Adaptive Mesh Method Research Articles

Numerical simulation of vapor condensation in gas-water stratified wavy pipe flow with varying interface location

When the natural gas with vapor is flowing in production pipeline, condensation occurs and leads to serious problems such as condensed liquid accumulation, pressure and flow rate fluctuations, and pipeline blockage or corrosion. The motivation is to study phase change of vapor and liquid level change during the condensing process of water-bearing natural gas characterized by coupled hydro-thermal transition and phase change process. A hydro-thermal-mass transfer coupling model is established to investigate the mechanisms and effects of the condensation on the gas-liquid two-phase wavy flow in production pipelines. The bipolar coordinate system is utilized to obtain a rectangular calculation domain. An adaptive meshing method is developed to automatically refine the grid near the wavy gas-liquid interface which is moving continuously. Large eddy simulation model is used to calculate turbulent viscosity. The pressure gradient, liquid holdup, velocity distribution, shear stress and temperature value are predicted and validated. A good agreement is achieved when compared with experimental data. During phase change process, the numerical model is well exploited to investigate mass transfer in pipeline flow. The temperature drop along the pipe leads to the reduction of gas mass flow rate and the rise of liquid level, which results in further pressure drop. Latent heat is released during the vapor condensing process which slows down the temperature drop. Larger temperature drop results in bigger liquid holdup while larger pressure drop causes smaller liquid holdup. The value of velocity with phase change is smaller than that without phase change while the temperature with phase change is higher. The highest temperature locates in gas phase. But near pipe wall the temperature of liquid region is higher than gas region. Thus, the numerical model can be widely applied to predict the pipeline operating parameters and global fluid properties which are essential to the design of downstream equipment and the guarantee of flow assurance.

High performance computation of residual stress and distortion in laser welded 301L stainless sheets

Transient thermo-mechanical simulation of stainless plate laser welding process was performed by a highly efficient and accurate approach-hybrid iterative substructure and adaptive mesh method. Especially, residual stress prediction was enhanced by considering various heat effects in the numerical model. The influence of laser welding heat input on residual stress and welding distortion of stainless thin sheets were investigated by experiment and simulation. X-ray diffraction (XRD) and contour method were used to measure the surficial and internal residual stress respectively. Effect of strain hardening, annealing and melting on residual stress prediction was clarified through a parametric study. It was shown that these heat effects must be taken into account for accurate prediction of residual stresses in laser welded stainless sheets. Reasonable agreement among residual stresses by numerical method, XRD and contour method was obtained. Buckling type welding distortion was also well reproduced by the developed thermo-mechanical FEM.

A Third Order Adaptive ADER Scheme for One Dimensional Conservation Laws

AbstractWe introduce a third order adaptive mesh method to arbitrary high order Godunov approach. Our adaptive mesh method consists of two parts, i.e., mesh-redistribution algorithm and solution algorithm. The mesh-redistribution algorithm is derived based on variational approach, while a new solution algorithm is developed to preserve high order numerical accuracy well. The feature of proposed Adaptive ADER scheme includes that 1). all simulations in this paper are stable for large CFL number, 2). third order convergence of the numerical solutions is successfully observed with adaptive mesh method, and 3). high resolution and non-oscillatory numerical solutions are obtained successfully when there are shocks in the solution. A variety of numerical examples show the feature well.

A New Adaptive Mesh Refinement Method in FEA Based on Magnetic Field Conservation at Elements Interfaces and Non-Conforming Mesh Refinement Technique

Mesh quality strongly affects the solution accuracy in electromagnetic finite-element analysis. Hence, the realization of adequate mesh generation becomes a very important task. Several adaptive meshing methods for automatic adjustments of the mesh density in accordance with the shape and complexity of the analyzed problem have been proposed. However, the most of them are not enough robust, some are quite laborious and could not be universally used for adaptive meshing of complex analysis models. In this paper, a new adaptive mesh refinement method based on magnetic field conservation at the border between finite elements is proposed. The proposed error estimation method provides easy mesh refinements, and generates smaller element within regions with large curvature of the magnetic flux lines. The proposed adaptive mesh refinement method based on non-conforming edge finite elements, which could avoid generation of flat or ill-shaped elements, was applied to a simple magnetostatic permanent magnet model. To confirm the validity and accuracy, the obtained results were compared with those obtained by means of the Zienkiewicz-Zhu (ZZ) error estimator. The results show that the computational error using the proposed method was reduced down to 1% compared with that of the ZZ method, which yields error of 8.6%, for the same model.

A parallel Self Mesh-Adaptive N-body method based on approximate inverses

A new parallel Self Mesh-Adaptive N-body method based on approximate inverses is proposed. The scheme is a three-dimensional Cartesian-based method that solves the Poisson equation directly in physical space, using modified multipole expansion formulas for the boundary conditions. Moreover, adaptive-mesh techniques are utilized to form a class of separate smaller n-body problems that can be solved in parallel and increase the total resolution of the system. The solution method is based on multigrid method in conjunction with the symmetric factored approximate sparse inverse matrix as smoother. The design of the parallel Self Mesh-Adaptive method along with discussion on implementation issues for shared memory computer systems is presented. The new parallel method is evaluated through a series of benchmark simulations using N-body models of isolated galaxies or galaxies interacting with dwarf companions. Furthermore, numerical results on the performance and the speedups of the scheme are presented.

A versatile embedded boundary adaptive mesh method for compressible flow in complex geometry

We present an embedded ghost fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost fluid regions and imposing boundary conditions on the fluid–solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The CNS equations are numerically solved by the second order multidimensional upwind method. Block-structured adaptive mesh refinement, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the embedded boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible flows to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.

An enthalpy method based on fixed-grid for quasi-steady modeling of solidification/melting processes of pure materials

We propose a quasi-steady enthalpy method based on fixed-grid to consider the latent heat of phase change during a solidification/melting process of a pure material. The latent heat of phase change released or absorbed at the solid-liquid interface disperses into a region at the interface in the proposed method. It is validated through comparing to the solutions obtained with the adaptive mesh method which is commonly accepted for its accuracy in modeling solidification/melting processes for pure materials. The effects of the dispersed region size and the phase change rate on the simulation accuracy of the proposed method are investigated. Based on the proposed method, a general form of the distribution function of the latent heat of phase change is proposed. The distribution of the latent heat of phase change in the dispersed region is controlled by selecting different forms of distribution function to improve the simulation accuracy. The selecting principle of the distribution function is proposed on the basis of concentrating the latent heat of phase change at the solid-liquid interface. By following the selecting principle, the accuracy can be controlled and the size of the dispersed region does not need to be determined in advance. Two distribution functions of the latent heat of phase change are investigated. Results show that the proper concentration of the latent heat of phase change at the solid-liquid interface is favorable for the simulation accuracy.

Moving Mesh Finite Element Method for Unsteady Navier-Stokes Flow

AbstractIn this paper, we use moving mesh finite element method based upon 4P1–P1 element to solve the time-dependent Navier-Stokes equations in 2D. Two-layer nested meshes are used including velocity mesh and pressure mesh, and velocity mesh can be obtained by globally refining pressure mesh. We use hierarchy geometry tree to store the nested meshes. This data structure make convienence for adaptive mesh method and the construction of multigrid preconditioning. Several numerical problems are used to show the effect of moving mesh.

The adaptive mesh method based on HOC difference scheme for convection diffusion equations with boundary layers

In this paper, an adaptive mesh method is proposed to generate orthogonal nonuniform mesh for 2D rectangular computational domain. The algorithm adopts the dimension split idea which redistribute the mesh on each direction sequently. This approach efficiently decreases the difficultly of algorithm and enables the adapted mesh to be orthogonal. The adaptive mesh method can redistribute the mesh based on the solution without specifying the location of the boundary layer or the grid distribution function to generate the nonuniform mesh in advance. To verify the effectiveness and robustness of the algorithm, the presented method combined with the HOC difference scheme on nonuniform grid is used to solve the 1D and 2D convection diffusion problems with boundary layers. Besides, the multigrid method is used to accelerate the iterative convergence speed. The numerical solutions of adaptive mesh is more flexible than uniform or nonuniform grids methods if the location of the boundary layers is unknown in advance.

A Self-Adaptive Numerical Method to Solve Convection-Dominated Diffusion Problems

Convection-dominated diffusion problems usually develop multiscaled solutions and adaptive mesh is popular to approach high resolution numerical solutions. Most adaptive mesh methods involve complex adaptive operations that not only increase algorithmic complexity but also may introduce numerical dissipation. Hence, it is motivated in this paper to develop an adaptive mesh method which is free from complex adaptive operations. The method is developed based on a range-discrete mesh, which is uniformly distributed in the value domain and has a desirable property of self-adaptivity in the spatial domain. To solve the time-dependent problem, movement of mesh points is tracked according to the governing equation, while their values are fixed. Adaptivity of the mesh points is automatically achieved during the course of solving the discretized equation. Moreover, a singular point resulting from a nonlinear diffusive term can be maintained by treating it as a special boundary condition. Serval numerical tests are performed. Residual errors are found to be independent of the magnitude of diffusive term. The proposed method can serve as a fast and accuracy tool for assessment of propagation of steep fronts in various flow problems.

A novel surface mesh deformation method for handling wing-fuselage intersections

This paper describes a method for mesh adaptation in the presence of intersections, such as wing-fuselage. Automatic optimization tools, using Computational Fluid Dynamics (CFD) simulations, face the problem to adapt the computational grid upon deformations of the boundary surface. When mesh regeneration is not feasible, due to the high cost to build up the computational grid, mesh deformation techniques are considered a cheap approach to adapt the mesh to changes on the geometry. Mesh adaptation is a well-known subject in the literature; however, there is very little work which deals with moving intersections. Without a proper treatment of the intersections, the use of automatic optimization methods for aircraft design is limited to individual components. The proposed method takes advantage of the CAD description, which usually comes in the form of Non-Uniform Rational B-Splines (NURBS) patches. This paper describes an algorithm to recalculate the intersection line between two parametric surfaces. Then, the surface mesh is adapted to the moving intersection in parametric coordinates. Finally, the deformation is propagated through the volumetric mesh. The proposed method is tested with the DLR F6 wing-body configuration.

Towards quantitative mesh pre-optimization for finite element analysis

ABSTRACTIn a previous research work, we introduced the concept of automatic mesh pre-optimization, also referred to as a priori mesh adaptation. Indeed, the basic idea underlying mesh pre-optimization is providing finite element analysis with meshes that have been adapted before analysis itself. It consists in automatically deriving mesh sizing functions from geometric features of the analysis domain. This allows providing the analyst with meshes that feature a certain degree of adaptation around sensitive zones or sensitive shapes (high curvature zones, narrow regions, sources of stress concentration, etc.) before any analysis, which also means before any a posteriori mesh adaptation. So far, mesh pre-optimization could not be considered as a quantitative adaptation since it does not explicitly target accuracy objectives, contrary to a posteriori mesh adaptation methods. This paper brings about new concepts in mesh pre-optimization that tend to make pre-optimization not only qualitative. It shows that, f...

Macroscopic Model for Head-On Binary Droplet Collisions in a Gaseous Medium.

In this Letter, coalescence-bouncing transitions of head-on binary droplet collisions are predicted by a novel macroscopic model based entirely on fundamental laws of physics. By making use of the lubrication theory of Zhang and Law [Phys. Fluids 23, 042102 (2011)], we have modified the Navier-Stokes equations to accurately account for the rarefied nature of the interdroplet gas film. Through the disjoint pressure model, we have incorporated the intermolecular van der Waals forces. Our model does not use any adjustable (empirical) parameters. It therefore encompasses an extreme range of length scales (more than 5 orders of magnitude): from those of the external flow in excess of the droplet size (a few hundred μm) to the effective range of the van der Waals force around 10nm. A state of the art moving adaptive mesh method, capable of resolving all the relevant length scales, has been employed. Our numerical simulations are able to capture the coalescence-bouncing and bouncing-coalescence transitions that are observed as the collision intensity increases. The predicted transition Weber numbers for tetradecane and water droplet collisions at different pressures show good agreement with published experimental values. Our study also sheds new light on the roles of gas density, droplet size, and mean free path in the rupture of the gas film.

Anisotropic mesh adaptation for image representation

Triangular meshes have gained much interest in image representation and have been widely used in image processing. This paper introduces a framework of anisotropic mesh adaptation (AMA) methods to image representation and proposes a GPRAMA method that is based on AMA and greedy-point removal (GPR) scheme. Different than many other methods that triangulate sample points to form the mesh, the AMA methods start directly with a triangular mesh and then adapt the mesh based on a user-defined metric tensor to represent the image. The AMA methods have clear mathematical framework and provide flexibility for both image representation and image reconstruction. A mesh patching technique is developed for the implementation of the GPRAMA method, which leads to an improved version of the popular GPRFS-ED method. The GPRAMA method can achieve better quality than the GPRFS-ED method but with lower computational cost.

Mono‐block and non‐matching multi‐block structured mesh adaptation based on aerodynamic functional total derivatives for RANS flow

SummaryAn enhanced goal‐oriented mesh adaptation method is presented based on aerodynamic functional total derivatives with respect to mesh nodes in a Reynolds‐Averaged Navier‐Stokes (RANS) finite‐volume mono‐block and non‐matching multi‐block‐structured grid framework. This method falls under the category of methods involving the adjoint vector of the function of interest. The contribution of a Spalart–Allmaras turbulence model is taken into account through its linearization. Meshes are adapted accordingly to the proposed indicator. Applications to 2D RANS flow about a RAE2822 airfoil in transonic, and detached subsonic conditions are presented for the drag coefficient estimation. The asset of the proposed method is patent. The obtained 2D anisotropic mono‐block mesh well captures flow features as well as global aerodynamic functionals. Interestingly, the constraints imposed by structured grids may be relaxed by the use of non‐matching multi‐block approach that limits the outward propagation of local mesh refinement through all of the computational domain. The proposed method also leads to accurate results for these multi‐block meshes but at a fraction of the cost. Finally, the method is also successfully applied to a more complex geometry, namely, a mono‐block mesh in a 3D RANS transonic flow about an M6 wing. Copyright © 2016 John Wiley & Sons, Ltd.

Optimal mass transport-based adaptive mesh method for phase-field models of two-phase fluid flows

In this paper, we present an efficient adaptive mesh method for solving phase-field model of a mixture of two-phase incompressible fluid flows. The adaptive mesh is generated by a coordinate transformation that is determined as the solution of the classical problem of the optimal mass transportation, also known as Monge–Kantorovich problem (MKP). The numerical solution of the MKP is computed by taking the gradient of the steady state solution of a parabolic Monge–Ampère equation (PMAE). Several numerical experiments are conducted to demonstrate the performance of the PMAE method for solving phase-field models. The numerical results illustrate that the adaptive mesh computed with PMAE method captures well the moving interface of the phase-field function.

Simulation of Flow Past a Cylinder With Adaptive Spectral Element Method

AbstractThe simulations of flow past a two-dimensional circular cylinder are conducted to investigate the feasibility of adaptive mesh refinement applied on curved spectral elements. The nonconforming spectral element method and adaptive meshes technique are used to the curve surfaces and observe whether any discontinuity of the solutions. The adaptive nonconforming spectral element method is implemented to compare with those obtained by conforming mesh method with respect to several existing numerical and experimental studies. Meanwhile, three kinds of estimated error base mesh adaptation are conducted to compare their accuracy and efficiency with conforming mesh method. The results show adaptive nonconforming mesh method is more efficient than the conforming method. Especially, the vorticity error based method performs highest accuracy and fastest convergence. The results show this mesh refinement technique is applicable on the curved elements with satisfactory accuracy. It releases this technique may be applied on the simulations of flow past objects with more general geometries.

On optimal simplicial 3D meshes for minimizing the Hessian-based errors

In this paper we derive a multi-dimensional mesh adaptation method which produces optimal meshes for quadratic functions, positive semi-definite. The method generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the tensor metric being computed based on interpolation error estimates. It does not depend, a priori, on the PDEs at hand in contrast to residual methods. The estimated error is then used to steer local modifications of the mesh in order to reach a prescribed level of error in Lp-norm or a prescribed number of elements. The Lp-norm of the estimated error is then minimized in order to get an optimal mesh. Numerical examples in 2D and 3D for analytic challenging problems and an application to a Computational Fluid Dynamics problem are presented and discussed in order to show how the proposed method recovers optimal convergence rates as well as to demonstrate its computational performance.

Topology optimization of incompressible Navier–Stokes problem by level set based adaptive mesh method

This paper presents a level set based adaptive mesh method for solving the topology optimization of incompressible Navier–Stokes problem. The objective is to minimize the dissipated power in the fluid, subject to the Navier–Stokes problem as state equations with a fluid volume constraint. The material distribution information that implicitly represented via level set function is considered as the design variable, which provides an easy way to construct the refinement indicator. Shape and topology sensitivity analysis suggest the steepest descent direction. By the proposed method, the computational expense is mainly focused near the interfaces, which lead to a significant reduction of the computational cost. Although illustrated by the Navier–Stokes problem, we would like to emphasize that our method is not restricted to this particular situation, it can be applied to a wide range of shape or topology optimization problems arising from the fluid dynamics.

Conditional ε-uniform boundedness of Galerkin projectors and convergence of an adaptive mesh method as applied to singularly perturbed boundary value problems

The Galerkin finite element method is applied to nonself-adjoint singularly perturbed boundary value problems on Shishkin meshes. The Galerkin projection method is used to obtain conditionally e-uniform a priori error estimates and to prove the convergence of a sequence of meshes in the case of an unknown boundary layer edge.