Dynamic Mesh Adaptation Research Articles

Additive Manufacturing simulations: An approach based on space partitioning and dynamic 3D mesh adaptation

Additive Manufacturing simulations: An approach based on space partitioning and dynamic 3D mesh adaptation

Parametric study of the laser energy absorption in high-power laser beam welding

Laser energy absorption on the keyhole wall is decisive for the thermodynamic behavior and the resultant weld properties in the high-power laser beam welding process. However, its highly transient nature on a microsecond scale makes the quantitative analysis challenging. In this paper, the influence of the relevant welding parameters on laser energy absorption is studied statistically by utilizing multiphysical modeling, in which the three-dimensional transient keyhole dynamics and thermo-fluid flow are calculated. A dynamic mesh adaption technique and a localized level-set-based ray-tracing method are employed to improve the model accuracy further. The results show that the focus position has a remarkable effect on the time-averaged laser absorption, and in contrast, the laser energy distribution regime is only slightly influenced by the welding speed in the studied parameter range (1.5–3.0 m/min). The absorption ratio of the laser energy on the keyhole front wall decreases with increasing welding speed and increases with upward-moving focus positions. The comparison between the calculated results and the experimental measurements ensures the validity of the proposed model.

A study on the hydroacoustic characterisation of a cavitating propeller by dynamic adaptive mesh refinement technique

Underwater radiated noise (URN) of a marine propeller has received significant interest in recent decades due to its implications on marine fauna. Therefore, an accurate prediction of URN at an early stage of the propeller design is becoming imperative. This study presents a numerical investigation into the noise prediction of a marine propeller, including cavitation and a comparison with experimental test results obtained from the URN database from the King's College D (KCD) standard propeller series. Amongst the propellers tested in the series, the member KCD-193 was chosen to scrutinise in this study due to the significant variance of the cavitation types experienced by this propeller member and consequent characteristic variations observed in its URN spectral response. Numerical URN predictions of different flow conditions, represented by the advance coefficient and cavitation number, were conducted to investigate their effects on the noise spectrum. These predictions were compared with the experimental results to enable interpretation of the impact of various aspects of the simulation on URN prediction accuracy. In this investigation, one of the most prominent noise sources, tip-vortex cavitation (TVC), was identified as a critical aspect that needs to be captured by the numerical simulations for accurate URN predictions using CFD simulations. The influence of TVC on the spectrum was observed to be significant. The inception and stable presence of TVC dominated the frequency response of the broadband hump. In order to address this, a systematic adaptive mesh refinement strategy was implemented based on the vortex criterion to solve the flow characteristics in the propeller slipstream accurately. To further complement this task, a correlation between the cavitation bubble growth and collapse phenomenon by the sensitivity of the broadband hump on the spectrum was established based on the experimental results. The central frequency of the broadband hump was observed to vary with the advance coefficient and cavitation number. The reduction in the cavitation number resulted in a shift of this hump towards lower frequencies. The URN level of the hump decreased slightly in the high frequency by the reduction in the advance coefficient and the developing cavitation, demonstrating the cushioning effect on the spectrum. An accurate assessment of the noise spectrum, as far as numerical predictions are concerned, particularly on the broadband hump frequency bandwidth, was directly associated with the resolution of the TVC.

Scalable implicit solvers with dynamic mesh adaptation for a relativistic drift-kinetic Fokker–Planck–Boltzmann model

In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker–Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source. We develop a new scalable fully implicit solver utilizing finite volume and conservative finite difference schemes and dynamic mesh adaptivity. A new data management framework in the PETSc library based on the p4est library is developed to enable simulations with dynamic adaptive mesh refinement (AMR), distributed memory parallelization, and dynamic load balancing of computational work. This framework and the runaway electron solver building on the framework are able to dynamically capture both bulk Maxwellian at the low-energy region and a runaway tail at the high-energy region. To effectively capture features via the AMR algorithm, a new AMR indicator prediction strategy is proposed that is performed alongside the implicit time evolution of the solution. This strategy is complemented by the introduction of computationally cheap feature-based AMR indicators that are analyzed theoretically. Numerical results quantify the advantages of the prediction strategy in better capturing features compared with nonpredictive strategies; and we demonstrate trade-offs regarding computational costs. The robustness with respect to model parameters, algorithmic scalability, and parallel scalability are demonstrated through several benchmark problems including manufactured solutions and solutions of different physics models. We focus on demonstrating the advantages of using implicit time stepping and AMR for runaway electron simulations.

Numerical study of a fish swimming in hydrokinetic turbine wake

The environmental effects of hydrokinetic turbines are still under investigation, reflecting the emerging status of this technology. This study investigates the interaction between hydrokinetic rotor wakes and fish swimming, revealing insights into fish biomechanics in complex flows and assessing the environmental implications of marine energy solutions. We conducted numerical simulations with the URANS approach and k−ω−SST turbulence closure model to predict three-dimensional turbulent flow in the OpenFOAM software. The hydrokinetic rotor wake was simulated employing the actuator line method, providing a computationally efficient alternative to full geometry simulations. For accurate replication of the motion of a fish-like tuna (Thunnus atlanticus), dynamic adaptive mesh discretization was employed. The results offer a comparative analysis of fish swimming performance within the wake rotor, particularly when immersed in the tip blade vortex, contrasted with scenarios where fish swim in undisturbed flow conditions. The analysis encompasses three-dimensional wake structures, force generation, efficiency, and equilibrium states (balancing drag and thrust) across varying Swimming numbers (Sw). Key findings include the enhanced attachment of the leading-edge vortex due to the caudal fin’s interaction with the tip blade vortex, resulting in improved auto-propulsive force production; a reduced tail stride frequency observed in fish swimming downstream of the rotor to achieve longitudinal force balance compared to unperturbed flow; and transverse hydrodynamic forces pushing fish radially away from the wake’s influence zone, potentially mitigating the risk of collision with turbine blades.

MODELING OF TWO-PHASE GAS-LIQUID SLUG FLOWS IN MICROCHANNELS

Even though numerical simulation of two-phase flows in microchannels has been attempted by many investigators, most efforts seem to have failed in correctly capturing the flow physics, especially the slug-flow regime characteristics. The presence of a thin liquid film in the order of 10 μm around the bubble (sometimes called gas pocket or gas slug) may be a contributing factor to the above difficulty. Typically, liquid films have a significant effect on the flow field. Thus, there is a strong motivation to employ numerical simulation methods to avoid some of the experimental difficulties. In this paper, the characteristics of two-phase slug flows in microchannels are calculated with the help of the volume-of-fluid (VOF) method. Formation of the slugs for different superficial velocities, capillary numbers, and gas volume fractions are investigated. The minimum mesh resolution required to capture the liquid film surrounding the gas bubble is reported employing a dynamic mesh adaptation methodology with interface tracking. Results are shown to be in good agreement with experimental data and empirical correlations.

Efficient two-dimensional simulation of primary reference fuel ignition under engine-relevant thermal stratification

Despite vast research on engine knock, there remains a limited understanding of the interaction between reaction front propagation, pressure oscillations, and fuel chemistry. To explore this through computational fluid dynamics, the adoption of advanced numerical methods is necessary. In this context, the current study introduces ARCFoam, a computational framework that combines dynamic mesh balancing, chemistry balancing, and adaptive mesh refinement with an explicit, density-based solver designed for simulating high-speed flows in OpenFOAM. First, the validity and performance of the solver are assessed by simulating directly initiated detonation in a hydrogen/air mixture. Second, the study explores the one/two-dimensional (1D/2D) hotspot ignition for the primary reference fuel and illuminates the impact of transitioning to 2D simulations on the predicted combustion modes. The 2D hotspot simulations reveal a variety of 2D physical phenomena, including the appearance of converging shock/detonation fronts as a result of negative temperature coefficient (NTC) behavior and shock wave reflection-induced detonation. The main results of the paper are as follows: (1) NTC chemistry is capable of drastically changing the anticipated reaction front propagation mode by manipulating the local/global reactivity distribution inside and outside the hotspot, (2) subsonic hotspot ignition can induce detonation (superknock) through the generation of shock waves and subsequent wall reflections, and (3) while the 1D framework predicts the initial combustion mode within the hotspot, significant differences between 1D and 2D results may emerge in scenarios involving ignition-to-detonation transitions and curvature effect on shock/detonation front propagation.

Investigation on close-coupled gas atomization for Fe-based amorphous powder production via simulation and industrial trials: Part I. Melt breakup behaviors during primary atomization

The primary atomization process is simulated by Volume of Fluid (VOF) model and dynamic adaptive mesh method. The influence of melt mass flow rate and atomization pressure on the breakup process is investigated, and the effect of hot gas atomization is also evaluated. The results show that the breakup is insufficient when the melt mass flow rate is larger than 0.075 kg s−1, while the liquid film breakup inducing the nozzle clogging occurs when the melt mass flow rate is too low (0.025 kg s−1). The backflow of droplets occurs at low atomization pressure (1.0 MPa), and various defects (satellite powders, hollow powders and needle-shaped powders) appear when the atomization pressure is larger than 3.0 MPa. Although the breakup efficiency can be significantly improved by increasing the gas temperature, severe deformation of the gas-liquid interface is induced due to the Kelvin–Helmholtz wave and gas-liquid interaction, easily leading to the formation of hollow powders. Besides, the gas-to-melt ratio (GMR) is identified as a simple criterion for predicting primary atomization breakup modes, with liquid film breakup occurring when GMR≥4.4 and "fountain" breakup occurring when GMR≤4.3. In this work, not only the gas-liquid interaction is systematically analyzed by establishing a flow-heat transfer-VOF coupling model, but also the GMR is proposed to predict the breakup mode in the industrial production, which can provide theoretical and methodological guidance for the optimization of atomization operational parameters.

On the effects of fractal geometry on reacting and nonreacting flows in a low-swirl burner: A numerical study with large-eddy simulation

Understanding and optimizing turbulence in combustion systems has a profound effect on combustion efficiency, emission reduction, and safety in applications ranging from industrial burners to propulsion systems in aerospace. This paper contributes to this pivotal field by investigating a real-scale low-swirl combustor utilizing a range of turbulence generation plates characterized by different blockage ratios and numbers of fractal pattern iterations. The work encompasses two states, namely nonreacting and premixed reacting modes, utilizing a large-eddy simulation method equipped with a dynamic Smagorinsky sub-grid model and adaptive mesh refinement for high accuracy. Verifying the robustness of the approach, the simulation aligns closely with experimental data, registering a maximum error of less than 0.9% in the swirl number. The research provides an insightful evaluation of the impact of four different fractal geometries on turbulence intensity, a vital element for attaining more complete combustion. Findings indicate a fractal with a 73% blockage ratio and four iteration levels enhances several key parameters including turbulence intensity, flow residence time, vorticity, and velocity gradient in the nonreacting mode. Conversely, a fractal with a 73% blockage ratio and three iteration levels shows the least progress in the reacting mode. Moreover, the paper delves into a comparative analysis of these two cases in the reacting mode, particularly observing the reaction zone. The appropriate fractal geometry unveiled significantly improves combustion efficiency, evidenced by an increased presence of the OH radical and a decrease in NO emission gas, thus demonstrating potential for wider application in enhancing combustion systems.

Design of a high fidelity Fluid–Structure Interaction solver using LES on unstructured grid

Despite promising experimental works, high fidelity numerical simulations of chordwise flexible blade are useful to better understanding. However, such simulation remains a challenging problem as it requires a Fluid–Structure Interaction (FSI) solver capable of accurately predicting the stall dynamics, while computing the deformation of a solid with complex geometry. In this paper, the authors propose a LES-based FSI solver using 3D solid elements for the solid and unstructured grid for fluid and solid solvers. This approach aims at being universal and is based on a partitioned coupling scheme, allowing low density ratios of the structure to the fluid. It uses an original pseudo-solid method for the mesh movement solving, specifically developed for this work. Besides, this solver is suited for massively parallel computing and can perform Dynamic Mesh Adaptation to be able to take into account any solid movement. Both fluid and solid solvers are validated independently before validation of the FSI solver against a 2D laminar benchmark, including mesh convergence study. The entire methodology is then successfully applied to experimental 3D complex case with high Reynolds number, confirming the potential of the FSI solver for its intended use, without geometry restriction. This is finally illustrated with a simulation of an experiment involving a chordwise flexible blade with large deformation, which has never been reproduced with a 3D LES approach in literature so far.

DeepFlame: A deep learning empowered open-source platform for reacting flow simulations

Recent developments in deep learning have brought many inspirations for the scientific computing community and it is perceived as a promising method in accelerating the computationally demanding reacting flow simulations. In this work, we introduce DeepFlame, an open-source C++ platform with the capabilities of utilising machine learning algorithms and offline-trained models to solve for reactive flows. We combine the individual strengths of the computational fluid dynamics library OpenFOAM, machine learning framework Torch, and chemical kinetics program Cantera. The complexity of cross-library function and data interfacing (the core of DeepFlame) is minimised to achieve a simple and clear workflow for code maintenance, extension and upgrading. As a demonstration, we apply our recent work on deep learning for predicting chemical kinetics (Zhang et al., 2022 [8]) to highlight the potential of machine learning in accelerating reacting flow simulation. A thorough code validation is conducted via a broad range of canonical cases to assess its accuracy and efficiency. The results demonstrate that the convection-diffusion-reaction algorithms implemented in DeepFlame are robust and accurate for both steady-state and transient processes. In addition, a number of methods aiming to further improve the computational efficiency, e.g. dynamic load balancing and adaptive mesh refinement, are explored. Their performances are also evaluated and reported. With the deep learning method implemented in this work, a speed-up of two orders of magnitude is achieved in a simple hydrogen ignition case when performed on a medium-end graphics processing unit (GPU). Further gain in computational efficiency is expected for hydrocarbon and other complex fuels. A similar level of acceleration is obtained on an AI-specific chip – deep computing unit (DCU), highlighting the potential of DeepFlame in leveraging the next-generation computing architecture and hardware. Program summaryProgram Title: DeepFlameCPC Library link to program files:https://doi.org/10.17632/3pg9xmypp3.1Developer's repository link:https://github.com/deepmodeling/deepflame-devLicensing provisions: GPLv3Programming language: C++Nature of problem: Solving chemically reacting flows with direct (quasi-direct) simulation methods is usually troubled by the following problems: 1. as the widely-used computational fluid dynamics (CFD) toolbox, OpenFOAM features limited ODE solvers for chemistry and oversimplified transport models, yielding non-negligible errors in simulation results; 2. the chemical source term evaluation is the most computationally expensive and usually accounts for more than 80% of total computing time.Solution method: An open-source platform bringing together the individual strengths of OpenFOAM, Cantera and PyTorch libraries is built in this study. In the present implementation, CVODE solvers, detailed transport models and deep learning algorithms are all adopted to assist the simulation of reacting flow. Note that here machine learning is introduced in combination with heterogeneous computing to accelerate the most demanding solving procedure for chemical source term evaluation.

On the effects of hybrid surface wettability on the structure of cavitating flow using implicit large eddy simulation

BackgroundSupercavitation flow is characterized by the presence of a supercavity, which can be unstable and cause unwanted motion or even loss of control of an object. To address this issue, flow control techniques are often employed. These techniques aim to manipulate the flow of liquid around the object and improve stability and control. Some of these methods include using control surfaces, injecting fluids, or more advanced techniques such as active flow control or smart materials. MethodThe aim of this study is to use computational methods to investigate the behaviour of supercavitation flow over a Clark-Y hydrofoil with different contact angle patterns (hybrid wettability) inspired by the Namib desert beetle. The hybrid wettability consists of six distinct patterns with a 160-degree contact angle for superhydrophobic surfaces and a five-degree contact angle for superhydrophilic surfaces. To predict the dynamic and unsteady behaviours of the supercavitation flow with a cavity number of 0.4, the implicit large eddy simulation (ILES) technique and Kunz mass transfer model are used. The compressive volume of fluid technique is used in conjunction with dynamic adaptive mesh refinement to track the interface between the vapour and liquid phases. The simulations are conducted using the interPhaseChangeFoam two-phase flow solver within the OpenFOAM framework. This study analyses the time-averaged and instantaneous fluid dynamic properties of the supercavitation flow of the hydrofoil with a hybrid surface, including pressure, velocity, vorticity fields, wake flow, recirculation zone, and liquid volume fraction. In addition, it examines the instantaneous cavity leading edge and flow separation, the vortical flow structure, vorticity stretching and dilatation, spanwise flow details, the creation of a low-pressure zone behind the hybrid hydrofoil, streamwise velocity fluctuations, and the cavity dynamics over an entire cycle. FindingsThe results show that the contact angle has a significant effect on the structure of the supercavitation flow. Specifically, the use of a superhydrophobic surface on the pressure side and trailing edge of a hydrofoil, along with a superhydrophilic surface on the leading edge, can reduce the thickness of the wake zone, the length of the cloud cavity, and flow instability. Additionally, this approach can delay the onset of cavitation.

An adjoint‐based solver with adaptive mesh refinement for efficient design of coupled thermal‐fluid systems

AbstractA multi‐objective continuous adjoint strategy based on the superposition of boundary functions for topology optimization of problems where the heat transfer must be enhanced and the dissipated mechanical power controlled at the same time, has been here implemented in a finite volume (FV), incompressible, steady flow solver supporting a dynamic adaptive mesh refinement (AMR) strategy. The solver models the transition from fluid to solid by a porosity field, that appears in the form of penalization in the momentum equation; the material distribution is optimized by the method of moving asymptotes (MMA). AMR is based on a hierarchical nonconforming h‐refinement strategy and is applied together with a flux correction to enforce conservation across topology changes. It is shown that a proper choice of the refinement criterium favors a mesh‐independent solution. Finally, a Pareto front built from the components of the objective function is used to find the best combination of the weights in the optimization cycle. Numerical experiments on two‐ and three‐dimensional test cases, including the aero‐thermal optimization of a simplified layout of a cooling system, have been used to validate the implemented methodology.

Numerical Investigation of Flow Patterns and Plug Hydrodynamics in a 3D T-junction Microchannel

A three-dimensional (3D) numerical simulation of a two-phase flow liquid/liquid is performed in a rectangular microchannel with a T-junction. The volume of fluid (VOF) method was used under ANSYS Fluent to capture the interface between the two phases. The dynamic mesh adaptation technique together with the assumption of symmetry plane helps us to reduce the computational cost. The study focuses on the flow patterns and hydrodynamics of plugs. So, the influence of the flow rate ratio $$q$$ , the capillary number $$Ca$$ , and the viscosity ratio on the liquid film, the plug/droplet shape, and velocity are examined here. Particularly, the plug/droplet lengths predicted by the simulation show good agreement with the experimental and correlation available in the literature. The results revealed six distinct flow patterns by dispersing water in a continuous phase of silicone oil. By decreasing the flow rate ratio as well as the viscosity ratio, the liquid film thickness increases in the corners and side planes. In turn, this greatly impacts the liquid film velocity and the plug velocity. Furthermore, capillary number (based on two-phase flow velocity) is also shown to have a greater impact than viscosity ratio and flow rate ratio on plug shape, with the curvature radii of the tail always larger than the front one.

An extensive study of shear thinning flow around a spherical particle for power-law and Carreau fluids

We develop and implement a high-order finite element formulation to solve incompressible shear thinning flows using power-law and Carreau rheology models. We verify the implementation using the Method of Manufactured Solutions (MMS) and demonstrate that the implementation preserves the order of accuracy of the FEM scheme. We run high-order flow-past-a-sphere simulations for Re ∈ [ 0 . 1 , 100 ] for Newtonian and shear thinning flows. Power-law simulations cover n ∈ [ 0 . 3 , 0 . 9 ] , Carreau simulations cover the same range of n and dimensionless relaxation times Λ ∈ [ 0 . 1 , 100 ] . We use 3D Cartesian grids, adopting a high-order sharp-interface immersed boundary method (IBM) to impose the no-slip boundary condition on the surface of the sphere. We use dynamic mesh adaptation with a Kelly error estimator to adaptively refine the grid. Newtonian drag coefficients are compared to Clift et al.’s model. Using the power-law model for shear thinning flow, results show that when decreasing n : the drag coefficient increases for Re ⪅ 5, it decreases for Re ⪆ 5, and that for higher Reynolds the wake region is longer and the separation point is moved upstream. These drag coefficient results are in adequation with previously established simulation results. We provide a new drag coefficient correlation for power-law fluids that is valid for a wide range of n and for Re ∈ [ 0 . 1 , 100 ] , with R 2 = 0 . 998 . The power-law model is singular in the zero-shear limit, and this limit is bound to occur in a flow-past-a-sphere geometry. For that matter, the Carreau model is well-posed. As the Carreau-modeled results show, the drag force on the sphere is considerably affected by the initial Newtonian plateau of the fluid. Drag coefficient results in the creeping flow regime are compared to experimental results, allowing validation of the numerical model. This work provides a better understanding of shear thinning flow past a sphere, for which the relationship between drag and flow regimes are highly nonlinear. • The effect of shear thinning flow past a sphere on the drag force is studied. • The open-source Computational Fluid Dynamics (CFD) software Lethe using a Finite Element Method (FEM) is employed. • A correlation for the drag coefficient for power-law fluid flow past a sphere is given, with a coefficient of determination R 2 = 0.998. • Power-law and Carreau drag coefficients are compared.

Breakup process modeling and production of FeSiAl magnetic powders by close-coupled gas atomization

Close-coupled gas atomization is extensively used in the industrial production of alloy powders due to the advantages of high efficiency, low cost and excellent powder properties. In order to investigate the complex gas-liquid interaction during atomization, primary atomization was simulated through the VOF (Volume of Fluid) model and the dynamic adaptive mesh method, and a two-way coupling DPM (Discrete Particle Model) was used to simulate secondary atomization. The results showed that under the low melt mass flow rate of 0.0050 kg s−1, the flow separation and droplet backflow occurred at the atomization pressure of 1 MPa, while gas-liquid interfaces deformed and rotated drastically when the atomization pressure is above 3 MPa, which led to the formation of hollow powders. When the melt mass flow rate was 0.0150 kg s−1, the d50 decreased from 40.7 to 38.4 μm as the atomization pressure increased from 2 to 3 MPa. However, the chance of collision between particles increased due to the decrease in the spray cone angle, and both the standard deviation of particle size and atomization efficiency deteriorated, which indicated that 2 MPa was the optimum atomization pressure. As the mass flow rate increased from 0.0050 to 0.0150 kg s−1, the gas to melt ratio decreased, but the d50 only increased from 32.3 to 40.7 μm, indicating that the mass flow rate of 0.0150 kg s−1 did not significantly affect the particle size distribution, but also contributed to improve the production efficiency and avoided the risk of the nozzle freeze-off. The d50 of the spherical FeSiAl powders produced by the industrial tests at 2 MPa and 0.0150 kg s−1 was 44.7 ± 2.1 μm, which was basically consistent with the simulation results, indicating that the parameter optimization by the coupling model developed in this study could provide theoretical and practical guidance for the preparation of high-performance alloy powders by gas atomization.

An adaptive numerical method for simulating diffusion flame jets

In this paper, we present an adaptive numerical methodology for a reacting three-dimensional low-Mach number flow. This computational strategy combines an adaptive mesh refinement (AMR), an implicit–explicit time stepping strategy (IMEX), an extension of increment-pressure projection method, and a mixture fraction to model the chemistry combustion dynamics. To accurately resolve sharp gradients, vorticity shedding, and localized small length scale flow features, dynamic adaptive mesh refinement (given by hierarchical nested Cartesian grid patches) is employed. That spatial dynamic adaptation is used in conjunction with a variable time step, second-order, linearly implicit time integration scheme. The capabilities of the present numerical method are demonstrated by numerical verification and simulation of two classical diffusion flame examples from literature.

HPC-enabling technologies for high-fidelity combustion simulations

With the increase in computational power in the last decade and the forthcoming Exascale supercomputers, a new horizon in computational modelling and simulation is envisioned in combustion science. Considering the multiscale and multiphysics characteristics of turbulent reacting flows, combustion simulations are considered as one of the most computationally demanding applications running on cutting-edge supercomputers. Exascale computing opens new frontiers for the simulation of combustion systems as more realistic conditions can be achieved with high-fidelity methods. However, an efficient use of these computing architectures requires methodologies that can exploit all levels of parallelism. The efficient utilization of the next generation of supercomputers needs to be considered from a global perspective, that is, involving physical modelling and numerical methods with methodologies based on High-Performance Computing (HPC) and hardware architectures. This review introduces recent developments in numerical methods for large-eddy simulations (LES) and direct-numerical simulations (DNS) to simulate combustion systems, with focus on the computational performance and algorithmic capabilities. Due to the broad scope, a first section is devoted to describe the fundamentals of turbulent combustion, which is followed by a general description of state-of-the-art computational strategies for solving these problems. These applications require advanced HPC approaches to exploit modern supercomputers, which is addressed in the third section. The increasing complexity of new computing architectures, with tightly coupled CPUs and GPUs, as well as high levels of parallelism, requires new parallel models and algorithms exposing the required level of concurrency. Advances in terms of dynamic load balancing, vectorization, GPU acceleration and mesh adaptation have permitted to achieve highly-efficient combustion simulations with data-driven methods in HPC environments. Therefore, dedicated sections covering the use of high-order methods for reacting flows, integration of detailed chemistry and two-phase flows are addressed. Final remarks and directions of future work are given at the end.

Fully automatic multigrid adaptive mesh refinement strategy with controlled accuracy for nonlinear quasi-static problems

We propose an adaptive mesh refinement (AMR) algorithm dedicated to the simulation of nonlinear quasi-static solid mechanics problems with complex local phenomena at the structural scale. The proposed method allows us to follow in time the evolution of studied phenomena in a fully-automatic (based on error estimators), precise (respecting user-prescribed accuracies) and efficient (in terms of memory space and computational time) way. This algorithm is based on the multilevel Local Defect Correction (LDC) refinement approach. We first introduce an algorithmic extension of the LDC method to nonlinear quasi-static problems and provide key aspects associated with its practical implementation. Generic still open AMR-related questions associated with dynamic mesh adaptation, such as fields transfer between time steps and discretization error control over time, are then addressed. We propose a straightforward and efficient error non accumulation strategy lying on the introduction of the unbalance residual as an initial source term of the problem. Moreover, a reliable remeshing algorithm is introduced, aiming to limit the number of mesh regenerations over time while guaranteeing the fulfillment of user-prescribed errors. The efficiency of the proposed algorithm is demonstrated on several numerical experiments, in 2D and 3D, with different types of material behavior as well as evolving loads. Thanks to its natural ability to generate a hierarchy of meshes of limited sizes that dynamically follow the evolution over time of studied phenomena, the proposed extension of the LDC method clearly appears to be of great potential for many challenging applications.

Wavetrisk-2.1: an adaptive dynamical core for ocean modelling

Abstract. This paper introduces wavetrisk-2.1 (i.e. wavetrisk-ocean), an incompressible version of the atmosphere model wavetrisk-1.x with free surface. This new model is built on the same wavelet-based dynamically adaptive core as wavetrisk, which itself uses dynamico's mimetic vector-invariant multilayer rotating shallow water formulation. Both codes use a Lagrangian vertical coordinate with conservative remapping. The ocean variant solves the incompressible multilayer shallow water equations with inhomogeneous density layers. Time integration uses barotropic–baroclinic mode splitting via an semi-implicit free surface formulation, which is about 34–44 times faster than an unsplit explicit time-stepping. The barotropic and baroclinic estimates of the free surface are reconciled at each time step using layer dilation. No slip boundary conditions at coastlines are approximated using volume penalization. The vertical eddy viscosity and diffusivity coefficients are computed from a closure model based on turbulent kinetic energy (TKE). Results are presented for a standard set of ocean model test cases adapted to the sphere (seamount, upwelling and baroclinic turbulence). An innovative feature of wavetrisk-ocean is that it could be coupled easily to the wavetrisk atmosphere model, thus providing a first building block toward an integrated Earth system model using a consistent modelling framework with dynamic mesh adaptivity and mimetic properties.