplified two-node method with 1×1 mesh per cell has comparable accuracy of FMFD with 4×4 meshes per cell, but cost less time. The method is suitable for whole core pin-wise calculation.

On the applicability limits of refined theories in describing of the flexural edge wave in plates

Исследуются пределы применимости уточненных теорий изгиба пластины при описании дисперсии изгибной краевой волны и амплитуды её возбуждения парой сосредоточенных скручивающих моментов, приложенных на торце. Методом численного сравнения с решением трехмерной задачи показано, что теория типа Тимошенко пригодна для описания краевой волны на частотах, не превосходящих 30% от первой частоты запирания. Уточненная теория изгиба пластин с приведенной инерцией в сочетании с классическими граничными условиями позволяет уточнить скорость волны по сравнению с теорией Кирхгофа, но значительно искажает амплитуду. The applicability limits of refined plate bending theories in describing of the flexural edge wave dispersion and its excitation amplitude are investigated. The wave is excited by a pair of twisting couples applied to the edge of the plate. Numerical comparison with the solution of 3D problem shows that Uflyand-Mindlin theory is applicable at the frequencies up to 30% of the first cut-off. The higher order asymptotic theory of plate bending with modified inertia and classical boundary conditions allows to improve the describing of the velocity comparing to Kirchhoff theory, but leads to a considerable error in describing of the amplitude.

Analysis of the behavior of OpenFOAM solvers for 3D problem of supersonic flow around a cone at an angle of attack

This paper is devoted to comparative analysis of numerical methods accuracy. Comparative estimation of accuracy is performed for numerical methods presented as solvers integrated to open sotware package OpenFOAM. Three different OpenFOAM solvers are selected to numerically solve the problem of supersonic flow around a cone. The angle of attack, cone half-angle and Mach number were varied in the selected ranges with a certain step. This approach is implemented using a generalized computational experiment that allows, based on parallel technologies, the simultaneous solution of the same basic problem with different input parameters. A number of test calculations were carried out. The deviation fields of gas-dynamic quantities for all solvers are analyzed. The construction of a generalized computational experiment made it possible to compare the accuracy of the considered solvers not only for one, separately taken problem, but for a class of problems specified by the ranges of variation of the determining parameters. Such an assessment of accuracy can be very useful for users of the software package when choosing a solver. Also, the results obtained can be useful for solver developers.

Simulation of Mechanical Behaviour of Materials Using Constant Boundary Elements - A Discussion on the Accuracy of Results for Beams

The Boundary Element Method (BEM) is one among the most popular simulation techniques employed to simulate mechanical behaviour of materials, including smart engineering materials. Although BEM is a quite well-established numerical technique, literature tells that the method may not be well suited to simulate structures where one or two of the dimensions is much smaller than the remaining dimension/s (for a 3D problem). Hence in this work, deflection of a cantilever beam is simulated using constant boundary elements to get a feel of the accuracy of the BEM when used to simulate such type of structures. Although the concept is not new, the study assumes significance because studies which list the results in detail are not readily found in the literature. In this study, the results are obtained for different mesh resolutions also. The results indicate that - as expected - constant boundary elements are not a good choice for simulating the mechanical behaviour of smart materials when the structural member to be simulated is thin. Although it is a known fact that constant boundary elements converge very slowly, the present study helps to get a clearer picture on the accuracy and the convergence rate that one can expect from constant boundary elements. This paper heavily borrows content from this author’s PhD thesis [1]. The geometry considered in this paper is a beam. One may also note that the author is publishing another paper [2] (“Simulation of Mechanical Behaviour of Materials using Constant Boundary Elements - A Discussion on the Accuracy of Results for Bars”) that is very similar to this paper except that the geometry considered in that paper is a bar.

Simulation of Mechanical Behaviour of Materials using Constant Boundary Elements - A Discussion on the Accuracy of Results for Bars

The Boundary Element Method (BEM) is one among the most popular simulation techniques employed to simulate mechanical behaviour of materials, including smart engineering materials. Although BEM is a quite well-established numerical technique, literature tells that the method may not be well suited to simulate structures where one or two of the dimensions is much smaller than the remaining dimension/s (for a 3D problem). Hence in this work, deflection of a cantilever beam is simulated using constant boundary elements to get a feel of the accuracy of the BEM when used to simulate such type of structures. Although the concept is not new, the study assumes significance because studies which list the results in detail are not readily found in the literature. In this study, the results are obtained for different mesh resolutions also. The results indicate that - as expected - constant boundary elements are not a good choice for simulating the mechanical behaviour of smart materials when the structural member to be simulated is thin. Although it is a known fact that constant boundary elements converge very slowly, the present study helps to get a clearer picture on the accuracy and the convergence rate that one can expect from constant boundary elements. This paper heavily borrows content from this author’s PhD thesis [1]. The geometry considered in this paper is a bar. One may also note that the author is publishing another paper [2] (“Simulation of Mechanical Behaviour of Materials using Constant Boundary Elements - A Discussion on the Accuracy of Results for Beams”) that is very similar to this paper except that the geometry considered in that paper is a beam.