Unstructured Mesh Adaptation Research Articles

Numerical simulation of three-dimensional breaking waves and its interaction with a vertical circular cylinder

Wave breaking plays an important role in wave-structure interaction. A novel control volume finite element method with adaptive unstructured meshes is employed here to study 3-D breaking waves. The numerical framework consists of a “volume of fluid” type method for the interface capturing and adaptive unstructured meshes to improve computational efficiency. The numerical model is validated against experimental measurements of breaking wave over a sloping beach and is then used to study the breaking wave impact on a vertical circular cylinder on a slope. Detailed complex interfacial structures during wave impact, such as plunging jet formation and splash-up are captured in the simulation, demonstrating the capability of the present method.

CosmosDG: An hp-adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

Abstract We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge–Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.

Simulating Flood Waves in Residential Areas

An approach to numerical simulation of flooding of residential areas is proposed. It involves modeling of all buildings and other structures in the flood plain, which can automatically be done with the help of modern software. Two-dimensional Saint-Venant equations on unstructured adaptive meshes are used without the need to introduce additional parameters and coefficients. The main advantage of the method is high accuracy and realism of modeling and graphical representation of flood waves and dam-break waves on residential areas. This method is validated against experimental data and real objects.

Numerical study of three-dimensional droplet impact on a flowing liquid film in annular two-phase flow

Annular flow with liquid entrainment occurs in a wide variety of two-phase flow system. A novel control volume finite element method with adaptive unstructured meshes is employed here to study three-dimensional droplet deposition process in annular two-phase flow. The numerical framework consists of a ‘volume of fluid’ type method for the interface capturing and a force-balanced continuum surface force model for the surface tension on adaptive unstructured meshes. The numerical framework is validated against experimental measurements of a droplet impact problem and is then used to study the droplet deposition onto a flowing liquid film at atmospheric and high pressure conditions. Detailed complex interfacial structures during droplet impact are captured during the simulation, which agree with the experimental observations, demonstrating the capability of the present method. It is found that the effect of the ambient pressure on the fluid properties and interfacial tension plays an important role in the droplet deposition process and the associated interfacial phenomena.

Edge-based anisotropic mesh adaptation of unstructured meshes with applications to compressible flows

An adaptation procedure using refinement, coarsening and smoothing with anisotropic considerations for unstructured meshes and its coupling with a compressible flow solver is presented in this work. The developed refinement strategy combines a Riemannian centred split of the edges. The coarsening methodology uses an edge collapse procedure where the collapse point is evaluated using anisotropic quality considerations. An accurate and anisotropic vertex smoothing algorithm that operates along the direction of the edges is presented. Edge and face swapping are also used together with the refinement coarsening and smoothing strategies to enhance anisotropic quality. The developed approach makes use of only simple mesh information and is applicable to two and three-dimensional meshes. The performance of the methodology is analysed for two-dimensional triangular meshes and three-dimensional tetrahedral meshes on analytical test cases and to solve steady-state inviscid compressible flows. The transonic flow past an airfoil, the supersonic flow around a sphere and the flow around a complex real-life application are performed.

State-of-the-art adaptive mesh generator implementation for dynamic asphaltene deposition in four-phase flow simulator in near well-bore region

Asphaltene deposition leads to rigorous problems in petroleum industry such as relative permeability reduction, wettability alterations, and blockage of the flow with additional pressure drop in wellbore tubing, etc. Many attempts have been undertaken to develop reliable and accurate models to predict phase behavior of asphaltene. However, previously published models cannot couple static and dynamic behaviors of reservoir and its fluids. In this communication, a novel four-phase flow simulator has been developed considering asphaltene deposition as one of the phases, using finite volume formulation. A novel adaptive unstructured mesh generator technique has been introduced in which dynamic properties of reservoir are combined with static field parameters. The results of this study illustrated that the proposed methodology can accurately predict the oil sample properties, and the amount of asphaltene precipitation. Moreover, it was found that the proposed approach is faster and computationally less expensive compared to fine structured model. The proposed strategy can be applied in any reservoir simulator and provides asphaltene phase behavior and reservoir properties with high degree of accuracy.

Ensemble data assimilation applied to an adaptive mesh ocean model

SummaryIn this study, a first attempt has been made to introduce mesh adaptivity into the ensemble Kalman fiter (EnKF) method. The EnKF data assimilation system was established for an unstructured adaptive mesh ocean model (Fluidity, Imperial College London). The mesh adaptivity involved using high resolution mesh at the regions of large flow gradients and around the observation points in order to reduce the representativeness errors of the observations. The use of adaptive meshes unavoidably introduces difficulties in the implementation of EnKF. The ensembles are defined at different meshes. To overcome the difficulties, a supermesh technique is employed for generating a reference mesh. The ensembles are then interpolated from their own mesh onto the reference mesh. The performance of the new EnKF data assimilation system has been tested in the Munk gyre flow test case. The discussion of this paper will focus on (a) the development of the EnKF data assimilation system within an adaptive mesh model and (b) the advantages of mesh adaptivity in the ocean data assimilation model. Copyright © 2016 John Wiley & Sons, Ltd.

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.

Finite-volume goal-oriented mesh adaptation for aerodynamics using functional derivative with respect to nodal coordinates

A new goal-oriented mesh adaptation method for finite volume/finite difference schemes is extended from the structured mesh framework to a more suitable setting for adaptation of unstructured meshes. The method is based on the total derivative of the goal with respect to volume mesh nodes that is computable after the solution of the goal discrete adjoint equation. The asymptotic behaviour of this derivative is assessed on regularly refined unstructured meshes. A local refinement criterion is derived from the requirement of limiting the first order change in the goal that an admissible node displacement may cause. Mesh adaptations are then carried out for classical test cases of 2D Euler flows. Efficiency and local density of the adapted meshes are presented. They are compared with those obtained with a more classical mesh adaptation method in the framework of finite volume/finite difference schemes 46. Results are very close although the present method only makes usage of the current grid.

Three-dimensional modeling of a thermal dendrite using the phase field method with automatic anisotropic and unstructured adaptive finite element meshing

Dendritic growth is computed with automatic adaptation of an anisotropic and unstructured finite element mesh. The energy conservation equation is formulated for solid and liquid phases considering an interface balance that includes the Gibbs-Thomson effect. An equation for a diffuse interface is also developed by considering a phase field function with constant negative value in the liquid and constant positive value in the solid. Unknowns are the phase field function and a dimensionless temperature, as proposed by [1]. Linear finite element interpolation is used for both variables, and discretization stabilization techniques ensure convergence towards a correct non-oscillating solution. In order to perform quantitative computations of dendritic growth on a large domain, two additional numerical ingredients are necessary: automatic anisotropic unstructured adaptive meshing [2,[3] and parallel implementations [4], both made available with the numerical platform used (CimLib) based on C++ developments. Mesh adaptation is found to greatly reduce the number of degrees of freedom. Results of phase field simulations for dendritic solidification of a pure material in two and three dimensions are shown and compared with reference work [1]. Discussion on algorithm details and the CPU time will be outlined.

An adaptive, residual based, splitting approach for the penalized Navier Stokes equations

The interest on Immersed Boundary Methods (IBM) is increasing in Computational Fluid Dynamics as they simplify the mesh generation problem. In this work, we consider an approach based on the addition of a penalty term to the Navier–Stokes equations to account for the wall boundary conditions. To discretize the resulting equations we use a residual distribution approach previously developed by some of the authors. To adapt the method to the IBM considered, we developed a new formulation of residual distribution based on a Strang splitting method in time, coupling an implicit asymptotic integration procedure of the penalization ODE with a simplified explicit residual distribution for the Navier–Stokes equations. The first method, provides an operator which is exact up to orders η2, with η the penalty parameter assuming values of the order of 10−10. A modification of the solution gradient reconstruction necessary for the evaluation of the viscous fluxes, is also introduced in the paper. This guarantees that correct physical values of the viscous stresses are recovered in vicinity of the solid. We show formally and numerically that the approach proposed is second order accurate for smooth solutions. We evaluate its potential for IBM by coupling the resulting method with unstructured mesh adaptation on wall boundaries. Several steady and time dependent tests are used to show the promising features of the method proposed.

Hybrid MPI-thread parallelization of adaptive mesh operations

Development of a hybrid MPI-thread programming system called PCU.Inter-thread message passing, including non-blocking collectives.A novel, scalable termination detection technique for communication rounds.Hybrid parallel scalability to 16K cores on an IBM Blue Gene/Q. Many of the world's leading supercomputer architectures are a hybrid of shared memory and network-distributed memory. Such an architecture lends itself to a hybrid MPI-thread programming model. We first present an implementation of inter-thread message passing based on the MPI and pthread libraries. In addition, we present an efficient implementation of termination detection for communication rounds. We use the term phased message passing to denote the communication interface based on this termination detection. This interface is then used to implement parallel operations for adaptive unstructured meshes, and the performance of resulting applications is compared to pure MPI operation. We also present new workflows enabled by the ability to vary the number of threads during runtime.

A GPU-accelerated adaptive discontinuous Galerkin method for level set equation

ABSTRACTThis paper presents a GPU-accelerated nodal discontinuous Galerkin method for the solution of two- and three-dimensional level set (LS) equation on unstructured adaptive meshes. Using adaptive mesh refinement, computations are localised mostly near the interface location to reduce the computational cost. Small global time step size resulting from the local adaptivity is avoided by local time-stepping based on a multi-rate Adams–Bashforth scheme. Platform independence of the solver is achieved with an extensible multi-threading programming API that allows runtime selection of different computing devices (GPU and CPU) and different threading interfaces (CUDA, OpenCL and OpenMP). Overall, a highly scalable, accurate and mass conservative numerical scheme that preserves the simplicity of LS formulation is obtained. Efficiency, performance and local high-order accuracy of the method are demonstrated through distinct numerical test cases.

Tracing Analytic Ray Curves for Light and Sound Propagation in Non-Linear Media.

The physical world consists of spatially varying media, such as the atmosphere and the ocean, in which light and sound propagates along non-linear trajectories. This presents a challenge to existing ray-tracing based methods, which are widely adopted to simulate propagation due to their efficiency and flexibility, but assume linear rays. We present a novel algorithm that traces analytic ray curves computed from local media gradients, and utilizes the closed-form solutions of both the intersections of the ray curves with planar surfaces, and the travel distance. By constructing an adaptive unstructured mesh, our algorithm is able to model general media profiles that vary in three dimensions with complex boundaries consisting of terrains and other scene objects such as buildings. Our analytic ray curve tracer with the adaptive mesh improves the efficiency considerably over prior methods. We highlight the algorithm's application on simulation of visual and sound propagation in outdoor scenes.

Towards a new multiscale air quality transport model using the fully unstructured anisotropic adaptive mesh technology of Fluidity (version 4.1.9)

Abstract. An integrated method of advanced anisotropic hr-adaptive mesh and discretization numerical techniques has been, for first time, applied to modelling of multiscale advection–diffusion problems, which is based on a discontinuous Galerkin/control volume discretization on unstructured meshes. Over existing air quality models typically based on static-structured grids using a locally nesting technique, the advantage of the anisotropic hr-adaptive model has the ability to adapt the mesh according to the evolving pollutant distribution and flow features. That is, the mesh resolution can be adjusted dynamically to simulate the pollutant transport process accurately and effectively. To illustrate the capability of the anisotropic adaptive unstructured mesh model, three benchmark numerical experiments have been set up for two-dimensional (2-D) advection phenomena. Comparisons have been made between the results obtained using uniform resolution meshes and anisotropic adaptive resolution meshes. Performance achieved in 3-D simulation of power plant plumes indicates that this new adaptive multiscale model has the potential to provide accurate air quality modelling solutions effectively.

A feature-based mesh adaptation for the unsteady high speed compressible flows in complex three-dimensional domains

We propose an unstructured mesh adaptation approach for unsteady high speed compressible Navier–Stokes applications involving blasts and explosions with the presence of strong shock waves propagating in three dimensional complex domains. The idea is to identify the locations of critical physics locally and then re-mesh these regions based on solution derived metrics. The approach ensures both geometry fidelity and mesh validity, especially for areas near complex geometries, a task that is always a challenge in mesh adaptation. The proposed adaptivity is applied for simulations of blast wave propagations and compared with available data in literature. The results show that the proposed method is fully robust and efficient for computational fluid dynamics (CFD) problems in complex three-dimensional domains.

Reservoir Modeling for Flow Simulation by Use of Surfaces, Adaptive Unstructured Meshes, and an Overlapping-Control-Volume Finite-Element Method

SummaryWe present new approaches to reservoir modeling and flow simulation that dispose of the pillar-grid concept that has persisted since reservoir simulation began. This results in significant improvements to the representation of multiscale geologic heterogeneity and the prediction of flow through that heterogeneity. The research builds on more than 20 years of development of innovative numerical methods in geophysical fluid mechanics, refined and modified to deal with the unique challenges associated with reservoir simulation.Geologic heterogeneities, whether structural, stratigraphic, sedimentologic, or diagenetic in origin, are represented as discrete volumes bounded by surfaces, without reference to a predefined grid. Petrophysical properties are uniform within the geologically defined rock volumes, rather than within grid cells. The resulting model is discretized for flow simulation by use of an unstructured, tetrahedral mesh that honors the architecture of the surfaces. This approach allows heterogeneity over multiple length-scales to be explicitly captured by use of fewer cells than conventional corner-point or unstructured grids.Multiphase flow is simulated by use of a novel mixed finite-element formulation centered on a new family of tetrahedral element types, PN(DG)–PN+1, which has a discontinuous Nth-order polynomial representation for velocity and a continuous (order N +1) representation for pressure. This method exactly represents Darcy-force balances on unstructured meshes and thus accurately calculates pressure, velocity, and saturation fields throughout the domain. Computational costs are reduced through dynamic adaptive-mesh optimization and efficient parallelization. Within each rock volume, the mesh coarsens and refines to capture key flow processes during a simulation, and also preserves the surface-based representation of geologic heterogeneity. Computational effort is thus focused on regions of the model where it is most required.After validating the approach against a set of benchmark problems, we demonstrate its capabilities by use of a number of test models that capture aspects of geologic heterogeneity that are difficult or impossible to simulate conventionally, without introducing unacceptably large numbers of cells or highly nonorthogonal grids with associated numerical errors. Our approach preserves key flow features associated with realistic geologic features that are typically lost. The approach may also be used to capture near-wellbore flow features such as coning, changes in surface geometry across multiple stochastic realizations, and, in future applications, geomechanical models with fracture propagation, opening, and closing.

Finite Element Model of Soil Water and Nutrient Transport with Root Uptake: Explicit Geometry and Unstructured Adaptive Meshing

In this paper, we consider a model of soil water and nutrient transport with plant root uptake. The ge-ometry of the plant root system is explicitly taken into account in the soil model. We first describe our modeling approach. Then, we introduce an adaptive mesh refinement procedure enabling us to accurately capture the geom-etry of the root system and small-scale phenomena in the rhizosphere. Finally, we present a domain decomposition technique for solving the problems arising from the soil model as well as some numerical results.

Study on high-Weber-number droplet collision by a parallel, adaptive interface-tracking method

AbstractWe have established a parallel, adaptive interface-tracking framework in order to conduct, based on the framework, direct simulation of binary head-on droplet collision in the high-Weber-number regime (from 200 to 1500) that exhibits complex topological changes and substantial length scale variations. The overall algorithms include a combined Eulerian and Lagrangian solver to track moving interfaces, conservative Lagrangian mesh modification and reconstruction, cell-based unstructured adaptive mesh refinement (AMR) in the Eulerian solver, and associated Eulerian and Lagrangian domain partitions to minimize communication overhead. Based on the combined computational and experimental efforts, we have resolved for the first time the free-surface instabilities of the colliding droplets at such high Weber number. We detail the characteristics of coalescence, stretch, end pinching, fingering, free-surface movement and drop breakup. The Taylor–Culick rim is present soon after the collision. Furthermore, we observe two types of longitudinal instabilities on the rim, namely, the Rayleigh–Taylor (RT)-type instability in the initial deceleration phase of the circular sheet right after droplet coalescence, and later the Rayleigh–Plateau (RP) instabilities. As the Taylor–Culick rim disintegrates in the retraction phase, fingering effect is profound and resulting in wider droplet size distribution.

A Full 3-D Dynamically Adaptive Unstructured Grid Finite-Volume Approach to Simulate Multiple Branching in Streamer Propagation

Electron-spot-induced multiple branching and trajectory deviation of streamer microdischarges in air was simulated using a 3-D unstructured adaptive mesh finite-volume approach along with the air plasma streamer model proposed by Morrow et al. Images illustrating the effect of electron spots on the propagation trajectory, i.e., deviation, simple branching, multiple branching, are presented and commented.