Adaptive Mesh Refinement Approach Research Articles

Predicting lift and drag coefficients during hypersonic Mars reentry using hyStrath

During hypersonic reentry, a spacecraft experiences several different fluid flow regimes, which usually require the application of different software frameworks to simulate the respective regimes. This study aims to evaluate the hyStrath library for predicting aerodynamic lift and drag coefficients of complex three-dimensional (3D) geometries during hypersonic Mars reentry, using flight data of the Viking 1 mission as reference. A range of altitudes (h=30−140 km) and Mach numbers (M=13−24) where flight data is available is considered, covering the rarefied, transitional, and continuum fluid flow regimes. The hyStrath library contains a set of modified solvers and state-of-the-art thermophysical and chemistry models within the framework of OpenFOAM, dedicated to modeling high-enthalpy hypersonic flow problems. Depending on the flow regime, the computational fluid dynamics solver hy2Foam or direct-simulation Monte Carlo solver dsmcFoam+ are employed in the study. Because hyStrath is based on OpenFOAM, it allows the use of an unstructured adaptive mesh refinement approach for arbitrary geometries. We obtain excellent results throughout all investigated flow regimes and Mach numbers with an average deviation of 1.5% and 2% from the measured lift and drag coefficients, respectively. The applicability of the framework for accurately modeling both rarefied and continuum Mars reentry problems of complex 3D geometries such as the Viking capsule is demonstrated.

DynAMO: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws

We introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial differential equations. However, traditional adaptive mesh refinement approaches for time-dependent problems typically rely only on instantaneous error indicators to guide adaptivity. As a result, standard strategies often require frequent remeshing to maintain accuracy. In the DynAMO approach, multi-agent reinforcement learning is used to discover new local refinement policies that can anticipate and respond to future solution states by producing meshes that deliver more accurate solutions for longer time intervals. By applying DynAMO to discontinuous Galerkin methods for the linear advection and compressible Euler equations in two dimensions, we demonstrate that this new mesh refinement paradigm can outperform conventional threshold-based strategies while also generalizing to different mesh sizes, remeshing and simulation times, and initial conditions.

A Selective Integration-Based Adaptive Mesh Refinement Approach for Accurate and Efficient Welding Process Simulation

To save computational time and physical memory in welding thermo-mechanical analysis, an accurate adaptive mesh refinement (AMR) method was proposed based on the feature of moving heat source during the welding. The locally refined mesh was generated automatically according to the position of the heat source to solve the displacement field. A background mesh, without forming a global matrix, was designed to maintain the accuracy of stress and strain after mesh coarsening. The solutions are always carried out on the refined computational mesh using a selective integration scheme. To evaluate the performance of the developed method, a fillet welding joint was first analyzed via validation of the accuracy of conventional FEM by experiment. Secondly, a larger fillet joint and its variations with a greater number of degrees of freedom were analyzed via conventional FEM and current AMR. The simulation results confirmed that the proposed method is accurate and efficient. An improvement in computational efficiency by 7 times was obtained, and memory saving is about 63% for large-scale models.

Development of a fully automatic damage simulation framework for quasi-brittle materials

This paper proposes a fully automatic analysis framework for static damage analysis of quasi-brittle materials exploiting adaptive mesh refinement approaches as well as adaptive load stepping techniques. The damage process is modelled using an integral-type nonlocal damage model which alleviates the mesh dependence issue. The scaled boundary finite element method and quadtree meshing algorithm are employed in the adaptive analysis. The quadtree algorithm is simple for adaptively remeshing and the mesh refinement is limited to local regions around the damage zones. The elements of the quadtree mesh are modelled by the scaled boundary finite element method, naturally resolving the hanging nodes encountered by the standard finite elements. Furthermore, the regular element shapes and small number of unique element patterns permit a significant reduction of computational cost on processing the element formulations, and an easy implementation of data transfer between two successive meshes. In the last step, the adaptive meshing strategy is combined with an automatic load stepping scheme to create a fully automatic analysis framework. By means of various numerical examples the performance of the proposed method predicting the damage evolution in structures is analysed in terms of its accuracy and efficiency.

Efficient GPU parallelization of adaptive mesh refinement technique for high-order compressible solver with immersed boundary

A new, highly parallelized, adaptive mesh refinement (AMR) library, equipped with an accurate immersed boundary (IB) method for solving the compressible Navier–Stokes system is presented. The library, named ADAM, is designed to efficiently exploit modern exascale GPU-accelerated supercomputers and it is implemented with a highly modular structure in order to make easy to leverage it for a wide range of CFD applications. The structured Cartesian grids at the basis of (octree) AMR approach allows to implement very high order accurate models retaining a low computational cost and high level of parallelization. The accurate IB method coupled with efficient AMR technique enables the simulation flows with complex (possibly moving and deforming) geometries. The library is applied to the simulation of a strong shock diffraction over a solid sphere and a detailed discussion concerning the physical results and the parallel performance obtained is presented.

Mechanism analysis and prediction of longitudinal cut wave pattern resistance based on CFD simulation

Inspired by ITTC 2021 (International Towing Tank Conference), this paper implements the Longitudinal Cut Method (LCM), a methodology to predict wave pattern resistance (Rwp), within Computational Fluid Dynamics (CFD) simulation to explore its mechanism and feasibility in predicting wave resistance (Rw). To accurately predict the free surface, a validation study, including the grid convergence index (GCI), wave profile, and wave pattern, is conducted for a Series 60 ship model. Next, Rwp is appropriately evaluated and compared with the experiment. The influence of the transverse wave component on the LCM analysis is also discussed. Furthermore, a comparison between the EFD (Experimental Fluid Dynamics) and CFD-based LCM is made through the analysis of the Wigley Catamaran, highlighting the advantages of the present approach. Finally, the limitations of the LCM theory are systematically discussed with the nonlinear bow wave analysis of a wall-sided ship model by introducing the local adaptive mesh refinement (LAMR) approach. For the fine hull form, LCM has been validated as a suitable methodology for directly predicting Rw and consequently the other primary resistance components (frictional resistance Rf and viscous pressure resistance Rpv) by one simulation. In contrast, due to energy dissipation of the non-negligible nonlinear local field wave component in the downstream wake region, Rw could be underestimated for the full hull form.

Objectivity in quasi-brittle structural failure via adaptive formulation and mesh refinement

In this work, the combined implementation of Adaptive Formulation Refinement (AFR) and Adaptive Mesh Refinement (AMR) strategies is proposed for the efficient and mesh objective evaluation of quasi-brittle fracture.A critical issue when computing localized structural failure is the spurious mesh bias dependence of the crack trajectories and collapse mechanisms that ensues when adopting the standard displacement-based finite element (FE) formulation. This problem is resolved by the introduction of the mixed strain/displacement FE formulation, which allows for local convergence, producing mesh objective results.On the one hand, the proposed AFR approach allows to adaptively switch between the standard and mixed FE formulations during the numerical simulation depending on the level of accuracy required in different regions of the domain. Within this framework, the more accurate mixed formulation is activated only in the areas where the crack onset and evolution take place, while the standard formulation is adopted for the rest of the structure.On the other hand, the adopted octree-based AMR strategy allows to adaptively refine only certain areas of the domain, also in function of the level of accuracy required. Using this methodology, it is possible to start the simulation with an initially relatively coarse mesh and adaptively introduce several levels of mesh refinement only in the regions of interest, where cracks appear and propagate. This approach guarantees the necessary mesh resolution to capture the fracture phenomenon accurately while further increasing the computational efficiency of the simulation. The subsequent adaptive coarsening of the FE mesh is also allowed.Structural failure and fracture propagation are reproduced via a local isotropic damage model. For this reason, a refinement/coarsening criterion defined in function of the equivalent effective stress is conveniently adopted with both AFR and AMR strategies.To assess the capabilities of the proposed method, a set of numerical simulations featuring benchmark problems and experiments is included. Results show the mesh objectivity and cost-efficiency of the approach combining AFR and AMR in fracture problems. The proposed model is able to reproduce experimental crack paths, collapse mechanisms and force–displacement curves with accuracy and without spurious mesh bias dependence.The paper includes a comparative assessment of the performance of the proposed method and the standard FE formulation exclusively, showing the superior performance of the AFR methodology and its mesh objectivity. Convergence of the computed results when introducing different levels of AMR is also verified. Computational efficiency of the AFR and AMR techniques is specifically assessed. The combination of AFR and AMR approaches allows to provide accurate and mesh objective results in quasi-brittle fracture problems with very significant savings in computational cost.

Local Mesh Refinement and Coarsening Based on Analysis-Suitable T-Splines Surface and Its Application in Contact Problem

AbstractIn contact analysis, reducing the computing time has been an issue under the premise of ensuring calculation accuracy around the region with violent stress changes. To improve computational efficiency for contact analysis in flexible multibody system, this paper proposes an adaptive local mesh refinement and coarsening approach based on analysis-suitable T-splines (ASTS). First, the kinematic model of thin plate is established based on analysis-suitable T-spline surface, and large deformation of flexible thin plate is described by the elastic model created by nonlinear Green–Lagrange strain. Second, to reduce computing time in contact analysis and ensure analysis accuracy, based on contact state and refinement distance, an effective adaptive local element mesh update method is proposed, which only refine locally on subject's refinement region and integrate redundant elements to reduce the degree-of-freedom (DOF) of system. Third, to analyze the system with varying mesh, a new solving algorithm with dynamic variables and geometry update routine is developed. Finally, performance of the proposed method in static and dynamic simulation is validated by four numerical examples. Results and consuming time of ASTS-based varying mesh prove the feasibility of the proposed method in contact problems.

An unstructured adaptive mesh refinement approach for computational fluid dynamics of reacting flows

A new Direct Numerical Simulation (DNS) code HAMISH with Adaptive Mesh Refinement (AMR) has been developed to simulate compressible reacting flow in a computationally economical manner. The focus is on problems where high gradients of temperature, density and species mass fraction remain localised, for example within the interior structure of flames. The resolution requirements of such local high-gradient regions often determine the global mesh spacing when uniform meshes are used. The numerical framework in HAMISH is based on an unstructured finite-volume approach together with a Runge-Kutta algorithm for time-stepping. The unstructured Cartesian mesh used in HAMISH allows for adaptive refinement and de-refinement of the local mesh depending on the demands of the flow physics and numerical accuracy. The code utilises an octree data structure and a Morton space-filling curve, allowing efficient cell division as well as straightforward parallel domain decomposition. The spatial discretisation scheme uses fourth-order polynomial reconstruction to evaluate the inter-cell fluxes. A third-order three-step explicit Runge-Kutta time-marching algorithm is used together with adaptive time-stepping with proportional-integral-type error control using an embedded Runge-Kutta scheme. The code is fully parallelised through domain decomposition over an arbitrary number of processors and exhibits a high level of parallel efficiency. In this paper the key capabilities of HAMISH are demonstrated based on a number of test cases. These test cases include (a) simulation of 1-D planar laminar premixed flames to demonstrate the capability of AMR in capturing the sharp gradients within the flame; (b) fully developed laminar channel flow, which shows that the code is capable of refining the mesh in the boundary layer next to the wall; (c) 2-D expanding flame under quiescent laminar condition, which demonstrates that the code is capable of dynamic local mesh refinement based on the position of the flame front; (d) 3-D non-reacting Taylor-Green vortex which demonstrates HAMISH can deal with vortical motion typical of turbulent flows; (e) 3-D premixed turbulent flame propagation under isotropic homogeneous decaying turbulence to demonstrate that the code can be employed for production level DNS of turbulent reacting flows.

Towards convergence of turbulent dynamo amplification in cosmological simulations of galaxies

ABSTRACT Our understanding of the process through which magnetic fields reached their observed strengths in present-day galaxies remains incomplete. One of the advocated solutions is a turbulent dynamo mechanism that rapidly amplifies weak magnetic field seeds to the order of ∼$\mu$G. However, simulating the turbulent dynamo is a very challenging computational task due to the demanding span of spatial scales and the complexity of the required numerical methods. In particular, turbulent velocity and magnetic fields are extremely sensitive to the spatial discretization of simulated domains. To explore how refinement schemes affect galactic turbulence and amplification of magnetic fields in cosmological simulations, we compare two refinement strategies. A traditional quasi-Lagrangian adaptive mesh refinement approach focusing spatial resolution on dense regions, and a new refinement method that resolves the entire galaxy with a high resolution quasi-uniform grid. Our new refinement strategy yields much faster magnetic energy amplification than the quasi-Lagrangian method, which is also significantly greater than the adiabatic compressional estimate indicating that the extra amplification is produced through stretching of magnetic field lines. Furthermore, with our new refinement the magnetic energy growth factor scales with resolution following $\propto {\Delta x}_\text{max}^{-1/2}$, in much better agreement with small-scale turbulent box simulations. Finally, we find evidence suggesting most magnetic amplification in our simulated galaxies occurs in the warm phase of their interstellar medium, which has a better developed turbulent field with our new refinement strategy.

A hybrid adaptive multiresolution approach for the efficient simulation of reactive flows

Computational studies that use block-structured adaptive mesh refinement (AMR) approaches suffer from unnecessarily high mesh resolution in regions adjacent to important solution features. This deficiency limits the performance of AMR codes. In this work a novel hybrid adaptive multiresolution (HAMR) approach to AMR-based calculations is introduced to address this issue. The multiresolution (MR) smoothness indicators are used to identify regions of smoothness on the mesh where the computational cost of individual physics solvers may be decreased by replacing direct calculations with interpolation. We suggest an approach to balance the errors due to the adaptive discretization and the interpolation of physics quantities such that the overall accuracy of the HAMR solution is consistent with that of the MR-driven AMR solution. The performance of the HAMR scheme is evaluated for a range of test problems, from pure hydrodynamics to turbulent combustion.

Block structured adaptive mesh refinement and strong form elasticity approach to phase field fracture with applications to delamination, crack branching and crack deflection

Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure. The phase field method for fracture uses a surrogate damage field to model crack propagation, eliminating the arduous need for explicit crack meshing. In this work a novel numerical framework is proposed for implementing hybrid phase field fracture in heterogeneous materials. The proposed method is based on the “reflux-free” method for solving, in strong form, the equations of linear elasticity on a block-structured adaptive mesh refinement (BSAMR) mesh. The use of BSAMR enables highly efficient and scalable regridding, facilitates the use of temporal subcycling for explicit time integration, and allows for ultra-high refinement at crack boundaries with minimal computational cost. The method is applied to a variety of simple heterogeneous structures: laminates, wavy interfaces, and circular inclusions. In each case a non-dimensionalized parameter study is performed to identify regions of behavior, varying both the geometry of the problem and the relative fracture energy release rate. In the laminate and wavy interface cases, regions of delamination and fracture correspond to simple analytical predictions. For the circular inclusions, the modulus ratio of the inclusion is varied as well as the delamination energy release rate and the problem geometry. In this case, a wide variety of behaviors was observed, including deflection, splitting, delamination, and pure fracture.

Efficient goal-oriented mesh refinement in 3-D finite-element modelling adapted for controlled source electromagnetic surveys

SUMMARY We developed a 3-D forward modelling code, which simulates controlled source electromagnetic problems in frequency domain using edge-based finite elements and a total electric field approach. To evaluate electromagnetic data acquired across complex subsurface structures, software performing accurate 3-D modelling is required, especially for incorporation in inversion approaches. Our modelling code aims at finding a good compromise between the necessary solution accuracy at the points of interest and the general problem size by using a goal-oriented mesh refinement strategy designed for models of variable electric conductivity and magnetic permeability. To formulate an improved error estimator suitable for controlled source electromagnetic problems, we developed literature approaches of mesh refinement further targeting three aspects. First, to generate a roughly homogeneously fine mesh discretization around all receiver sites, our new error estimator weights the adjoint source term by the approximate decay of the electric field with increasing distance from the primal source using the expression for a homogeneous half-space. This causes almost no additional computational cost. Second, the error estimator employed in the refinement approach can be optimized for models with pronounced conductivity and magnetic permeability contrasts as often encountered in, for example, mineral prospecting scenarios by optionally including terms that measure the continuity of the normal component of current flow and the tangential component of the magnetic field across interfaces of abutting elements. Third, to avoid amplitude-dependent over-refining of the mesh, we formulate our element-wise error estimators relative to the local amplitude of the electromagnetic field. In this work, we evaluate the implemented adaptive mesh refinement approach and its solution accuracy comparing our solutions for simple 1-D models and a model with 3-D anomalies to semi-analytic 1-D solutions and a second-order finite-element code, respectively. Furthermore, a feasibility study for controlled-source electromagnetic measurements across ferrous mineral deposits is conducted. The numerical experiments demonstrate that our new refinement procedure generates problem-specific finite-element meshes and yields accurate solutions for both simple synthetic models and realistic survey scenarios. Especially for the latter, characteristics of our code, such as the possibility of modelling extended sources as well as including arbitrary receiver distributions and detailed subsurface anomalies, are beneficial.

Numerical Simulation of Combustion Behavior of DI Diesel Engine with Conjunction of AMR and Embedding Refinement Strategies


 
 
 Currently, computational fluid dynamics has become an effective supplement to experimentation in the analysis and development of various engineering systems including internal combustion engines. In fact, multi-dimensional modelling of IC engines is less extensive and less time consuming than experimentation. In this aim, CONVERGE code was used to study the combustion behavior in a DI engine with various mesh control techniques including embedding and Adaptive Mesh Refinement (AMR). The simulation covers the compression, spray, combustion and expansion. A single spray plume and 1/6th of the combustion cylinder (60 degrees) is simulated. In light of the simulation results it is extremely recommended to use AMR approach in conjunction with embedding around the nozzle for running engine simulations.
 
 

Numerical Method for Particulate-Induced High-Speed Boundary-Layer Transition Simulations

A new numerical method to efficiently simulate particulate interactions with high-speed transitional boundary-layer flows is presented. A particulate solver, employing Crowe’s correlation, is used to calculate the particulate trajectory. The solver is fully coupled via a particulate–flow interaction source term to a nonlinear disturbance flow solver based on the compressible Navier–Stokes equations. To efficiently simulate the particulate–flow interactions, an adaptive mesh refinement approach is used to capture the wide range of temporal and spatial scales present in the laminar–turbulent transition process. The particulate impingement simulations for a flow over a 14 deg wedge and two different particulate impingement locations employing the newly developed numerical approach are compared against simulations using a conventional static-mesh approach. For the flow conditions considered, oblique first-mode instability waves dominate the early stage of the transition process. In the second part of this paper, the differences between pulse and particulate impingement simulations are investigated in two and three dimensions for a flat-plate boundary-layer flow where two-dimensional second-mode instability waves are most amplified in the primary instability regime.

Finite element procedures for computing normals and mean curvature on triangulated surfaces and their use for mesh refinement

In this paper we consider finite element approaches to computing the mean curvature vector and normal at the vertices of piecewise linear triangulated surfaces. In particular, we adopt a stabilization technique which allows for first order L2-convergence of the mean curvature vector and apply this stabilization technique also to the computation of continuous, recovered, normals using L2-projections of the piecewise constant face normals. Finally, we use our projected normals to define an adaptive mesh refinement approach to geometry resolution where we also employ spline techniques to reconstruct the surface before refinement. We compare our results to previously proposed approaches.

Numerical results for adaptive (negative norm) constrained first order system least squares formulations

We perform a followup computational study of the recently proposed space–time first order system least squares ( FOSLS ) method subject to constraints referred to as CFOSLS where we now combine it with the new capability we have developed, namely, parallel adaptive mesh refinement (AMR) in 4D. The AMR is needed to alleviate the high memory demand in the combined space time domain and also allows general (4D) meshes that better follow the physics in space–time. With an extensive set of computational experiments, performed in parallel, we demonstrate the feasibility of the combined space–time AMR approach in both two space plus time and three space plus time dimensions.

Phase-field-lattice Boltzmann simulation of dendrite motion using an immersed boundary method

A phase-field-lattice Boltzmann model (PF-LBM) coupled with immersed boundary method is developed to simulate the growth and motion of dendrites against convection. A conservative phase-field model is employed to maintain mass conservation. A parallel adaptive mesh refinement (Para-AMR) approach is developed to improve the computational efficiency. Multi-dendrite growth and motion against 3-D cavity flow is simulated and simulation results reveal the morphological transition of moving dendrites, together with collision and coalescence. The interaction between dendrite and flow is accurately restored, enabling one to grasp and understand the microstructure evolution in practical solidification condition.

Adaptive mesh refinement for simulating fluid‐structure interaction using a sharp interface immersed boundary method

SummaryIn this article, adaptive mesh refinement (AMR) is performed to simulate flow around both stationary and moving boundaries. The finite‐difference approach is applied along with a sharp interface immersed boundary (IB) method. The Lagrangian polynomial is employed to facilitate the interpolation from a coarse to a fine grid level, while a weighted‐average formula is used to transfer variables inversely. To save memory, the finest grid is only generated in the local areas close to the wall boundary, and the mesh is dynamically reconstructed based on the location of the wall boundary. The Navier‐Stokes equations are numerically solved through the second‐order central difference scheme in space and the third‐order Runge‐Kutta time integration. Flow around a circular cylinder rotating in a square domain is firstly simulated to examine the accuracy and convergence rate. Then three cases are investigated to test the validity of the present method: flow past a stationary circular cylinder at low Reynolds numbers, flow past a forced oscillating circular cylinder in the transverse direction at various frequencies, and a free circular cylinder subjected to vortex‐induced vibration in two degrees of freedom. Computational results agree well with these in the literature and the flow fields are smooth around the interface of different refinement levels. The effect of refinement level has also been evaluated. In addition, a study for the computational efficiency shows that the AMR approach is helpful to reduce the total node number and speed up the time integration, which could prompt the application of the IB method when a great near‐wall spatial resolution is required.

An adaptive mesh refinement approach based on optimal sparse sensing

We introduce a new approach for adaptive mesh refinement in which adaptivity is driven by low rank decomposition and optimal sensing of the dynamically evolving flow field. This method seeks an ordered set of locations for mesh adaptation from the instantaneous data-driven basis of an online proper orthogonal decomposition of the velocity, which organizes features into sparse optimal orthogonal modes based on an energy norm. The sensing is achieved via a computationally expedient discrete empirical interpolation method using rank-revealing QR factorization (Drmac and Gugercin SIAM J Sci Comput 38(2):A631–A648, 2016). The methodology is applicable to a wide range of numerical discretizations, and is tested on a spatiotemporally evolving incompressible turbulent jet, a complex wind turbine wake, and supersonic flow over a forward-facing step. The proposed approach is demonstrated to predict accurate velocity statistics and yield significantly smaller grids in comparison to gradient-based methods. The algorithm is seen to focus refinement in the vicinity of dynamically significant regions such as those characterized by high turbulence kinetic energy, coherent structures and shock interactions. Moreover, the approach does not require parameters or thresholds, which may be difficult to obtain for complex flows, to be known a priori to facilitate mesh adaptation.