Adaptive Mesh Method Research Articles

A dual-mesh method for efficient thermal stress analysis of large-scale welded structures

Transient thermo-mechanical analysis of welding problem requires tremendous computation cost. To accelerate the thermal analysis of large-scale welded structures, an efficient computation scheme based on heat transfer localization and dual meshes was proposed. The computation accuracy is guaranteed by a local fine mesh model with size determined by a theoretical solution and a global coarse mesh model with equivalent heat input. The validity and accuracy of the dual-mesh method were verified using an experimental bead-on-plate model. By extending the weld length, the computation time of the proposed method was proved to be almost linearly dependent on the model scale. The thermal analysis of fillet welding of a large panel structure with 6-m-long weld was accelerated by 10 times over conventional finite element analysis and 2.2 times over adaptive mesh method. Meanwhile, the physical memory consumption was also greatly reduced by the dual-mesh method. Such efficient computation method enables fast evaluation of welding stress and distortion which are vital for manufacturing process and structure performance.

Optimal radio resource allocation to achieve a low BER in PD‐NOMA–based heterogeneous cellular networks

AbstractIn this paper, the problem of downlink radio resource allocation for a power‐domain nonorthogonal multiple‐access–based heterogeneous cellular network is investigated. We propose two scenarios: (1) resource allocation with exclusive subcarrier allocation and (2) resource allocation considering intercell interference. The aim of this paper is to obtain joint subcarrier and power allocation for the two considered system models by addressing the maximization of the users' sum rate subject to the bit error rate constraint, the successive interference cancellation constraint, subcarrier constraints, and the transmit power restriction of each base station. To solve the corresponding optimization problems, an alternating method is applied by decoupling the proposed problems into two subproblems, namely, subcarrier allocation problem and power allocation problem, where they are solved by using the mesh adaptive direct search algorithm and different successive convex approximation methods, respectively. Moreover, to evaluate the optimality gap of the alternating method, the proposed problems are solved using an optimal method, namely, monotonic optimization with high complexity as a benchmark. As the results show, with the bit error rate constraint, the link‐level performance, at the cost of a decreasing system sum rate, is improved.

An adaptive mesh method for time dependent singularly perturbed differential-difference equations

AbstractIn this paper, a time dependent singularly perturbed differential-difference convection-diffusion equation is solved numerically by using an adaptive grid method. Similar boundary value problems arise in computational neuroscience in determination of the behaviour of a neuron to random synaptic inputs. The mesh is constructed adaptively by using the concept of entorpy function. In the proposed scheme, prior information of the width and position of the layers are not required. The method is independent of perturbation parameterεand gives us an oscillation free solution, without any user introduced parameters. Numerical examples are presented to show the accuracy and efficiency of the proposed scheme.

A numerical model for continuous impact pile driving using ALE adaptive mesh method

Pile installation through consecutive hammer impacts is called impact pile driving which has increasingly exploited as the most efficient method, though the generated ground vibrations have great potential to undermine its surrounding structures. However, correct numerical simulation of pile driving process to credibly predict the ground vibrations has been the main problem to date. Hence, to significantly improve the predictions of ground vibrations, a continuous pile driving model from the ground surface to final installation depth, unlike previous common discontinuous pile driving, was employed using an arbitrary Lagrangian-Eulerian (ALE) adaptive mesh method, accurate simulation of the pile-soil interaction, and elimination of previous researchers simplified assumptions. The results were verified with field measurements which indicate a remarkably better match compared to the previous numerical studies. Moreover, an elastic pile consideration rather than rigid conditions was led to a better consistency of the ground vibration results with field measurements.

Improving the Rotational Stiffness of Compact Aerostatic Guideway by Micro-Structures Optimization

To meet the requirement for the exact computation of rotational stiffness, this paper puts forward a mesh adaptation based analysis method for a compact multi-throttle aerostatic guideway and its constituent micro-structure. Contrary to previous methods that substituted or even ignored them, the dimensionless thickness pertaining to the depth of the micro-structure is restored and incorporated into each computational grids. The mesh adaptation procedures accept the dimensionless thickness as an intermediate variable for the target mesh and apply local modifications to adapt the mesh to match the specified size. Then, the varying regularity of rotational stiffness by micro-structures can be studied by k- $\varepsilon $ turbulence model when tilt. The tilt angle, although small, leads to a wedge-shaped film and then an uneven pressure distribution which has been also taken into consideration. Guided by the mesh adaptation method, a vertical compact guideway with high rotational stiffness of $7.22\times 10^{3}$ Nm/rad is designed and manufactured for photolithography. The experiments verify its practical accuracy and effectiveness.

Mesh Adaptation Method for Optimal Control With Non-Smooth Control Using Second-Generation Wavelet

A mesh adaptation method is proposed for solving optimal control problems with non-smooth control. The original optimal control problem (OCP) is transcribed into a nonlinear programming (NLP) problem by using the Runge-Kutta discretization method, in which the NLP can be solved by using standard nonlinear programming codes. The method employs collocations from the dyadic background points, which used for the second-generation wavelet (SGW) translation simultaneously. The SGW is used to approximate the control variables and get the wavelet coefficients once they are obtained. In regions contain discontinuities, the magnitude of the relevant wavelet coefficients is large than other regions. The corresponding dyadic background points are reserved as the collocation points. Furthermore, the approximation error of the control and/or state variables can be predicted by a given threshold. Thus, the accuracy and efficiency can be balanced in a simple way. Finally, the method is demonstrated by three numerical examples from the open literature.

Adaptive Solution to Two-Dimensional Partial Differential Equations in Curved Domains Using the Monge--Ampére Equation

We present a finite difference method for mesh generation and adaptation with application to the solution of partial differential equations in curved domains. For mesh generation, we construct a ma...

An Adaptive Moving Mesh Method for Forced Curve Shortening Flow.

We propose a novel adaptive moving mesh method for the numerical solution of a forced curve shortening geometric evolution equation. Control of the mesh quality is obtained using a tangential mesh velocity derived from a mesh equidistribution principle, where a positive adaptivity measure or monitor function is approximately equidistributed along the evolving curve. Central finite differences are used to discretize in space the governing evolution equation for the position vector, and a second-order implicit scheme is used for the temporal integration. Simulations are presented indicating the generation of meshes which resolve areas of high curvature and are of second-order accuracy. Furthermore, the new method delivers improved solution accuracy compared to the use of uniform arc-length meshes.

Supercomputer Simulations of Fluid-Structure Interaction Problems Using an Immersed Boundary Method

The paper describes a supercomputer application in simulations of fluid-structure interaction problems. A compressible flow solver based on a high-accuracy scheme for unstructured hybrid meshes is considered. It combines an immersed boundary method with a dynamic mesh adaptation method in order to represent motion of solid objects in a turbulent flow. The use of immersed boundaries allows you to dynamically adapt the mesh resolution near moving solid surfaces without changing the mesh topology. Multilevel MPI + OpenMP parallelization of these components fits well with the architecture of modern cluster systems. The proposed implementation can engage thousands of CPU cores in one simulation efficiently. An example application is presented in which a high-speed turbulent flow around a cavity with a deflector is simulated.

Numerical simulation of floods from multiple sources using an adaptive anisotropic unstructured mesh method

The coincidence of two or more extreme events (precipitation and storm surge, for example) may lead to severe floods in coastal cities. It is important to develop powerful numerical tools for improved flooding predictions (especially over a wide range of spatial scales - metres to many kilometres) and assessment of joint influence of extreme events. Various numerical models have been developed to perform high-resolution flood simulations in urban areas. However, the use of high-resolution meshes across the whole computational domain may lead to a high computational burden. More recently, an adaptive isotropic unstructured mesh technique has been first introduced to urban flooding simulations and applied to a simple flooding event observed as a result of flow exceeding the capacity of the culvert during the period of prolonged or heavy rainfall. Over existing adaptive mesh refinement methods (AMR, locally nested static mesh methods), this adaptive unstructured mesh technique can dynamically modify (both, coarsening and refining the mesh) and adapt the mesh to achieve a desired precision, thus better capturing transient and complex flow dynamics as the flow evolves.In this work, the above adaptive mesh flooding model based on 2D shallow water equations (named as Floodity) has been further developed by introducing (1) an anisotropic dynamic mesh optimization technique (anisotropic-DMO); (2) multiple flooding sources (extreme rainfall and sea-level events); and (3) a unique combination of anisotropic-DMO and high-resolution Digital Terrain Model (DTM) data. It has been applied to a densely urbanized area within Greve, Denmark. Results from MIKE 21 FM are utilized to validate our model. To assess uncertainties in model predictions, sensitivity of flooding results to extreme sea levels, rainfall and mesh resolution has been undertaken. The use of anisotropic-DMO enables us to capture high resolution topographic features (buildings, rivers and streets) only where and when is needed, thus providing improved accurate flooding prediction while reducing the computational cost. It also allows us to better capture the evolving flow features (wetting-drying fronts).

Mesh Optimization for Discontinuous Galerkin Methods Using a Continuous Mesh Model

A method for anisotropic mesh adaptation and optimization for high-order discontinuous Galerkin schemes is presented. Given the total number of degrees of freedom, a metric-based method is proposed, which aims to globally optimize the mesh with respect to the norm of the error. This is done by minimizing a suitable error model associated with the approximation space. Advantages of using a metric-based method in this context are several. First, it facilitates changing and manipulating the mesh in a general anisotropic way. Second, defining a suitable continuous interpolation operator allows the use of an analytic optimization framework that operates on the metric field, rather than the discrete mesh. The formulation of the method is presented as well as numerical experiments in the context of convection–diffusion systems.

A mesh adaptive method for dynamic well stimulation

We utilize the adaptive meshing features of an asynchronous spacetime discontinuous Galerkin (aSDG) FE method to address rock fracturing in reservoir stimulations under high rate loadings. Our aSDG implementation adaptively aligns the element boundaries with crack-path trajectories obtained as a part of the solution and no discontinuous features are introduced within the elements. We propose a novel rate-dependent interfacial damage model to represent fracture processes on crack surfaces while the model incorporates various contact modes under transient settings. Several examples are discussed to demonstrate the effectiveness of our approach in resolving dynamic fracturing driven by the high internal fluid pressure.

A Moving Mesh Method for Mathematical Model of Capillary Formation in Tumor Angiogenesis

Using adaptive mesh methods is one of the strategies to improve numerical solutions in time-dependent partial differential equations. Moving mesh method is an adaptive mesh method. In this method, an increase in the number of mesh points is not needed for increasing the accuracy and efficiency of numerical solutions. Highly accurate solutions only can be obtained by concentrating points in areas where more accuracy is needed and decreasing the number of points in smooth areas. In this paper, moving mesh method is applied for the mathematical model of capillary formation in tumor angiogenesis. Numerical results show that this method leads to stable solutions for large values of cell diffusion coefficient in addition to enjoying necessary accuracy and efficiency.

Adaptive mesh method applied to the thermal hydraulic program of system code with a judging criterion based on the matrix error

In this paper, an adaptive mesh method is described and applied to the one-dimension thermal hydraulic program in a system code for simulating the two-phase flow problems. The adaptive mesh method has been widely used to solve various engineering problems, but it is still rarely applied in existing thermal hydraulic system codes which are of great significance for reactor design and analysis. Compared with the uniform mesh, the mesh size could be adjusted automatically. It is helpful to locate the discontinuity points or deal with the large gradient solutions with this method, especially for some local phenomena that occur in phase transfer or two phase flow problems. Based on it, the computational accuracy and efficiency are improved, when solving the partial difference equations. The applicability of the adaptive mesh method in a system code is a major issue, and the first step is studying the feasibility of the adaptive mesh method in thermal hydraulic programs. In this paper, the finite volume method and the Newton-Raphson algorithm are applied in the code as the numerical method of two-fluid model. Furthermore, the code also includes heat transfer models, friction models and a flow regime map, which are important in simulating hydraulic phenomena. Depending on the algorithm, a judging criterion for determining the location where mesh refinement is needed is proposed. Three typical numerical examples are given to verify the feasibility and effectiveness of the adaptive mesh algorithm in solving the one-dimension two-phase flow problems of local phenomena and show great agreement with theoretical or experiment results.

Tetrahedral mesh adaptation for Lagrangian shock hydrodynamics

Lagrangian shock hydrodynamics simulations will fail to proceed past a certain time if the mesh is approaching tangling. A common solution is an Arbitrary Lagrangian Eulerian (ALE) form, in which the mesh is improved (remeshing) and the solution is remapped onto the improved mesh. The simplest remeshing techniques involve moving only the nodes of the mesh. More advanced remeshing techniques involve altering the mesh connectivity in portions of the domain in order to prevent tangling. Work has been done using Voronoi-based polygonal mesh generators and 2D quad/triangle mesh adaptation. This paper presents the use of tetrahedral mesh adaptation methods as the remeshing step in an otherwise Lagrangian finite element shock hydrodynamics code called Alexa.

A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4 with an application to the thermocline oscillations of Lake Tanganyika

Abstract. The discontinuous Galerkin (DG) finite element method is well suited for the modelling, with a relatively small number of elements, of three-dimensional flows exhibiting strong velocity or density gradients. Its performance can be highly enhanced by having recourse to r-adaptivity. Here, a vertical adaptive mesh method is developed for DG finite elements. This method, originally designed for finite difference schemes, is based on the vertical diffusion of the mesh nodes, with the diffusivity controlled by the density jumps at the mesh element interfaces. The mesh vertical movement is determined by means of a conservative arbitrary Lagrangian–Eulerian (ALE) formulation. Though conservativity is naturally achieved, tracer consistency is obtained by a suitable construction of the mesh vertical velocity field, which is defined in such a way that it is fully compatible with the tracer and continuity equations at a discrete level. The vertically adaptive mesh approach is implemented in the three-dimensional version of the geophysical and environmental flow Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM 3D; www.climate.be/slim). Idealised benchmarks, aimed at simulating the oscillations of a sharp thermocline, are dealt with. Then, the relevance of the vertical adaptivity technique is assessed by simulating thermocline oscillations of Lake Tanganyika. The results are compared to measured vertical profiles of temperature, showing similar stratification and outcropping events.

A fast framework construction and visualization method for particle-based fluid

Fast and vivid fluid simulation and visualization is a challenge topic of study in recent years. Particle-based simulation method has been widely used in the art animation modeling and multimedia field. However, the requirements of huge numerical calculation and high quality of visualization usually result in a poor computing efficiency. In this work, in order to improve those issues, we present a fast framework for 3D fluid fast constructing and visualization which parallelizes the fluid algorithm based on the GPU computing framework and designs a direct surface visualization method for particle-based fluid data such as WCSPH, IISPH, and PCISPH. Considering on conventional polygonization or adaptive mesh methods may incur high computing costs and detail losses, an improved particle-based method is provided for real-time fluid surface rendering with the screen-space technology and the utilities of the modern graphics hardware to achieve the high performance rendering; meanwhile, it effectively protects fluid details. Furthermore, to realize the fast construction of scenes, an optimized design of parallel framework and interface is also discussed in our paper. Our method is convenient to enforce, and the results demonstrate a significant improvement in the performance and efficiency by being compared with several examples.

Finite element wear prediction using adaptive meshing at the modular taper interface of hip implants.

The use of modular components in total hip arthroplasty introduced an additional interface with the potential for fretting and corrosion to occur. Fretting and corrosion at this interface have been reported as a potential cause of early failure of the implant system. Using finite element (FE) analyses the mechanics at the taper junction can be studied. However, most FE studies are based on a single load condition and do not take geometry changes over time into account. Therefore, in this study an FE routine was developed, in which adaptations to the implant geometry are made to account for material removal during the fretting process. Material removal was simulated based on Archard's Law, incorporating contact pressure, micromotions and a wear factor which used input from in vitro fretting tests. A wear factor of 2.7*10-5mm3/Nmm was used to match the FE predicted volumetric wear to the measured experimental volumetric wear of 0.79mm3 after 10 million cycles. The maximum experimental wear depth found was 30.5 ± 17µm, while the FE predicted a maximum wear depth of 27µm. The adaptive meshing method has delivered results that are more similar to the experimental test data in comparison to the results from modelling a single cycle without adaptive meshing.

On the mesh nonsingularity of the moving mesh PDE method

The moving mesh PDE (MMPDE) method for variational mesh generation and adaptation is studied theoretically at the discrete level, in particular the nonsingularity of the obtained meshes. Meshing functionals are discretized geometrically and the MMPDE is formulated as a modified gradient system of the corresponding discrete functionals for the location of mesh vertices. It is shown that if the meshing functional satisfies a coercivity condition, then the mesh of the semi-discrete MMPDE is nonsingular for all time if it is nonsingular initially. Moreover, the altitudes and volumes of its elements are bounded below by positive numbers depending only on the number of elements, the metric tensor, and the initial mesh. Furthermore, the value of the discrete meshing functional is convergent as time increases, which can be used as a stopping criterion in computation. Finally, the mesh trajectory has limiting meshes which are critical points of the discrete functional. The convergence of the mesh trajectory can be guaranteed when a stronger condition is placed on the meshing functional. Two meshing functionals based on alignment and equidistribution are known to satisfy the coercivity condition. The results also hold for fully discrete systems of the MMPDE provided that the time step is sufficiently small and a numerical scheme preserving the property of monotonically decreasing energy is used for the temporal discretization of the semi-discrete MMPDE. Numerical examples are presented.

Toward the design of a novel hybrid parallel N-body method in scope of modern cloud architectures

A hybrid parallel self mesh-adaptive N-body method based on approximate inverses and multiprojection techniques is proposed. This method is a three-dimensional hybrid parallel mesh-type N-body scheme based on the solution of the Poisson equation in the physical space with boundary conditions obtained from multipole expansion formulas. In order to improve the accuracy of the solution, especially in shallow regions, a self mesh-adaptive scheme is used to create a hierarchy of independent smaller N-body problems. The parallelization of the scheme is based on a uniform partitioning of the bodies with respect to available computer nodes, and communications are required only for the computation of the density and potential distributions. The proposed scheme is suitable for large-scale galaxy simulations with millions of bodies on high-resolution meshes, for distributed HPC systems with multicore computer nodes. Moreover, large-scale galaxy simulations are performed on modern Cloud environments in order to examine the applicability and performance. Implementation issues concerning the proposed scheme are also discussed. The parallel performance and speedup of the hybrid parallel N-body method on HPC systems as well as on Cloud environments are presented and discussed.