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Title: OpenACC directive-based GPU acceleration of an implicit reconstructed discontinuous Galerkin method for compressible flows on 3D unstructured grids

Abstract

In this study, we use a combination of modeling techniques to describe the relationship between fracture radius that might be accomplished in a hypothetical enhanced geothermal system (EGS) and drilling distance required to create and access those fractures. We use a combination of commonly applied analytical solutions for heat transport in parallel fractures and 3D finite-element method models of more realistic heat extraction geometries. For a conceptual model involving multiple parallel fractures developed perpendicular to an inclined or horizontal borehole, calculations demonstrate that EGS will likely require very large fractures, of greater than 300 m radius, to keep interfracture drilling distances to ~10 km or less. As drilling distances are generally inversely proportional to the square of fracture radius, drilling costs quickly escalate as the fracture radius decreases. It is important to know, however, whether fracture spacing will be dictated by thermal or mechanical considerations, as the relationship between drilling distance and number of fractures is quite different in each case. Information about the likelihood of hydraulically creating very large fractures comes primarily from petroleum recovery industry data describing hydraulic fractures in shale. Those data suggest that fractures with radii on the order of several hundred meters may, indeed, bemore » possible. The results of this study demonstrate that relatively simple calculations can be used to estimate primary design constraints on a system, particularly regarding the relationship between generated fracture radius and the total length of drilling needed in the fracture creation zone. Comparison of the numerical simulations of more realistic geometries than addressed in the analytical solutions suggest that simple proportionalities can readily be derived to relate a particular flow field.« less

Authors:
 [1];  [2];  [1];  [1];  [1];  [1]
  1. North Carolina State Univ., Raleigh, NC (United States)
  2. Idaho National Lab. (INL), Idaho Falls, ID (United States)
Publication Date:
Research Org.:
Idaho National Lab. (INL), Idaho Falls, ID (United States)
Sponsoring Org.:
USDOE Office of Energy Efficiency and Renewable Energy (EERE)
OSTI Identifier:
1364112
Report Number(s):
INL/CON-16-39864
DOE Contract Number:
AC07-05ID14517
Resource Type:
Conference
Resource Relation:
Conference: 50th US Rock Mechanics/Geomechanics Symposium, Houston, TX (United States), 26-29 Jun 2016
Country of Publication:
United States
Language:
English
Subject:
15 GEOTHERMAL ENERGY; enhanced geothermal system

Citation Formats

Lou, Jialin, Xia, Yidong, Luo, Lixiang, Luo, Hong, Edwards, Jack, and Mueller, Frank. OpenACC directive-based GPU acceleration of an implicit reconstructed discontinuous Galerkin method for compressible flows on 3D unstructured grids. United States: N. p., 2016. Web. doi:10.2514/6.2016-1815.
Lou, Jialin, Xia, Yidong, Luo, Lixiang, Luo, Hong, Edwards, Jack, & Mueller, Frank. OpenACC directive-based GPU acceleration of an implicit reconstructed discontinuous Galerkin method for compressible flows on 3D unstructured grids. United States. doi:10.2514/6.2016-1815.
Lou, Jialin, Xia, Yidong, Luo, Lixiang, Luo, Hong, Edwards, Jack, and Mueller, Frank. 2016. "OpenACC directive-based GPU acceleration of an implicit reconstructed discontinuous Galerkin method for compressible flows on 3D unstructured grids". United States. doi:10.2514/6.2016-1815. https://www.osti.gov/servlets/purl/1364112.
@article{osti_1364112,
title = {OpenACC directive-based GPU acceleration of an implicit reconstructed discontinuous Galerkin method for compressible flows on 3D unstructured grids},
author = {Lou, Jialin and Xia, Yidong and Luo, Lixiang and Luo, Hong and Edwards, Jack and Mueller, Frank},
abstractNote = {In this study, we use a combination of modeling techniques to describe the relationship between fracture radius that might be accomplished in a hypothetical enhanced geothermal system (EGS) and drilling distance required to create and access those fractures. We use a combination of commonly applied analytical solutions for heat transport in parallel fractures and 3D finite-element method models of more realistic heat extraction geometries. For a conceptual model involving multiple parallel fractures developed perpendicular to an inclined or horizontal borehole, calculations demonstrate that EGS will likely require very large fractures, of greater than 300 m radius, to keep interfracture drilling distances to ~10 km or less. As drilling distances are generally inversely proportional to the square of fracture radius, drilling costs quickly escalate as the fracture radius decreases. It is important to know, however, whether fracture spacing will be dictated by thermal or mechanical considerations, as the relationship between drilling distance and number of fractures is quite different in each case. Information about the likelihood of hydraulically creating very large fractures comes primarily from petroleum recovery industry data describing hydraulic fractures in shale. Those data suggest that fractures with radii on the order of several hundred meters may, indeed, be possible. The results of this study demonstrate that relatively simple calculations can be used to estimate primary design constraints on a system, particularly regarding the relationship between generated fracture radius and the total length of drilling needed in the fracture creation zone. Comparison of the numerical simulations of more realistic geometries than addressed in the analytical solutions suggest that simple proportionalities can readily be derived to relate a particular flow field.},
doi = {10.2514/6.2016-1815},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2016,
month = 9
}

Conference:
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  • Here, an OpenACC directive-based graphics processing unit (GPU) parallel scheme is presented for solving the compressible Navier–Stokes equations on 3D hybrid unstructured grids with a third-order reconstructed discontinuous Galerkin method. The developed scheme requires the minimum code intrusion and algorithm alteration for upgrading a legacy solver with the GPU computing capability at very little extra effort in programming, which leads to a unified and portable code development strategy. A face coloring algorithm is adopted to eliminate the memory contention because of the threading of internal and boundary face integrals. A number of flow problems are presented to verify the implementationmore » of the developed scheme. Timing measurements were obtained by running the resulting GPU code on one Nvidia Tesla K20c GPU card (Nvidia Corporation, Santa Clara, CA, USA) and compared with those obtained by running the equivalent Message Passing Interface (MPI) parallel CPU code on a compute node (consisting of two AMD Opteron 6128 eight-core CPUs (Advanced Micro Devices, Inc., Sunnyvale, CA, USA)). Speedup factors of up to 24× and 1.6× for the GPU code were achieved with respect to one and 16 CPU cores, respectively. The numerical results indicate that this OpenACC-based parallel scheme is an effective and extensible approach to port unstructured high-order CFD solvers to GPU computing.« less
  • A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on unstructured tetrahedral grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not needmore » to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on unstructured grids. The preliminary results indicate that this RDG method is stable on unstructured tetrahedral grids, and provides a viable and attractive alternative for the discretization of the viscous and heat fluxes in the Navier-Stokes equations.« less
  • A set of implicit methods are proposed for a third-order hierarchical WENO reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. An attractive feature in these methods are the application of the Jacobian matrix based on the P1 element approximation, resulting in a huge reduction of memory requirement compared with DG (P2). Also, three approaches -- analytical derivation, divided differencing, and automatic differentiation (AD) are presented to construct the Jacobian matrix respectively, where the AD approach shows the best robustness. A variety of compressible flow problems are computed to demonstrate the fast convergence property of the implemented flowmore » solver. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results on complex geometries indicate that this low-storage implicit method can provide a viable and attractive DG solution for complicated flows of practical importance.« less
  • A reconstruction-based discontinuous Galerkin method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. In this method, an in-cell reconstruction is used to obtain a higher-order polynomial representation of the underlying discontinuous Galerkin polynomial solution and an inter-cell reconstruction is used to obtain a continuous polynomial solution on the union of two neighboring, interface-sharing cells. The in-cell reconstruction is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. The inter-cell reconstruction is devised to remove an interface discontinuity of the solution and its derivatives and thusmore » to provide a simple, accurate, consistent, and robust approximation to the viscous and heat fluxes in the Navier-Stokes equations. A parallel strategy is also devised for the resulting reconstruction discontinuous Galerkin method, which is based on domain partitioning and Single Program Multiple Data (SPMD) parallel programming model. The RDG method is used to compute a variety of compressible flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results demonstrate that this RDG method is third-order accurate at a cost slightly higher than its underlying second-order DG method, at the same time providing a better performance than the third order DG method, in terms of both computing costs and storage requirements.« less