Multiscale Flow Simulation Research Articles

Capsule polymer flooding for enhanced oil recovery

To solve the problems of shear degradation and injection difficulties in conventional polymer flooding, the capsule polymer flooding for enhanced oil recovery (EOR) was proposed. The flow and oil displacement mechanisms of this technique were analyzed using multi-scale flow experiments and simulation technology. It is found that the capsule polymer flooding has the advantages of easy injection, shear resistance, controllable release in reservoir, and low adsorption retention, and it is highly capable of long-distance migration to enable viscosity increase in deep reservoirs. The higher degree of viscosity increase by capsule polymer, the stronger the ability to suppress viscous fingering, resulting in a more uniform polymer front and a larger swept range. The release performance of capsule polymer is mainly sensitive to temperature. Higher temperatures result in faster viscosity increase by capsule polymer solution. The salinity has little impact on the rate of viscosity increase. The capsule polymer flooding is suitable for high-water-cut reservoirs for which conventional polymer flooding techniques are less effective, offshore reservoirs by polymer flooding in largely spaced wells, and medium to low permeability reservoirs where conventional polymers cannot be injected efficiently. Capsule polymer flooding should be customized specifically, with the capsule particle size and release time to be determined depending on target reservoir conditions to achieve the best displacement effect.

Adaptive unified gas-kinetic scheme for diatomic gases with rotational and vibrational nonequilibrium

Multiscale nonequilibrium physics at large variations of local Knudsen number are encountered in applications of aerospace engineering and micro-electro-mechanical systems, such as high-speed flying vehicles and low pressure of the encapsulation. An accurate description of flow physics in all flow regimes within a single computation requires a genuinely multiscale method. The adaptive unified gas-kinetic scheme (AUGKS) is developed for such multiscale flow simulation. The AUGKS applies discretized velocity space to accurately capture the non-equilibrium physics in the multiscale UGKS, and adaptively employs continuous distribution functions following Chapman–Enskog expansion to efficiently recover near-equilibrium flow region in GKS. The UGKS and GKS are dynamically connected at the cell interface through the fluxes from the discretized and continuous gas distribution functions, which avoids any buffer zone between them. In this study, the AUGKS with rotation and vibration non-equilibrium is developed based on a multiple temperature relaxation model. The real gas effect in different flow regimes has been properly captured. To capture aerodynamic heating accurately, the heat flux modifications from the rotation and vibration modes are also included in the current scheme. Unstructured discrete particle velocity space is adopted to further improve the computational performance of the AUGKS. Numerical tests, including Sod tube, normal shock structure, high-speed flow around the two-dimensional cylinder and three-dimensional sphere and space vehicles, and an unsteady nozzle plume flow from the continuum flow to the background vacuum, have been conducted to validate the current scheme. In comparison with the original UGKS, the current scheme speeds up the computation, reduces the memory requirement, and maintains the equivalent accuracy for multiscale flow simulation, which provides an effective tool for nonequilibrium flow simulations, especially for the flows at low and medium speed.

An approach for multiscale two-phase flow simulation in the direct simulation Monte Carlo framework

To simulate multiscale gas flow with solid particles, Burt's model, based on the Direct Simulation Monte Carlo (DSMC) framework, is widely used to predict gas–solid interactions under the assumption of a negligibly small solid particle diameter compared to the local gas mean free path. However, Burt's model could become inaccurate when the solid particle is large relative to the local gas mean free path. This study introduces the Gas–Solid Synchronous (GSS) model, which predicts gas–solid interactions in continuum gas regions without assuming the local gas flow regime around a solid particle. Similar to Burt's model, the GSS model includes gas-to-solid and solid-to-gas interaction models to consider bidirectional interaction between two phases. The GSS gas-to-solid model is established by selecting accurate semi-empirical force and heat transfer models in comparison with DSMC simulation results. The GSS solid-to-gas model is developed based on the principles of momentum and energy conservation and validated against Burt's solid-to-gas model. The results show that Burt's model could overestimate the interphase force and heat transfer rates when its assumption on solid particle diameter does not hold, but it can reproduce non-equilibrium characteristics of two-phase flows where gas velocity distribution functions do not follow the Maxwell–Boltzmann distribution. By contrast, the GSS model can accurately predict gas–solid interaction in continuum gas flows, while it cannot capture the non-equilibrium nature of two-phase flows. The characteristics and limitations of the two models indicate that using a valid model for each gas–solid interaction could be crucial for accurate simulation of multiscale two-phase flows.

Personalized coronary and myocardial blood flow models incorporating CT perfusion imaging and synthetic vascular trees

Computational simulations of coronary artery blood flow, using anatomical models based on clinical imaging, are an emerging non-invasive tool for personalized treatment planning. However, current simulations contend with two related challenges – incomplete anatomies in image-based models due to the exclusion of arteries smaller than the imaging resolution, and the lack of personalized flow distributions informed by patient-specific imaging. We introduce a data-enabled, personalized and multi-scale flow simulation framework spanning large coronary arteries to myocardial microvasculature. It includes image-based coronary anatomies combined with synthetic vasculature for arteries below the imaging resolution, myocardial blood flow simulated using Darcy models, and systemic circulation represented as lumped-parameter networks. We propose an optimization-based method to personalize multiscale coronary flow simulations by assimilating clinical CT myocardial perfusion imaging and cardiac function measurements to yield patient-specific flow distributions and model parameters. Using this proof-of-concept study on a cohort of six patients, we reveal substantial differences in flow distributions and clinical diagnosis metrics between the proposed personalized framework and empirical methods based purely on anatomy; these errors cannot be predicted a priori. This suggests virtual treatment planning tools would benefit from increased personalization informed by emerging imaging methods.

Nonequilibrium Flow Simulations Using Unified Gas-Kinetic Wave-Particle Method

Nonequilibrium flows are commonly encountered in aerospace engineering applications such as spacecraft reentry, rocket launch, and satellite attitude control. Numerical simulations help greatly in the understanding of nonequilibrium flow, multiscale effects, and the dynamics in these applications. Coupling particle transport and collision within the gas evolution process, the unified gas-kinetic wave-particle (UGKWP) method has been developed for multiscale flow simulation, offering a strategy that strikes a balance between accuracy and efficiency. In the present study, the UGKWP method simulates challenging flow problems with large Knudsen number variations, including supersonic flow around a sphere, hypersonic flow around a space vehicle, nozzle plume into vacuum, and side-jet impingement on the hypersonic flow. The UGKWP accurately captures complex flow structures and has been verified through experimental data or direct simulation Monte Carlo results. Regarding computational cost, the UGKWP method requires only 60 GiB of memory to simulate the three-dimensional space vehicle with 560,593 cells under various flow conditions, which is manageable even on personal workstations. Given its excellent efficiency and accuracy, the UGKWP method shows its substantial benefits in simulating multiscale flow for aerospace engineering applications.

Self-Diffusiophoresis and Symmetry-Breaking of a Janus Dimer: Analytic Solution

A self-diffusiophoretic problem is considered for a chemically active dimer consisting of two equal touching spherical colloids that are exposed to different fixed-flux and fixed-rate surface reactions. A new analytic solution for the autophoretic mobility of such a catalytic Janus dimer is presented in the limit of a small Péclet number and linearization of the resulting Robin-type boundary value problem for the harmonic solute concentration. Explicit solutions in terms of the physical parameters are first obtained for the uncoupled electrostatic and hydrodynamic problems. The dimer mobility is then found by employing the reciprocal theorem depending on the surface slip velocity and on the normal component of the shear stress acting on the inert dimer. Special attention is given to the limiting case of a Janus dimer composed of an inert sphere and a chemically active sphere where the fixed-rate reaction (Damköhler number) is infinitely large. Examples are given, comparing the numerical and approximate analytic solutions of the newly developed theory. Singular points arising in the model are discussed for a dimer with a fixed-rate reaction, and the flow field around the dimer is also analysed. The new developed theory introduces a fast way to compute the mobility of a freely suspended dimer and the induced flow field around it, and thus can also serve as a sub grid scale model for a multi-scale flow simulation.

Adaptive wave-particle decomposition in UGKWP method for high-speed flow simulations

With wave-particle decomposition, a unified gas-kinetic wave-particle (UGKWP) method has been developed for multiscale flow simulations. With the variation of the cell Knudsen number, the UGKWP method captures the transport process in all flow regimes without the kinetic solver’s constraint on the numerical mesh size and time step being determined by the kinetic particle mean free path and particle collision time. In the current UGKWP method, the cell Knudsen number, which is defined as the ratio of particle collision time to numerical time step, is used to distribute the components in the wave-particle decomposition. The adaptation of particles in the UGKWP method is mainly for the capturing of the non-equilibrium transport. In this aspect, the cell Knudsen number alone is not enough to identify the non-equilibrium state. For example, in the equilibrium flow regime with a Maxwellian distribution function, even at a large cell Knudsen number, the flow evolution can be still modelled by the Navier-Stokes solver. More specifically, in the near space environment both the hypersonic flow around a space vehicle and the plume flow from a satellite nozzle will encounter a far field rarefied equilibrium flow in a large computational domain. In the background dilute equilibrium region, the large particle collision time and a uniform small numerical time step can result in a large local cell Knudsen number and make the UGKWP method track a huge number of particles for the far field background flow in the original approach. But, in this region the analytical wave representation can be legitimately used in the UGKWP method to capture the nearly equilibrium flow evolution. Therefore, to further improve the efficiency of the UGKWP method for multiscale flow simulations, an adaptive UGKWP (AUGKWP) method is developed with the introduction of an additional local flow variable gradient-dependent Knudsen number. As a result, the wave-particle decomposition in the UGKWP method is determined by both the cell and gradient Knudsen numbers, and the use of particles in the UGKWP method is solely to capture the non-equilibrium flow transport. The current AUGKWP method becomes much more efficient than the previous one with the cell Knudsen number only in the determination of wave-particle composition. Many numerical tests, including Sod shock tube, normal shock structure, hypersonic flow around cylinder, flow around reentry capsule, and an unsteady nozzle plume flow, have been conducted to validate the accuracy and efficiency of the AUGKWP method. Compared with the original UGKWP method, the AUGKWP method achieves the same accuracy, but has advantages in memory reduction and computational efficiency in the simulation for flows with the co-existing of multiple regimes.

Special Connections for Representing Multiscale Heterogeneities in Reservoir Simulation

Summary The significant quantities of oil contained in fractured karst reservoirs in Brazilian presalt fields add new challenges to the development of upscaling procedures to reduce time on numerical simulations. This work aims to represent multiscale heterogeneities in reservoir simulators based on special connections between matrix, karst, and fracture mediums, both modeled in different grid domains within a single porosity flow model. The objective of this representation is to strike a good balance between accuracy and simulation time. Therefore, this work extends the approach of special connections developed by Correia et al. (2019) to integrate both karst and fracture mediums modeled in different grid domains and block scales. The transmissibility calculation between the three domains is a combination of the conventional formulation based on two-point flux approximation schemes and the matrix-fracture fluid transfer formulation. The flow inside each domain is governed by Darcy’s equation and implicitly solved by the simulator. For proper validation and numerical verification, we applied the methodology to a simple case (two-phase and three-phase flow) and a real case (two-phase flow). For the simple case, the reference model is a refined grid model with (1) an arrangement of large conduits (karsts), which are poorly connected; (2) a well-connected and orthogonal system of fractures; and (3) a background medium (matrix). The real case is a section of a Brazilian presalt field, characterized as a naturally fractured carbonate reservoir. The reference is the geological model. The simulation model consists of a structural model with different gridblock sizes according to the scale of the heterogeneities—small-scale karst geometries, medium-scale matrix properties, and larger-scale fracture features—interconnected by special connections. The results for both cases show a significant performance improvement regarding a dynamic matching response with the reference model, within a suitable simulation time and maintaining the dynamic resolution according to the representative elementary volume of heterogeneities, without using an unstructured grid. In comparison to the reference model, for the simple case and the real case, the simulation time was reduced by 42% and 87%, respectively. The proposed method contributes to a multiscale flow simulation solution to manage heterogeneous geological scenarios using structured grids while preserving the high resolution of small-scale heterogeneities and providing a good relationship between accuracy and simulation time.

Tissue-growth-based synthetic tree generation and perfusion simulation

Biological tissues receive oxygen and nutrients from blood vessels by developing an indispensable supply and demand relationship with the blood vessels. We implemented a synthetic tree generation algorithm by considering the interactions between the tissues and blood vessels. We first segment major arteries using medical image data and synthetic trees are generated originating from these segmented arteries. They grow into extensive networks of small vessels to fill the supplied tissues and satisfy the metabolic demand of them. Further, the algorithm is optimized to be executed in parallel without affecting the generated tree volumes. The generated vascular trees are used to simulate blood perfusion in the tissues by performing multiscale blood flow simulations. One-dimensional blood flow equations were used to solve for blood flow and pressure in the generated vascular trees and Darcy flow equations were solved for blood perfusion in the tissues using a porous model assumption. Both equations are coupled at terminal segments explicitly. The proposed methods were applied to idealized models with different tree resolutions and metabolic demands for validation. The methods demonstrated that realistic synthetic trees were generated with significantly less computational expense compared to that of a constrained constructive optimization method. The methods were then applied to cerebrovascular arteries supplying a human brain and coronary arteries supplying the left and right ventricles to demonstrate the capabilities of the proposed methods. The proposed methods can be utilized to quantify tissue perfusion and predict areas prone to ischemia in patient-specific geometries.

Investigation Into Hybridization of the Two-Fluid Model and Phase-Field Model for Multi-Scale Two-Phase Flow Simulations

Abstract To simulate heterogeneous bubbly flows, a hybrid method has been developed in several studies by combining the two-fluid model and the interface tracking method. Since this original hybrid method is based on the one-pressure modeling, which is a common approach for the two-fluid model, unphysical flow would occur in the flow where the surface tension is dominant. To resolve this inherent weakness of one-pressure modeling, we proposed a new formulation of the hybrid method in this study. The proposed hybrid method includes no pressure term in the dispersed phase because we regarded the dispersed phase as a group of discrete particles. The phase-field method is employed as the interface-tracking method. The proposed hybrid method was validated in several numerical simulations. Using the static bubble problem, we confirmed that in the proposed hybrid method simulation, there is no unphysical flow that is observed in the original hybrid method. In the bubble plume problem, we compared the bubble plume behavior and the time-averaged void fraction of the simulation results with those of previously reported experiments and found good agreement between them. From these validations, we confirmed that the proposed hybrid method was applicable to heterogeneous bubbly flow simulation, and it avoided the weakness which the original hybrid method has.

Introducing CRYOWRF v1.0: multiscale atmospheric flow simulations with advanced snow cover modelling

Abstract. Accurately simulating snow cover dynamics and the snow–atmosphere coupling is of major importance for topics as wide-ranging as water resources, natural hazards, and climate change impacts with consequences for sea level rise. We present a new modelling framework for atmospheric flow simulations for cryospheric regions called CRYOWRF. CRYOWRF couples the state-of-the-art and widely used atmospheric model WRF (the Weather Research and Forecasting model) with the detailed snow cover model SNOWPACK. CRYOWRF makes it feasible to simulate the dynamics of a large number of snow layers governed by grain-scale prognostic variables with online coupling to the atmosphere for multiscale simulations from the synoptic to the turbulent scales. Additionally, a new blowing snow scheme is introduced in CRYOWRF and is discussed in detail. CRYOWRF's technical design goals and model capabilities are described, and the performance costs are shown to compare favourably with existing land surface schemes. Three case studies showcasing envisaged use cases for CRYOWRF for polar ice sheets and alpine snowpacks are provided to equip potential users with templates for their research. Finally, the future roadmap for CRYOWRF's development and usage is discussed.

Recent Advances in Multiscale Digital Rock Reconstruction, Flow Simulation, and Experiments during Shale Gas Production

The complex and multiscale nature of shale gas transport imposes new challenges to the already well-developed techniques for conventional reservoirs, especially digital core analysis. Multiscale complicated pore systems and distinctive properties limit most reconstruction methods not applicable. High-precision imaging experiments play a key role in the characterization of pore structures and mineral components. While the exhilarating breakthroughs in physical experimental methods and hybrid superposition methods have made significant achievements in shale digital rock reconstruction, rapidly evolving deep learning methods also present a promising option. Benefiting from the digital rock techniques, the pore-scale flow of shale gas can be directly simulated based on digital rock or indirectly modeled using the pore network model. It is precise and realistic to investigate the shale gas flow at the pore scale considering the desorption, surface diffusion, and slippage in nanopores. In this paper, we reviewed the recent advances in off-mentioned methods and processes and presented a hand for the research in this field.

A multi-degree-of-freedom gas kinetic multi-prediction implicit scheme

A multi-scale implicit multi-degree-of-freedom (MDOF) kinetic model with molecular translational, rotational and vibrational effects is presented. The evolution and exchange of energy among translational, rotational and vibrational degrees of freedom are demonstrated by three coupled relaxation processes. An orthogonal polynomial system is used to involve heat-transfer and viscosity properties in construction of a sequence of objective distribution functions at various relaxation stages. Based on finite volume discrete velocity method framework, the asymptotic preserving discrete unified gas-kinetic scheme (DUGKS) flux is adopted to preserve particle motion information. A second-order prediction scheme based on the Navier-Stokes flux is constructed to predict macroscopic variables from macroscopic residuals for implicit DUGKS iteration, which contains a multiple prediction methodology. The current MDOF kinetic model provides a concrete insight into energy exchange between the rotational and vibrational degrees of freedom during molecular inelastic collisions. The accurate prediction procedure significantly accelerates convergence. Several numerical test cases, including rarefied gas flow in lid-driven cavity, variable specific heat ratio shock structure, hypersonic circular cylinder flows at different Knudsen and Mach numbers, and hypersonic flat plate flow, are performed to validate the accuracy and efficiency of present model. All numerical results of the present method agreed well with those of the reference data. A 2∼3 orders-of-magnitude improvements in computational efficiency of the multi-scale implicit method are achieved compared with the explicit method. It demonstrated that the present method is a promising scheme considering vibration-rotation-translation energy exchange of poly-atomic molecules for the fast simulation of multi-scale flows from low-speed incompressible flow to hypersonic flow, from continuum to rarefied regime.

SPARTACUS: An open-source unified stochastic particle solver for the simulation of multiscale nonequilibrium gas flows

Recently, a unified stochastic particle (USP) method [14] has been developed for the simulation of multiscale nonequilibrium gas flows. Compared with the conventional stochastic particle methods, such as the direct simulation Monte Carlo (DSMC) method, USP can be applied with much larger time steps and cell sizes as it couples the effects of particle movements and collisions. To extend the applicability of USP to complex nonequilibrium gas flows, we develop a USP solver referred to as SPARTACUS within the framework of SPARTA, which is a widely used software based on the DSMC method for the simulation of rarefied gas flows. Inheriting from SPARTA, SPARTACUS is parallelized with the message passing interface (MPI), and it is open-source under the GNU General Public License (GPL) and released in an online repository with essential documentation, tutorial examples, and benchmark cases. To evaluate the performance of SPARTACUS, the test cases cover from one to three dimensional flows with a wide range of the Knudsen number and Mach number, including Couette flow, lid-driven cavity flow, hypersonic flow past a cylinder, and supersonic flow around a blunt body. The results obtained by SPARTACUS in the rarefied and continuum regimes are in good agreement with DSMC and computational fluid dynamics (CFD) results, respectively. Moreover, SPARTACUS has significant computational efficiency advantage over traditional DSMC solvers, especially for three-dimensional nonequilibrium gas flows. In addition, SPARTACUS shows comparable parallel efficiency with SPARTA, so it is promising to be applied with high performance computing for the simulation of complex multiscale gas flows encountered in engineering problems. Program summaryProgram Title: SPARTACUSCPC Library link to program files:https://doi.org/10.17632/pyb343w7zv.1Developer's repository link:https://github.com/KKFeng/spartacusLicensing provisions: GNU General Public License version 2Programming language: C++External routines/libraries: SPARTA (http://sparta.sandia.gov/)Nature of problem: Multiscale simulation of nonequilibrium gas flows using unified stochastic particle method.Solution method: Unified Stochastic Particle (USP) method.

Paired and Unpaired Deep Learning Methods for Physically Accurate Super-Resolution Carbonate Rock Images

X-ray micro-computed tomography (micro-CT) has been widely leveraged to characterise the pore-scale geometry of subsurface porous rocks. Recent developments in super-resolution (SR) methods using deep learning allow for the digital enhancement of low-resolution (LR) images over large spatial scales, creating SR images comparable to high-resolution (HR) ground truth images. This circumvents the common trade-off between resolution and field-of-view. An outstanding issue is the use of paired LR and HR data, which is often required in the training step of such methods but is difficult to obtain. In this work, we rigorously compare two state-of-the-art SR deep learning techniques, using both paired and unpaired data, with like-for-like ground truth data. The first approach requires paired images to train a convolutional neural network (CNN), while the second approach uses unpaired images to train a generative adversarial network (GAN). The two approaches are compared using a micro-CT carbonate rock sample with complicated micro-porous textures. We implemented various image-based and numerical verifications and experimental validation to quantitatively evaluate the physical accuracy and sensitivities of the two methods. Our quantitative results show that the unpaired GAN approach can reconstruct super-resolution images as precise as the paired CNN method, with comparable training times and dataset requirements. This unlocks new applications for micro-CT image enhancement using unpaired deep learning methods; image registration is no longer needed during the data processing stage. Decoupled images from data storage platforms can be exploited to train networks for SR digital rock applications. This opens up a new pathway for various applications related to multi-scale flow simulations in heterogeneous porous media.

A suite of Richardson preconditioners for semi-implicit all-scale atmospheric models

The paper documents a suite of preconditioners for Krylov-subspace solvers of elliptic boundary-value problems (BVPs) that underlie semi-implicit integrations of the nonhydrostatic equations governing the dynamics of all-scale atmospheric flows. Effective preconditioning of the linear operators inherent in the semi-implicit models lies at the heart of the state-of-the-art multiscale-flow simulation. This is especially evident in simulations of global weather and climate—posed on a thin spherical shell—where some form of direct tridiagonal inversion of the operator in the vertical is crucial to relax the often enormous stiffness of the problem. The documented preconditioners stem from the Richardson's (1910) idea of augmenting an elliptic BVP with a transient diffusion equation. Exploiting this idea for mixed explicit-implicit pseudo-time-stepping schemes leads to a broad suite of stationary-iteration solvers, including the many classical algorithms. Here, the high-performance all-scale EULAG model (Smolarkiewicz et al. (2014) [58]), with a flexible three-dimensional decomposition of MPI tasks, is furnished with the preconditioners akin to the classical alternating-direction-implicit (ADI) algorithms, generalized to optional permutations of parallel tridiagonal inversions. The utility of various options is found to be problem dependent, in terms of computational accuracy as well as efficiency. The main thrust of the work is on the long-range forecasts using large anisotropic grids. The relative efficiency and/or accuracy gains attainable with the developed preconditioners are illustrated for idealized scenarios representative of atmospheric flows from planetary to a single-cloud and laboratory scales. The key insight that best encapsulates the significance and novelty of the present work is that there is no single “super-preconditioner” that will perform best in all cases, yet the suite as a whole offers substantial gains in the model performance.

An Investigation of Uncertainty Propagation in Non-equilibrium Flows

ABSTRACT Considerable uncertainties can exist between the field solutions of coarse-grained fluid models and the real-world flow physics. To study the emergence, propagation, and evolution of uncertainties poses great opportunities and challenges to develop both sound theories and reliable numerical methods. In this paper, we study the stochastic behaviour of multi-scale gaseous flows from molecular to hydrodynamic level, especially focussing on the non-equilibrium effects. The theoretical analysis is presented based on the gas kinetic model and its upscaling macroscopic system with random inputs. A newly developed stochastic kinetic scheme is employed to conduct numerical simulation of multi-scale and non-equilibrium flows. Different kinds of uncertainties are involved in the gas evolutionary processes. New physical observations, such as the synchronous travel pattern between mean fields and uncertainties, sensitivity of different orders of uncertainties and the influence of boundary effects from continuum to rarefied regimes, are identified and analysed.

Aspects of Multiscale Flow Simulation with Potential to Enhance Reservoir Engineering Practice

Summary A multiscale sequential fully implicit (MS SFI) reservoir simulation method implemented in a commercial simulator is applied to a set of reservoir engineering problems to understand its potential. Our assessment highlights workflows where the approach brings substantial performance advantages and insight generation. The understanding gained during commercialization on approximately 40 real-world models is illustrated through simpler but representative data sets, available in the public domain. The main characteristics of the method and key features of the implementation are briefly discussed. The robust fully implicit (FI) simulation method is used as a benchmark. The implementation of the MS SFI method is found to faithfully reproduce FI results for black-oil problems. We provide evidence and analysis of why the MS SFI approach can achieve high levels of performance and fidelity. The method supports the solution of unique problems that would benefit from incorporating multiscale geology and multiscale flow physics. The MS SFI implementation was used to successfully simulate a typical sector model used for field pilots at extremely high “whole core” scale resolution within a practical time frame leveraging high-performance computing (HPC). This could not be achieved with the FI approach. A combination of MS SFI and HPC offers immense potential to simulate geological models using grids to capture mesoscopic or laminar scale geology. The method, by design, demands fewer computing resources than FI, making it far more cost-effective to use for such high-resolution models. We conclude that the MS SFI method has a distinct capability to enhance reservoir engineering practice in the areas of high-resolution simulation-driven workflows in context of subsurface uncertainty quantification, field development planning, and reservoir performance optimization. NOTE: This paper is also published as part of the 2021 SPE Reservoir Simulation Conference Special Issue.

Numerical simulation and analysis of multi-scale cavitating flows

Abstract

An efficient algorithm of the unified stochastic particle Bhatnagar-Gross-Krook method for the simulation of multi-scale gas flows

The unified stochastic particle method based on the Bhatnagar-Gross-Krook model (USP-BGK) has been proposed recently to overcome the low accuracy and efficiency of the traditional stochastic particle methods, such as the direct simulation Monte Carlo (DSMC) method, for the simulation of multi-scale gas flows. However, running with extra virtual particles and space interpolation, the previous USP-BGK method cannot be directly transplanted into the existing DSMC codes. In this work, the implementation of USP-BGK is simplified using new temporal evolution and spatial reconstruction schemes. As a result, the present algorithm of the USP-BGK method is similar to the DSMC method and can be implemented efficiently based on any existing DSMC codes just by modifying the collision module.