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FALCON (Fracturing And Liquid CONvection) is a hybrid continuous/discontinuous Galerkin finite element geothermal reservoir simulation code based on the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework being developed and used for multiphysics applications. In the present work, a suite of verification and validation (V&V) test problems for FALCON was defined to meet the design requirements, and solved to the interests of enhanced geothermal system modeling and simulation. The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of FALCON solution methods. The test problems vary in complexity from a single mechanical or thermal process, to coupled thermo-hydro-mechanical processes in geological porous medium. Numerical results obtained by FALCON agreed well with either the available analytical solutions or experimental data, indicating the verified and validated implementation of these capabilities in FALCON. Whenever possible, some form of solution verification has been attempted to identify sensitivities in the solution methods, and suggest best practices when using the FALCON code. [ABSTRACT FROM AUTHOR]

A space and time third-order discontinuous Galerkin method based on a Hermite weighted essentially non-oscillatory reconstruction is presented for the unsteady compressible Euler and Navier-Stokes equations. At each time step, a lower-upper symmetric Gauss-Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge-Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third-order accuracy of convergence in both space and time, while requiring remarkably less storage than the standard third-order discontinous Galerkin methods, and less computing time than the lower-order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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 implementation 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. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: A reconstructed discontinuous Galerkin (RDG) method based on a hierarchical WENO reconstruction, termed HWENO (P1P2) in this paper, designed not only to enhance the accuracy of discontinuous Galerkin methods but also to ensure the nonlinear stability of the RDG method, is presented for solving the compressible Euler equations on tetrahedral grids. In this HWENO (P1P2) method, a quadratic polynomial solution (P2) is first reconstructed using a Hermite WENO reconstruction from the underlying linear polynomial (P1) discontinuous Galerkin solution to ensure the linear stability of the RDG method and to improve the efficiency of the underlying DG method. By taking advantage of handily available and yet invaluable information, namely the derivatives in the DG formulation, the stencils used in the reconstruction involve only von Neumann neighborhood (adjacent face-neighboring cells) and thus are compact. The first derivatives of the quadratic polynomial solution are then reconstructed using a WENO reconstruction in order to eliminate spurious oscillations in the vicinity of strong discontinuities, thus ensuring the nonlinear stability of the RDG method. The developed HWENO (P1P2) method is used to compute a variety of flow problems on tetrahedral meshes to demonstrate its accuracy, robustness, and non-oscillatory property. The numerical experiments indicate that the HWENO (P1P2) method is able to capture shock waves within one cell without any spurious oscillations, and achieve the designed third-order of accuracy: one order accuracy higher than the underlying DG method. [Copyright &y& Elsevier]

Abstract: A Hermite WENO reconstruction-based discontinuous Galerkin method RDG(P1P2), designed not only to enhance the accuracy of discontinuous Galerkin method but also to ensure linear stability of the RDG method, is presented for solving the compressible Euler equations on tetrahedral grids. In this RDG(P1P2) method, a quadratic polynomial solution (P2) is first reconstructed using a least-squares method from the underlying linear polynomial (P1) discontinuous Galerkin solution. By taking advantage of handily available and yet invaluable information, namely the derivatives in the DG formulation, the stencils used in the reconstruction involve only von Neumann neighborhood (adjacent face-neighboring cells) and thus are compact and consistent with the underlying DG method. The final quadratic polynomial solution is then obtained using a WENO reconstruction, which is necessary to ensure linear stability of the RDG method. The developed RDG method is used to compute a variety of flow problems on tetrahedral meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical experiments demonstrate that the developed RDG(P1P2) method is able to maintain the linear stability, achieve the designed third-order of accuracy: one order accuracy higher than the underlying DG method without significant increase in computing costs and storage requirements. [Copyright &y& Elsevier]

A new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya–Babuška–Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie–Chow interpolation or by using a Petrov–Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes, and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ C F L ≤ 100 . The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos. [ABSTRACT FROM AUTHOR]