Dynamic Mesh Adaptation Research Articles

Experimental and numerical investigations on propagating modes of detonations: Detonation wave/boundary layer interaction

In the present work the propagating modes of detonation wave in supersonic hydrogen–air mixtures are investigated in narrow rectangular channels. To clarify the effect of the detonation wave interaction with the boundary layer on the evolution and propagation of detonation phenomenon, high-speed laser schlieren experiments and adaptive Navier–Stokes (NS) simulations (pseudo-DNS) combined with a detailed reaction model are performed. The experimental results show that after successful ignition, two propagating modes are observed and can be classified as Oblique shock-induced combustion/Mach stem-induced detonation (OSIC/MSID) and pure Oblique shock-induced combustion (OSIC). For the OSIC/MSID mode, a Mach stem induced overdriven detonation is generated in the middle of the main flow. For the pure OSIC mode, no detonation wave but two oblique shock-induced combustion regions are generated throughout the whole channel with the overall structure taking a thwartwise V shape. The OSIC/MSID and pure OSIC propagation modes are further confirmed by pseudo-DNS employing a detailed reaction model and dynamic adaptive mesh refinement for the same conditions as utilized in the experiments. The numerical results show that because of subsonic combustion near the walls induced by the boundary layers, the OSIC/MSID is not entirely symmetrical, while for the pure OSIC mode, larger fluctuations are observed along the oblique shock waves resulting from enhanced instabilities due to additional chemical heat release.

Quantitative 3D phase field modelling of solidification using next-generation adaptive mesh refinement

Phase field (PF) models are one of the most popular methods for simulating solidification microstructures due to their fundamental connections to the physics of phase transformations. However, these methods are numerically very stiff due to the multiple length scales in a solidifying material, from the nanoscopic solid-liquid interface, to dendritic structures on the order of hundreds of microns. While this problem can be greatly alleviated by thin-interface analytical treatments of the PF equations, additional numerical methods are required to explore experimentally relevant sample sizes and times scales. It was shown about 18years ago that the use of dynamic adaptive mesh refinement (AMR) can alleviate this problem by exploiting the simple fact that the majority of the solidification kinetics occur at the solid-liquid interface, which scales with a lower dimensionality than the embedding system itself. AMR methods, together with asymptotic analysis, nowadays provide one of the most efficient numerical strategies for self-consistent quantitative PF modelling of solidification microstructure processes. This paper highlights the latest developments in the AMR technique for 3D modelling of solidification using classical phase field equations. This includes a move away from finite element techniques to faster finite differencing through the use of dynamic mini-meshes which are each associated with each node of a 3D Octree data structure, and distributed MPI parallelism that uses a new communication algorithm to decompose a 3D domain into multiple adaptive meshes that are spawned on separate cores. The numerical technique is discussed, followed by demonstrations of the new AMR algorithm on select benchmark solidification problems, as well as some illustrations of multi-phase modelling using a recently developed multi-order parameter phase field model.

Technology Focus: Reservoir Simulation (July 2017)

Technology Focus Benchmark cases are a good thing. They provide a systematic means to compare processes, technologies, and performance that benefits companies, industry, and research organizations. One notable benchmark was deliberated at a 2008 SPE Applied Technology Workshop in the picturesque Belgium town of Bruges. This particular challenge involved history matching followed by forecast optimization. The goal was to maximize a 20-year net present value (NPV). The results were published as SPE-119094-PA in 2010. The Bruges study has since become the basis of numerous articles and simulation-based studies and continues to be influential to this day. Now, almost 10 years later, a new benchmark challenge has been set: Olympus. This has different, but no less challenging, objectives, and the goal is, once again, to maximize a 20-year NPV subject to some stated constraints. Olympus has been set by Integrated System Approaches for Petroleum Production 2 (ISAPP-2), a research partnership between Delft University of Technology and the Netherlands Organization for Applied Scientific Research (TNO), who originated the original Bruges challenge, along with Eni, Statoil, and Petrobras as industrial partners. For this, we owe a debt of thanks. Issues identified in the original Bruges exercise have been addressed, and a more streamlined benchmarking procedure has been defined. The ambition is no less broad and can be concisely stated as “field-development optimization under uncertainty.” While Olympus has no history-matching component (which formed part of the Bruges challenge), we are now faced with geological uncertainties related to faulting, fault throws, barriers, and channeling. The ensemble of 50 Olympus reservoir models provides such geological uncertainties that we must face when dealing with real field-development planning studies. The participant must decide how many producers and injectors to drill and where to drill them, along with their operational management during a 20-year production forecast. All this, of course, is addressed in the presence of geological uncertainty. One can imagine the results will vary considerably in formulation, ambition, and approach. I hope that this will not be considered a winner-take-all competition because that goes against the spirit of such a benchmark. The reward will ultimately turn out to be increased insight and appreciation of new approaches and techniques that will be shared throughout the industry. So, I humbly request that you consider participating in this challenge. Clear and concise online material is available from the ISAPP-2 website (www.isapp2. com/optimization-challenge), which also instructs you on how to download model files. The gauntlet has been thrown down, and I know that we, as an industry, have the wherewithal to pick it up. Recommended additional reading at OnePetro: www.onepetro.org. SPE 182637 Probabilistic Uncertainty Quantification of a Complex Field Using Advanced Proxy-Based Methods and GPU-Based Reservoir Simulation by N. Goodwin, Essence Products and Services, et al. SPE 181686 Effects of Confined Space on Production From Tight Reservoirs by Brian C. Stimpson, Texas A&M University, et al. SPE 182636 Dynamic Mesh Adaptivity for Immiscible Viscous Fingering by A. Adam, Imperial College London, et al. SPE 182718 A Massively Parallel Semicoarsening Multigrid Linear Solver on Multicore and Multi-GPU Architectures by A.M. Manea, Stanford University, et al. IPTC 18955 Building More-Realistic 3D Facies-Indicator Models by Thomas Le Blévec, Imperial College, et al.

Analysis of thermodiffusive cellular instabilities in continuum combustion fronts.

We explore numerically the morphological patterns of thermodiffusive instabilities in combustion fronts with a continuum fuel source, within a range of Lewis numbers and ignition temperatures, focusing on the cellular regime. For this purpose, we generalize the recent model of Brailovsky etal. to include distinct process kinetics and reactant heterogeneity. The generalized model is derived analytically and validated with other established models in the limit of infinite Lewis number for zero-order and first-order kinetics. Cellular and dendritic instabilities are found at low Lewis numbers. These are studied using a dynamic adaptive mesh refinement technique that allows very large computational domains, thus allowing us to reduce finite-size effects that can affect or even preclude the emergence of these patterns. Our numerical linear stability analysis is consistent with the analytical results of Brailovsky etal. The distinct types of dynamics found in the vicinity of the critical Lewis number, ranging from steady-state cells to continued tip splitting and cell merging, are well described within the framework of thermodiffusive instabilities and are consistent with previous numerical studies. These types of dynamics are classified as "quasilinear" and characterized by low-amplitude cells that may be strongly affected by the mode selection mechanism and growth prescribed by the linear theory. Below this range of Lewis number, highly nonlinear effects become prominent and large-amplitude, complex cellular and seaweed dendritic morphologies emerge.

Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation

A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.

A dynamically adaptive lattice Boltzmann method for thermal convection problems

AbstractUtilizing the Boussinesq approximation, a double-population incompressible thermal lattice Boltzmann method (LBM) for forced and natural convection in two and three space dimensions is developed and validated. A block-structured dynamic adaptive mesh refinement (AMR) procedure tailored for the LBM is applied to enable computationally efficient simulations of moderate to high Rayleigh number flows which are characterized by a large scale disparity in boundary layers and free stream flow. As test cases, the analytically accessible problem of a two-dimensional (2D) forced convection flow through two porous plates and the non-Cartesian configuration of a heated rotating cylinder are considered. The objective of the latter is to advance the boundary conditions for an accurate treatment of curved boundaries and to demonstrate the effect on the solution. The effectiveness of the overall approach is demonstrated for the natural convection benchmark of a 2D cavity with differentially heated walls at Rayleigh numbers from 103up to 108. To demonstrate the benefit of the employed AMR procedure for three-dimensional (3D) problems, results from the natural convection in a cubic cavity at Rayleigh numbers from 103up to 105are compared with benchmark results.

A dynamic adaptation method based on unstructured mesh for solving sloshing problems

A dynamic mesh-adaptation algorithm based on an unstructured mesh was used to solve sloshing problems by a finite element method. The free surface evolution of sloshing with a low filling ratio is so violent that a local mesh coarsening/refinement (LCR) technique can be effectively used to resolve the flow field near the interface of two immiscible fluids. Since an implicit discretization method was employed to solve the incompressible Navier-Stokes equations, an assembled global matrix was generated using a dynamic compressed sparse row (CSR) method. The proposed algorithm was validated by comparing the simulation results with those of a non-adaptive method with respect to wall impact pressures and mass conservation. Numerical results showed that relative mass error strongly depends on mesh resolution near the interface. Results of adaptive simulations were found to be comparable with those of non-adaptive simulations only if a similar mesh resolution was used near the interface. Moreover, adaptive simulations were about two times faster than the non-adaptive ones. The effect of the adaptive zone and smoothing zone on the impact pressure was also examined for the proposed algorithm.

Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization

We present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of viscous fingering instabilities in heterogeneous porous media and Hele–Shaw cells are illustrated. EG is formulated by enriching the conforming continuous Galerkin finite element method (CG) with piecewise constant functions. The method provides locally and globally conservative fluxes, which are crucial for coupled flow and transport problems. Moreover, EG has fewer degrees of freedom in comparison with discontinuous Galerkin (DG) and an efficient flow solver has been derived which allows for higher order schemes. Dynamic adaptive mesh refinement is applied in order to reduce computational costs for large-scale three dimensional applications. In addition, entropy residual based stabilization for high order EG transport systems prevents spurious oscillations. Numerical tests are presented to show the capabilities of EG applied to flow and transport.

Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity

A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach.

Investigation of shock focusing in a cavity with incident shock diffracted by an obstacle

Experiments and numerical simulations were carried out in order to investigate the focusing of a shock wave in a test section after the incident shock has been diffracted by an obstacle. A conventional shock tube was used to generate the planar shock. Incident shock Mach numbers of 1.4 and 2.1 were tested. A high-speed camera was employed to obtain schlieren photos of the flow field in the experiments. In the numerical simulations, a weighted essentially non-oscillatory (WENO) scheme of third-order accuracy supplemented with structured dynamic mesh adaptation was adopted to simulate the shock wave interaction. Good agreement between experiments and numerical results is observed. The configurations exhibit shock reflection phenomena, shock–vortex interaction and—in particular—shock focusing. The pressure history in the cavity apex was recorded and compared with the numerical results. A quantitative analysis of the numerically observed shock reflection configurations is also performed by employing a pseudo-steady shock transition boundary calculation technique. Regular reflection, single Mach reflection and transitional Mach reflection phenomena are observed and are found to correlate well with analytic predictions from shock reflection theory.

High fidelity anisotropic adaptive variational multiscale method for multiphase flows with surface tension

We propose in this work an adaptive variational multiscale method for two-fluid flows with surface tension. A level set function is used to provide a precise position of the interfaces. The implementation of the surface tension in the context of the Continuum Surface Force is proposed to circumvent the capillary time step restriction. The obtained system is then solved using a new derived Variational Multiscale stabilized finite element method designed to handle the abrupt changes at the interface and large density and viscosity ratios. Combined with an a posteriori error estimator, we show that anisotropic mesh adaptation provides highly stretched elements at the interfaces and thus yield an accurate modeling framework for two-phase incompressible isothermal flows. Stable and accurate results are obtained for all two- and three-dimensional numerical examples. To the best of our knowledge, these are the first simulation results for representative time-dependent three-dimensional two-fluid flow problems using an implicit treatment of the surface tension and a dynamic unstructured anisotropic mesh adaptation.

Validation of the FAST forecast model for the storm surges due to hurricanes Wilma and Ike

Kelly et al. (Coast Eng J 57(4):1–30, 2015) present a finite volume dynamic adaptive mesh model based on Osher’s approximate Riemann solver for the prediction of storm surges over complex landscapes. Here, the model described in that paper is extended to use distributed memory parallel block tree-based mesh refinement via the PARAMESH library. The resulting model, called the fully adaptive storm tide (FAST) model, can thus be run on massively parallel supercomputers. In this paper, we validate the FAST model by conducting numerical simulations of the storm surges due to hurricanes Wilma (2005) on Lake Okeechobee and Ike (2008) in the Gulf of Mexico. The storm surge due to Wilma on Lake Okeechobee is interesting as it can be considered as an almost idealized case which comprises a closed system. The case of hurricane Ike is more complex as it involves a coastline and additional features such as barrier islands and tidally controlled boundaries. For both cases, results obtained using the FAST model compare favorably with the measured water elevation and high-water mark data. Moreover, we show that, with sufficient computational resource, low runtimes are possible for real-world surge simulations. The FAST model therefore has the potential to run the ensemble predictions necessary to account for the variability that is inherent in hurricane forecasting.

A Generalized Feed-Forward Dynamic Adaptive Mesh Refinement and Derefinement Finite-Element Framework for Metal Laser Sintering—Part II: Nonlinear Thermal Simulations and Validations2

A novel multiscale thermal analysis numerical tool has been developed to address the micro–macro interactions involved in localized melting and sintering processes, such as laser sintering of metals exhibiting nonlinear thermal response. The method involves extension of a feed-forward dynamic adaptive mesh refinement and derefinement finite-element framework to incorporate nonlinear thermal phenomenon in the vicinity of the energy source and further reduce computational time and complexity when simulating spatiotemporally periodic problems posed by metal laser sintering. The thermal and microstructural predictions computed using this framework are in good agreement with the thermal contours measured using a forward-looking infrared (FLIR) imaging system and microstructures observed using an optical microscope.

A unified a posteriori error estimate of local discontinuous Galerkin approximations for reactive transport problems

To solve reactive transport problems in porous media, local discontinuous Galerkin (LDG) approximations are investigated. Based on the duality technique and the residual error notations, a unified a posteriori error estimate in L2(L2) norm is obtained, which is usually used for guiding anisotropic and dynamic mesh adaptivity.

A Generalized Feed Forward Dynamic Adaptive Mesh Refinement and Derefinement Finite Element Framework for Metal Laser Sintering—Part I: Formulation and Algorithm Development

A novel multiscale thermal analysis framework has been formulated to extract the physical interactions involved in localized spatiotemporal additive manufacturing processes such as the metal laser sintering. The method can be extrapolated to any other physical phenomenon involving localized spatiotemporal boundary conditions. The formulated framework, named feed forward dynamic adaptive mesh refinement and derefinement (FFD-AMRD), reduces the computational burden and temporal complexity needed to solve the many classes of problems. The current study is based on application of this framework to metals with temperature independent thermal properties processed using a moving laser heat source. The melt pool diameters computed in the present study were compared with melt pool dimensions measured using optical micrographs. The strategy developed in this study provides motivation for the extension of this simulation framework for future work on simulations of metals with temperature-dependent material properties during metal laser sintering.

Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model.

In this paper we analyze the effects of introducing the fractional-in-space operator into a Lotka-Volterra competitive model describing population super-diffusion. First, we study how cross super-diffusion influences the formation of spatial patterns: a linear stability analysis is carried out, showing that cross super-diffusion triggers Turing instabilities, whereas classical (self) super-diffusion does not. In addition we perform a weakly nonlinear analysis yielding a system of amplitude equations, whose study shows the stability of Turing steady states. A second goal of this contribution is to propose a fully adaptive multiresolution finite volume method that employs shifted Grünwald gradient approximations, and which is tailored for a larger class of systems involving fractional diffusion operators. The scheme is aimed at efficient dynamic mesh adaptation and substantial savings in computational burden. A numerical simulation of the model was performed near the instability boundaries, confirming the behavior predicted by our analysis.

Modeling of Free Surface Flows Using Improved Material Point Method and Dynamic Adaptive Mesh Refinement

AbstractThe study uses the material point method (MPM) and dynamic adaptive mesh refinement (AMR) technique to simulate incompressible free surface flows. The MPM can be regarded as a quasi-meshless method in which the background grid acts like a scratch pad while the material point (hereafter referred to as particle) motion overlies it. The states of the particles are updated through the solutions on the background grid. The artificial compressibility coefficient is employed to treat incompressible flows as slightly compressible flows within the MPM framework. Boundary conditions, such as free surfaces and reflective walls (both slip and no-slip conditions), are implemented and tested using the ghost-cell method. A generalized far-field characteristic boundary for wave propagation simulation has been established. Typical water wave propagation and violent wave breaking involving discontinuous free surfaces are simulated as well as compared to the arbitrary Lagrangian-Eulerian (ALE) method. The results in...

A three‐field stabilized finite element method for fluid‐structure interaction: elastic solid and rigid body limit

SummaryWe propose a full Eulerian framework for solving fluid‐structure interaction (FSI) problems based on a unified formulation in which the FSIs are modelled by introducing an extra stress in the momentum equation. The obtained three‐field velocity, pressure and stress system is solved using a stabilized finite element method. The key feature of this unified formulation is the ability to describe different kind of interactions between the fluid and the structure, which can be either elastic or a perfect rigid body, without the need of treating this last case via penalization. The level‐set method combined with a dynamic anisotropic mesh adaptation is used to track the fluid‐solid interface. Copyright © 2015 John Wiley & Sons, Ltd.

CFD simulation for secondary breakup of coal–water slurry drops using OpenFOAM

The main objective of this study is to gain insight into dynamic behavior of coal–water slurry (CWS) drops during secondary breakup. In the case of Bingham liquids (CWS) considered here, this endeavor requires a thorough understanding of the influence of the shear-thinning and viscoplastic fluid rheology on the flow inside the deforming drops. In numerical analysis, a coupled technique including Large Eddy Simulation (LES) and smoothed volume of fluid (VOF) was used with a dynamic adaptive mesh. The effects of variations in secondary breakup and viscoplastic liquid rheological parameters on Sauter mean diameter (SMD), droplet aspect ratio, and dynamic average viscosity were studied in detail. The results show good predictions for the breakup regimes. Moreover, an effective constant viscosity leading to a similar Newtonian breakup regime was detected in all cases. According to the analogy between secondary and primary breakups, the results can be used to better understand the CWS jet breakup.

Anisotropic Mesh Adaptivity and Control Volume Finite Element Methods for Numerical Simulation of Multiphase Flow in Porous Media

Numerical simulation of multiphase flow in porous media is of great importance in a wide range of applications in science and engineering. The governing equations are the continuity equation and Darcy’s law. A novel control volume finite element (CVFE) approach is developed to discretize the governing equations in which a node-centered control volume approach is applied for the saturation equation, while a CVFE method is used for discretization of the pressure equation. We embed the discrete continuity equation into the pressure equation and ensure that the continuity equation is exactly enforced. Furthermore, the scheme is equipped with dynamic anisotropic mesh adaptivity which uses a metric tensor field approach, based on the curvature of fields of interest, to control the size and shape of elements in the metric space. This improves the resolution of the mesh in the zones of dynamic interest. Moreover, the mesh adaptivity algorithm employs multi-constraints on element size in different regions of the porous medium to resolve multi-scale transport phenomena. The advantages of mesh adaptivity and the capability of the scheme are demonstrated for simulation of flow in several challenging computational domains. The scheme captures the key features of flow while preserving the initial geometry and can be applied for efficient simulation of flow in heterogeneous porous media and geological formations.