James E. McClure

On the dynamics and kinematics of two-fluid-phase flow in porous media

A model formulated in terms of both conservation and kinematic equations for phases and interfaces in two-fluid-phase flow in a porous medium system is summarized. Macroscale kinematic equations are derived as extensions of averaging theorems and do not rely on conservation principles. Models based on both conservation and kinematic equations can describe multiphase flow with varying fidelity. When only phase-based equations are considered, a model similar in form to the traditional model for two-fluid-phase flow results. When interface conservation and kinematic equations are also included, a novel formulation results that naturally includes evolution equations that express dynamic changes in fluid saturations, pressures, the capillary pressure, and the fluid-fluid interfacial area density in a two-fluid-system. This dynamic equation set is unique to this work, and the importance of the modeled physics is shown through both microfluidic experiments and high-resolution lattice Boltzmann simulations. The validation work shows that the relaxation of interface distribution and shape toward an equilibrium state is a slow process relative to the time scale typically allowed for a system to approach an apparent equilibrium state based upon observations of fluid saturations and external pressure measurements. Consequently, most pressure-saturation data intended to denote an equilibrium state are likely a sampling from a dynamic system undergoing changes of interfacial curvatures that are not typically monitored. The results confirm the importance of kinematic analysis in combination with conservation equations for faithful modeling of system physics.

A novel heterogeneous algorithm to simulate multiphase flow in porous media on multicore CPU–GPU systems

Abstract Multiphase flow implementations of the lattice Boltzmann method (LBM) are widely applied to the study of porous medium systems. In this work, we construct a new variant of the popular “color” LBM for two-phase flow in which a three-dimensional, 19-velocity (D3Q19) lattice is used to compute the momentum transport solution while a three-dimensional, seven velocity (D3Q7) lattice is used to compute the mass transport solution. Based on this formulation, we implement a novel heterogeneous GPU-accelerated algorithm in which the mass transport solution is computed by multiple shared memory CPU cores programmed using OpenMP while a concurrent solution of the momentum transport is performed using a GPU. The heterogeneous solution is demonstrated to provide speedup of 2.6 × as compared to multi-core CPU solution and 1.8 × compared to GPU solution due to concurrent utilization of both CPU and GPU bandwidths. Furthermore, we verify that the proposed formulation provides an accurate physical representation of multiphase flow processes and demonstrate that the approach can be applied to perform heterogeneous simulations of two-phase flow in porous media using a typical GPU-accelerated workstation.

Mapped Chebyshev Pseudospectral Method for Unsteady Flow Analysis

A mapped Chebyshev pseudospectral method is developed as an accurate and yet efficient approach to solve unsteady flows. Preserving the conservation laws, the method discretizes a spatial-derivative term implicitly, whereas a time-derivative term is treated explicitly using the mapped Chebyshev collocation operator. Because standard Chebyshev points make the corresponding spectral derivative matrix ill-conditioned due to uneven distribution of the Chebyshev points clustered heavily toward the ends of the interval, an inverse sine mapping function is applied to the Chebyshev collocation operator so that the point distribution becomes more uniform in a time domain and mitigates numerical instabilities correspondingly. Computations of unsteady flows, including the one-dimensional Burgers’ equation and two-dimensional airfoil flows under oscillation and plunging motions, are carried out. Numerical results of the present study are compared with those of the conventional time-marching solution method and the ha...

Petascale Application of a Coupled CPU-GPU Algorithm for Simulation and Analysis of Multiphase Flow Solutions in Porous Medium Systems

Large-scale simulation can provide a wide range of information needed to develop and validate theoretical models for multiphase flow in porous medium systems. In this paper, we consider a coupled solution in which a multiphase flow simulator is coupled to an analysis approach used to extract the interfacial geometries as the flow evolves. This has been implemented using MPI to target heterogeneous nodes equipped with GPUs. The GPUs evolve the multiphase flow solution using the lattice Boltzmann method while the CPUs compute up scaled measures of the morphology and topology of the phase distributions and their rate of evolution. Our approach is demonstrated to scale to 4,096 GPUs and 65,536 CPU cores to achieve a maximum performance of 244,754 million-lattice-node updates per second (MLUPS) in double precision execution on Titan. In turn, this approach increases the size of systems that can be considered by an order of magnitude compared with previous work and enables detailed in situ tracking of averaged flow quantities at temporal resolutions that were previously impossible. Furthermore, it virtually eliminates the need for post-processing and intensive I/O and mitigates the potential loss of data associated with node failures.

Asynchronous in situ connected-components analysis for complex fluid flows

The simulation of multiscale physics is an important challenge for scientific computing. For this class of problem, large three-dimensional simulations are performed to advance scientific inquiry. On massively parallel computing systems, the volume of data generated by such approaches can become a productivity bottleneck if the raw data generated from the simulation is analyzed in a post-processing step. To address this, we present a physics-based framework for in situ data reduction that is theoretically grounded in multiscale averaging theory. We show how task parallelism can be exploited to concurrently perform a variety of analysis tasks with data-dependent costs, including the generation of iso-surfaces, morphological analyses, and connected components analysis. All analyses are performed in parallel using distributed memory and use the same domain decomposition as the simulation. A task management framework is constructed to leverage available parallelism within a node for analysis. The capabilities of the framework are to launch asynchronous analysis threads, manage dependencies between different tasks, promote data locality and minimize the impact of data transfers. The framework is applied to analyze GPU-based simulations of two-fluid-phase flow in porous media, generating a set of averaged measures that represents the overall system behavior. We demonstrate how the approach can be applied to perform physically-consistent analysis over fluid sub-regions determined from connected components analysis. Simulations performed on Oak Ridge National Labs Titan supercomputer are profiled to demonstrate the performance of the associated multi-threaded in situ analysis approach for typical production simulation of two-fluid-phase flow.