An adaptive mesh refinement algorithm for compressible two-phase flow in porous media

Pau, George Shu Heng; Bell, John B.; Almgren, Ann S.; Fagnan, Kjiersten; Lijewski, Michael J.

doi:10.1007/s10596-011-9270-2

Cited by 41 publications

(22 citation statements)

References 38 publications

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“…Applications of BoxLib include compressible hypersonic flows for cosmology [18], reactive flows for radiating systems such as supernovae [17], low Mach number flows for stellar convection [23] terrestrial combustion [26], and fluctuating hydrodynamics [24], porous media flows [25], and others. In most of these applications, the physical properties of the simulations are expressed in FORTRAN kernels, while BoxLib itself handles domain decomposition, AMR, memory management, parallelization (both MPI and OpenMP), boundary condition information, inter-node communication, and disk I/O.…”

Section: Case Study 2 -Nyx/boxlibmentioning

confidence: 99%

Evaluating and Optimizing the NERSC Workload on Knights Landing

Barnes

Cook

Deslippe

et al. 2016

2016 7th International Workshop on Performance Modeling, Benchmarking and Simulation of High Performance Computer Systems (PMBS

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Abstract-NERSC has partnered with 20 representative application teams to evaluate performance on the Xeon-Phi Knights Landing architecture and develop an application-optimization strategy for the greater NERSC workload on the recently installed Cori system. In this article, we present early case studies and summarized results from a subset of the 20 applications highlighting the impact of important architecture differences between the Xeon-Phi and traditional Xeon processors. We summarize the status of the applications and describe the greater optimization strategy that has formed.

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Section: Case Study 2 -Nyx/boxlibmentioning

confidence: 99%

Evaluating and Optimizing the NERSC Workload on Knights Landing

Barnes

Cook

Deslippe

et al. 2016

2016 7th International Workshop on Performance Modeling, Benchmarking and Simulation of High Performance Computer Systems (PMBS

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“…[44,43,11,50,56]) and adaptive mesh refinement (AMR) (see e.g. [8,7,41,2,67,48,12,53,60,34]) are two examples of adding adaptivity to structured grids. Unfortunately, octrees and similar hierarchical structures suffer from issues similar to unstructured meshes such as cache incoherency and costly domain decomposition.…”

Section: Introductionmentioning

confidence: 99%

An adaptive discretization of compressible flow using a multitude of moving Cartesian grids

Qiu

Fedkiw

2016

Journal of Computational Physics

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We present a novel method for simulating compressible flow on a multitude of Cartesian grids that can rotate and translate. Following previous work, we split the time integration into an explicit step for advection followed by an implicit solve for the pressure. A second order accurate flux based scheme is devised to handle advection on each moving Cartesian grid using an effective characteristic velocity that accounts for the grid motion. In order to avoid the stringent time step restriction imposed by very fine grids, we propose strategies that allow for a fluid velocity CFL number larger than 1. The stringent time step restriction related to the sound speed is alleviated by formulating an implicit linear system in order to find a pressure consistent with the equation of state. This implicit linear system crosses overlapping Cartesian grid boundaries by utilizing local Voronoi meshes to connect the various degrees of freedom obtaining a symmetric positive-definite system. Since a straightforward application of this technique contains an inherent central differencing which can result in spurious oscillations, we introduce a new high order diffusion term similar in spirit to ENO-LLF but solved for implicitly in order to avoid any associated time step restrictions. The method is conservative on each grid, as well as globally conservative on the background grid that contains all other grids. Moreover, a conservative interpolation operator is devised for conservatively remapping values in order to keep them consistent across different overlapping grids. Additionally, the method is extended to handle two-way solid fluid coupling in a monolithic fashion including cases (in the appendix) where solids in close proximity do not properly allow for grid based degrees of freedom in between them.

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“…DLGR techniques were introduced and evolved in reservoir simulation since the 1980s (Bell and Shubin, 1983;Berger and Oliger, 1984;Heinemann et al, 1983;Han et al, 1987;Schmidt and Jacobs, 1988;Nilsson et al, 2005;Edwards and Christie, 1993). Different DLGR methods have been developed for both finite-element (FE) and finite-volume (FV) methods and for both sequential (Pau et al, 2012) and fully implicit (FIM) (Boerrigter et al, 2011) simulation strategies. Recent advancements have also shown their applicability to more complex physics (Faigle et al, 2014;Jackson et al, 2015), including multiphase flows with compositional effects (Boerrigter et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Algebraic Dynamic Multilevel (ADM) Method for Immiscible Multiphase Flow in Heterogeneous Porous Media with Capillarity

Cusini¹,

Kruijsdijk²,

Hajibeygi³

2016

Proceedings

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SUMMARYAn algebraic dynamic multilevel method (ADM) is developed for fully-implicit (FIM) simulations of multiphase flow in heterogeneous porous media with strong non-linear physics. The fine-scale resolution is defined based on the heterogeneous geological one. Then, ADM constructs a space-time adaptive FIM system on a dynamically defined multilevel nested grid. The multilevel resolution is defined using an error estimate criterion, aiming to minimize the accuracy-cost trade-off. ADM is algebraically described by employing sequences of adaptive multilevel restriction and prolongation operators. Finite-volume conservative restriction operators are considered whereas different choices for prolongation operators are employed for different unknowns. The ADM method is applied to challenging heterogeneous test cases with strong nonlinear heterogeneous capillary effects. It is illustrated that ADM provides accurate solution by employing only a fraction of the total number of fine-scale grid cells. ADM is an important advancement for multiscale methods because it solves for all coupled unknowns (here, both pressure and saturation) simultaneously on arbitrary adaptive multilevel grids. At the same time, it is a significant step forward in the application of dynamic local grid refinement techniques to heterogeneous formations without relying on upscaled coarse-scale quantities.

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An adaptive mesh refinement algorithm for compressible two-phase flow in porous media

Cited by 41 publications

References 38 publications

Evaluating and Optimizing the NERSC Workload on Knights Landing

Evaluating and Optimizing the NERSC Workload on Knights Landing

An adaptive discretization of compressible flow using a multitude of moving Cartesian grids

Algebraic Dynamic Multilevel (ADM) Method for Immiscible Multiphase Flow in Heterogeneous Porous Media with Capillarity

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