Mesh Deformation Method Research Articles

CFD simulations on the wind and thermal environment in urban areas with complex terrain under calm conditions

Cities experience the most severe hot and polluted environment under calm conditions. To understand how complex urban terrain affects the wind and thermal environment, a city scale simulation was conducted with CFD (Computational Fluid Dynamics) and field transformation method to analyze the urban heat island circulations. A multi-layer refinement and mesh deformation methods were used to generate high-resolution terrain-fitted mesh. The complex urban terrain was composed of idealized hills and ridges. The simulations show that the urban center area is 3 ∼ 4 °C warmer than the urban edge areas, although the surface heat flux remains the same in all urban areas. The hills and ridges in cities intensify the warming effect in the center area by blocking horizontal convergence flow. The strong updraft flows above the hills and ridges acts as a wall and blocks the horizontal flow, generating multiple convection cells between hills and ridges. These split cells cause stripes-like, snowflake-like, and hairpin high-temperature zone. Natural hills and ridges more effectively reduce the near-ground temperature and the high-temperature area than built-up hills and ridges. This model is used to simulate the wind and thermal environments in real urban areas and shows good practical applicability.

A new mesh deformation method using quaternion and displacement normal propagation for high quality and high efficiency

Mesh deformation technology is widely used in aerodynamic applications like unsteady flow, aeroelasticity, and aerodynamic shape optimization because of its low computational costs and consistent mesh connectivity. In order to raise deformed mesh quality and improve efficiency, a new mesh deformation method based on quaternion and displacement normal propagation (named QN method) is introduced in this paper. The boundary points propagate their displacements composed of translational vectors and quaternions to corresponding volume points along the normal direction under the control of the damping function, which preserves the mesh shape and guarantees the quality near boundaries, including orthogonality and normal size. It can also prevent the volume points from being interfered by other less relevant boundary points, so dealing with complex displacement fields effectively. In addition, it avoids complicated matrix and interpolation operations, thus saving lots of computational costs. For mesh with complex topology, a hybrid method combining the QN method and the radial basis function method (RBF method) is investigated to broaden application scenarios, which are applied to the mesh with normal correspondence inside the boundary layer and the mesh outside, respectively. Benefitting from effective handling for the near-wall elements by the QN method, the RBF interpolation part in the hybrid method requires minor support points to carry out valid large deformation, improving the deformation efficiency greatly compared to the individual RBF method. Five typical test cases with different deformation modes and mesh characteristics are implemented, showing better performance of the proposed method in deformed mesh quality and deformation efficiency.

Application of deep learning reduced-order modeling for single-phase flow in faulted porous media

Our research is positioned within the framework of subsurface resource utilization for sustainable economies. We concentrate on modeling the underground single-phase fluid flow affected by geological faults using numerical simulations. The study of such flows is characterized by strong uncertainites in the data defing the problem due to the difficulty of taking precise measurements in the subsoil. We aim to demonstrate the feasibility of a reduced order model that is both reliable and computationally efficient, thereby facilitating the incorporation of uncertainties. We account for the uncertainities of the properties of the rock and the geometry of the fault. The latter is achieved by using a radial basis function mesh deformation method. This approach benefits from a mixed-dimensional framework to model the rock matrix and faults as n and n-1 dimensional domains, allowing for non-conforming meshes. Our primary focus is on a reduced-order model capable of reproducing flow variables across the entire domain. We utilize the Deep Learning Reduced Order Model (DL-ROM), a nonintrusive neural network-based technique, and we compare it against the traditional Proper Orthogonal Decomposition (POD) method across various scenarios. The most relevant contributions of this work are: the proof of concept of the use of neural network for reduced order models for subsoil flow, dealing with non-affine problems and mixed dimensional domain. Additionally, we generalize an existing mesh deformation method for discontinuous deformation maps. Our analysis highlights the capability of reduced order model, highlighting DL-ROM’s capacity to expedite complex analyses with promising accuracy and efficiency, making multi-query analyses with various quantities of interest affordable.

Numerical optimisation of the active lift turbines using OpenFoam's overset method

This work presents a preliminary study of the numerical optimization of "active lift turbine" using computational fluid dynamics (CFD). This active lift turbine is designed to improve efficiency of vertical axis energy recovery turbines (wind and tidal turbines). It uses a crank rod system to convert normal forces into momentum in order to improve the yield.
 After a validation work of CFD model in two dimensions, the numerical optimization of the tidal turbine system is carried out. In fact, due to the specific characteristics of the active lift turbine, the blades do not follow a circular trajectory (Fig. \ref{fig:combined}). The OpenFoam overset module is therefore chosen because it allows to control the motion of the blades easily \cite{Chalmers}. The Overset method allows a good performance evaluation and limits the risk of numerical divergence that could be caused by mesh deformation methods; Moreover it limits the computation time compared to remeshing methods. However, it is more expensive than a more traditional Arbitrary Mesh Interface method \cite{Openfoam}, which is not suitable for the active lift turbine simulations.
 The impact of several parameters on the performances is studied. The simulations are performed for a range of operating conditions including different inflow velocities, angles of attack and active flow turbine settings (like the amplitude of the radius variation, see Fig \ref{fig:combined}). The results are evaluated in terms of the turbine power output and efficiency.
 The results show the importance of numerical simulation for the development of new types of energy recovery systems. It allows a better understanding of the interactions between the turbine and the fluid, and of the operation of such systems.
 Further studies are required for the active lift turbine: conventional attempts at optimisation are not perfectly suited to this system. Improving the lift/drag ratio makes less sense when the normal forces should also be taken into account to improves the performances. Furthermore, other aspects of operation should be analysed: variation of the turbulence rate, implementation of boundary layer re-attachment systems...

Data-driven non-intrusive shape-topology optimization framework for curved shells

Aiming at obtaining an optimal configuration of curved shells in the compact design space, it is an effective way to perform the shape and topology optimization simultaneously. Considering the complexity in solving the coupled shape and topology optimization problem, this paper presents an easy-to-implement data-driven non-intrusive shape-topology optimization framework for curved shells, including two steps. In the off-line step, the shape equation-driven mesh deformation method is firstly proposed, contributing to using a small number of design variables for fast shape change and optimization of the skin of curved shell without re-modeling and re-meshing. Latin hypercube sampling is used to generate sample points as the input data in the design space, and the corresponding skin shape is obtained. In each design domain determined by different skin shapes, the topology optimizations are performed in parallel or by multiple optimization solvers, after that above multi-source optimization results are collected into the output dataset. The mapping relationship is trained between the input data and output data via surrogate modeling technique, and this non-intrusive concept contributes to integrating the independent shape and topology optimization into a single-loop data-driven optimization. The cross validation-Voronoi adaptive model updating method is used to improve the prediction accuracy. In the on-line step, the single-loop data-driven optimization is carried out using covariance matrix adaptive evolution strategy and adaptive optimization updating method, which can obtain optimized results more efficiently than direct topology optimization or shape optimization method. In order to verify the effectiveness of the proposed data-driven non-intrusive shape-topology optimization framework, three optimization examples are carried out. Example results show that compared with the results by the single topology optimization, the strain energy results by the proposed framework can be reduced by 20.55%, 15% and 51.6%, respectively, highlighting the outstanding optimization ability of the proposed framework.

On numerical simulation of fluid - structure interaction problems using variational multiscale methods

This paper focus on the numerical approximation of a simplified two dimensional aeroelastic problem, where the flexibly supported airfoil with a control section is considered. In this case the coupling of the control section with other mode can cause a decrease of the flutter velocity. The problem is mathematically described using the fully coupled formulation of the incompressible viscous fluid flow over a flexibly structure, whose motion is modeled by system of ordinary differential equations. The incompressible flow is described by the system of Navier–Stokes equations written in the Arbitrary Lagrangian Eulerian form in order to treat the motion of the computational domain. The numerical approximation is treated using the variational multiscale approach using the algebraic subgrid scale model. The construction of the ALE mapping is based on a robust mesh deformation method. The numerical results are presented.

Aerodynamic shape optimization based on discrete adjoint and RBF

This paper presents a new framework for Aerodynamic Shape Optimization (ASO) implemented inside the open-source software SU2. A parametrized surface is iteratively morphed to improve a desired aerodynamic coefficient. At each loop, the computational grid must be updated. The radial basis function (RBF) mesh deformation technique is introduced to extend the capability to explore the design space. RBF is implemented with some state-of-the-art data reduction systems to lower the computational cost. The Discrete Adjoint is adopted to compute the sensitivity in combination with Automatic Differentiation to calculate the required Jacobians. RBF is differentiated as well, resulting in a method-dependent surface sensitivity. The gradient-based algorithm “Sequential Least Squares Programming” drives the research of the minimum. The study demonstrates that the presented combination is more robust than an ASO, including linear elasticity analogy (ELA) as mesh deformation method. It can handle complex geometries and apply larger displacements, making possible the optimization of a wing-winglet configuration and a rotating wind turbine. Results are presented in two and three-dimensions for compressible and incompressible flows, showing a stronger reduction of the drag without affecting the lift.

Two-Stage Intelligent Layout Design of Curved Cabin Door

As one of the most complex and critical components of spacecraft, the structural design of the curved cabin door faces two challenges. On the one hand, it is difficult to obtain innovative configurations for the cabin door in the preliminary design stage. On the other hand, the traditional optimization design algorithm is inefficient in the detailed design stage. In this paper, a two-stage intelligent method for the layout design of the curved cabin door is proposed. In the first stage, the innovative stiffener layout of the cabin door is obtained based on the topology optimization method. Then the mesh deformation method is used for rapid modeling and geometric reconstruction. In the second stage, a recently proposed powerful evolutionary algorithm, named elite-driven surrogate-assisted Covariance Matrix Adaptation Evolution Strategy (ES-CMA-ES), is employed to optimize the parameters of the cabin door and its surrounding thin-wall structure. To verify the effectiveness of the proposed method, a curved cabin door example from the spacecraft (cargo spaceship) is carried out. Compared with the traditional orthogrid stiffener design, the mass of the optimal design is reduced by 52.21% while satisfying the constraints, which indicates the excellent optimization ability of the proposed method and demonstrates huge potential for improving the carrying capacity and efficiency of the spacecraft.

Multidisciplinary sensitivity analysis for turbine blade considering thickness uncertainties

Abstract This work presents an approach for sensitivity analysis of turbine cooling blade with surface thickness uncertainties, combining mesh deformation method, neural network model and multidisciplinary analysis. Normally, for even tiny shape changes, conventional geometry-based method failed easily during the auto-processing analysis. Therefore, mesh deformation method was utilized to capture the tiny size changes in the multidisciplinary analysis for both the fluid and the structure meshes. The neural network model is constructed by design of experiments to reduce the computational cost. Sensitivity analysis of the multidisciplinary system of blade is performed by numerical difference algorithm with the neural network model. Results showed that the proposed method was effective and practical in engineering.

A data-driven modelling and optimization framework for variable-thickness integrally stiffened shells

The integrally stiffened shells possess the advantages of high specific strength, high specific rigidity and excellent sealing performance, which have been widely used in the load-carrying structure of next-generation manned spacecraft and cargo spacecraft. However, the automatic modelling and optimization of the variable-thickness (VT) integrally stiffened shell are challenging due to the diverse stiffener configurations and the VT skin at multiple corners. To address this issue, a novel data-driven modelling and optimization framework is proposed for the VT integrally stiffened shell in this paper. Firstly, a novel mesh deformation method is proposed for modelling the VT integrally stiffened shell combining the radial basis function (RBF) surrogate model and nonuniform rational B-splines (NURBS). By means of the RBF surrogate model, the mapping relationship between the background mesh domain of curved shell and the target mesh domain of flat plate is trained, and then the equal-thickness (ET) stiffened flat plate is transformed into the VT stiffened flat plate by moving coordinates of nodes. In order to realize the accurate description of the VT stiffened flat plate, NURBS method is used to describe the coordinates of nodes. Finally, the VT stiffened flat plate is transformed into the VT integrally stiffened shell by the mapping relationship. In order to verify the accuracy of the proposed method, a skin-stiffener verticality detection method is proposed for stiffened curved shells. Moreover, based on the deep neural network (DNN) method, a data-driven stiffener layout optimization method is established to minimize the structural weight of the VT integrally stiffened shell. To illustrate the effectiveness of the proposed method, an example of the integrally stiffened shell under internal pressure is carried out. The average value of the detection results of skin-stiffener verticality for the integrally stiffened shell under internal pressure is less than 0.29°, indicating the high accuracy of the proposed modelling method. Compared with the initial result and the optimal result of the equal-thickness integrally stiffened shell, the optimal result of the VT integrally stiffened shell achieves a structural weight reduction of 14.77% and 10.31%, respectively. Optimization results indicate the effectiveness of the proposed optimization framework and the advantage of VT integrally stiffened shells in lightweight design.

CFD simulation of floating body motion with mooring dynamics: Coupling MoorDyn with OpenFOAM

It is increasingly popular to use Computational Fluid Dynamics (CFD) models to study floating structures subjected to ocean waves, especially when it comes to applications of floating offshore wind turbines and Wave Energy Converters (WECs). Mooring dynamics are currently lacking in most of these applications. This paper presents a coupled simulation study of moored floating body motion by coupling two open-source libraries: a finite volume CFD toolbox, OpenFOAM, and a lumped-mass mooring model, MoorDyn. The instantaneous floating body position and velocity are passed from the body motion solver in the CFD model to the mooring model to calculate the fairlead kinematics. The mooring reaction forces, which are calculated by MoorDyn after updating the mooring system states, are then returned to the body motion solver to update the floating body motion. Both mesh deformation and overset mesh methods are used as the mesh motion solver in the CFD model to account for the floating body motion. The coupled model was validated against experimental measurements for a floating box moored with four catenary lines under the action of regular waves, which came from a preliminary test campaign for WECs. Apart from the lumped-mass mooring model, the present work also coupled a quasi-static mooring model and a finite element model with the floating body motion solver in OpenFOAM. The mooring line tensions predicted by these models were compared. The coupled model equipped with three mooring line codes may be further used to carry out survivability studies of FOWTs and WECs subject to severe sea states.

Multi-objective aerodynamic optimization of two-dimensional hypersonic forebody-inlet based on the heuristic algorithm

Nowadays, the forebody-inlet integrated design optimization becomes more and more important in improving the performance of hypersonic vehicles. And several achievements have been made to improve the performance of the two-dimensional hypersonic forebody-inlet integrated vehicle. However, all these works are faced with many defects. For example, the work adopting the gradient algorithm is easy to be trapped in the local optimum solution. The data-driven optimization method is with a low level of accuracy. Moreover, the geometry parameterization methods adopted in those optimization procedures are hardly implemented to complex configurations. In this study, a global-searching multi-objective optimization framework is proposed to overcome these limitations and to carry out multi-objective optimization of the two-dimensional hypersonic forebody-inlet shape. The framework includes the Free-Form Deformation (FFD) method, the mesh deformation method, the high-accuracy Reynolds Averaged Navier-Stokes (RANS) solver, and the global-searching heuristic algorithm. Results obtained by this framework indicate that the total pressure recovery coefficient, the pressure rising ratio, and the mass flow coefficient are increased by 3.97%, 9% and 7.35%, respectively, which suggests that the optimization framework proposed in this study is promising to be widely used in practical engineering applications.

Three-Dimensional Wheat Modelling Based on Leaf Morphological Features and Mesh Deformation

The three-dimensional (3D) morphological structure of wheat directly reflects the interrelationship among genetics, environments, and cropping systems. However, the morphological complexity of wheat limits its rapid and accurate 3D modelling. We have developed a 3D wheat modelling method that is based on the progression from skeletons to mesh models. Firstly, we identified five morphological parameters that describe the 3D leaf features of wheat from amounts of 3D leaf digitizing data at the grain filling stage. The template samples were selected based on the similarity between the input leaf skeleton and leaf templates in the constructed wheat leaf database. The leaf modelling was then performed using the as-rigid-as-possible (ARAP) mesh deformation method. We found that 3D wheat modelling at the individual leaf level, leaf group, and individual plant scales can be achieved. Compared with directly acquiring 3D digitizing data for 3D modelling, it saves 79.9% of the time. The minimum correlation R2 of the extracted morphological leaf parameters between using the measured data and 3D model by this method was 0.91 and the maximum RMSE was 0.03, implying that this method preserves the morphological leaf features. The proposed method provides a strong foundation for further morphological phenotype extraction, functional–structural analysis, and virtual reality applications in wheat plants. Overall, we provide a new 3D modelling method for complex plants.

A Hybrid Model Method for Accurate Surface Deformation and Incision Based on FEM and PBD

In some simulations like virtual surgery, an accurate surface deformation method is needed. Many deformation methods focus on the whole model swing and twist. Few methods focus on surface deformation. For the surface deformation method, two necessary characteristics are needed: the accuracy and real-time performance. Some traditional methods, such as position-based dynamics (PBD) and mass-spring method (MSM), focus more on the real-time performance. Others like the finite element method (FEM) focus more on the accuracy. To balance these two characteristics, we propose a hybrid mesh deformation method for accurate surface deformation based on FEM and PBD. Firstly, we construct a hybrid mesh, which is composed of a coarse volume mesh and a fine surface mesh. Secondly, we implement FEM on coarse volume mesh and PBD on fine surface mesh, and the deformation of fine surface mesh is constrained by the displacement of the coarse volume mesh. Thirdly, we introduced a small incision process for our proposed method. Finally, we implemented our method on a simple deformation simulation and a small incision simulation. The result shows an accurate surface deformation performance by implementing our method. The incision effect shows the compatibility of our proposed method. In conclusion, our proposed method acquires a better trade-off between accuracy and real-time performance.

RANS Computation of the Mean Forces and Moments, and Wave-Induced Six Degrees of Freedom Motions for a Ship Moving Obliquely in Regular Head and Beam Waves

Ship maneuvering performance in waves has attracted much attention in recent years. One of main research efforts for this problem has been devoted to the high-accuracy computation of hydrodynamic forces and moments, as well as wave-induced motions, for ships performing maneuvering motions in waves. The objective of this article is to present a numerical study on the computation of the mean forces and moments, and wave-induced six degrees of freedom motions for a ship moving obliquely in regular head and beam waves. The RANS (Reynolds-Averaged Navier-Stokes) solver based on OpenFOAM is used for this purpose. The RANS computations herein are carried out in a horizontal coordinate system. The numerical wave maker with prescribing values of flow variables on the domain boundaries is applied for the wave generation in the computational domain. However, in order to prevent wave reflection, relaxed zones adjacent to the wave maker boundaries are set up. A new program module is inserted into OpenFOAM to update the flow velocity and wave evaluation on the wave-maker boundaries and in the relaxed zones during the RANS computation. The mesh deformation method is employed to allow the ship to perform motions in space. However, a virtual spring system is attached to the ship so as to restrain the surge, sway and yaw, while heave, pitch and roll are completely free, so that the ship is able to oscillate periodically around a certain position in space. The computed mean forces and moments with the inertia effects agree fairly well with the experimental data, and the computed wave-induced motions are also in quite reasonable agreement with the experimental data. This study shows a very successful computation, as well as the procedure of the RANS results processing.

Effects of Running Speed on Coupling between Pantograph of High-Speed Train and Tunnel Based on Aerodynamics and Multi-Body Dynamics Coupling

(1) Background: The ratio of railway tunnel to line is larger, which produces tunnel entrance and exit effect, aerodynamic resistance, and sudden pressure changes. When the train passes through the tunnels at high-speed, the interaction between the pantograph on it and its surrounding air intensifies and the coupling effects between the pantograph and tunnel become more significant; (2) Methods: A coupling method between aerodynamics and multi-body dynamics is proposed based on hybrid meshing and grid motion. The layered grid motion method is combined with the viscous mesh deformation method with swift, effective data exchange. The significant coupling effects between the pantograph and tunnel are revealed; (3) Results: The influence laws and evolution mechanism of running speed as it affects important service characteristics and behaviors of the pantograph are accurately quantified. Noteworthy factors include the temporal characteristics of panhead aerodynamic lift, the contact force between the pantograph and catenary, vertical displacement and acceleration of the contact strip, the phase diagram of the contact strip, and various frequency-domain characteristics. The action mechanism of running speed on the coupling effect between the pantograph and tunnel is comprehensively and accurately revealed by the proposed method; (4) Conclusions: The larger service characteristics amplitudes of the high-speed pantograph appear at low frequencies and are not multiple frequencies of the basic frequency. By comparisons, the coupling calculation results are closer to the test results than the non-coupling results regardless of the maximum, minimum, or mean.

Graph-Guided Deformation for Point Cloud Completion

For a long time, the point cloud completion task has been regarded as a pure generation task. After obtaining the global shape code through the encoder, a complete point cloud is generated using the shape priorly learnt by the networks. However, such models are undesirably biased towards prior average objects and inherently limited to fit geometry details. In this letter, we propose a Graph-Guided Deformation Network, which respectively regards the input data and intermediate generation as controlling and supporting points, and models the optimization guided by a graph convolutional network(GCN) for the point cloud completion task. Our key insight is to simulate the least square Laplacian deformation process via mesh deformation methods, which brings adaptivity for modeling variation in geometry details. By this means, we also reduce the gap between the completion task and the mesh deformation algorithms. As far as we know, we are the first to refine the point cloud completion task by mimicing traditional graphics algorithms with GCN-guided deformation. We have conducted extensive experiments on both the simulated indoor dataset ShapeNet, outdoor dataset KITTI, and our self-collected autonomous driving dataset Pandar40. The results show that our method outperforms the existing state-of-the-art algorithms in the 3D point cloud completion task.

Application of mesh deformation and adaptive method in hullform design optimization

Application of mesh deformation and adaptive method in hullform design optimization

Generating three-dimensional drape model based on projection and mesh deformation

In order to generate the three-dimensional (3D) mesh of draped fabric based on a two-dimensional (2D) fabric projection, the 3D point cloud of draped fabric was scanned via a self-built 3D scanning device followed by triangulation. The 3D boundary of fabric drape model and the two-dimensional contour of the projection of the fabric drape model were extracted respectively. Two neural networks were constructed to bridge the 2D fabric drape projection and the 3D boundary of draped fabric. With the trained neural networks, the 3D boundary of draped fabric could be inferred by merely referring a 2D projection of draped fabric. Six reference triangular meshes with different triangle density were generated. Driven by two mesh deformation methods, Laplacian deformation and Poisson deformation, the reference mesh was deformed into 3D mesh similar to scanned fabric drape models (meshes). The result shows that the generated models have a high agreement with the scanned meshes. In addition, the Laplacian deformation outperforms Poisson deformation in generating 3D fabric drape models.

Time-Domain Aeroelasticity Analysis by a Tightly Coupled Fluid-Structure Interaction Methodology

A tightly coupled fluid-structure interaction (FSI) methodology is developed for aeroelasticity analysis in the time domain. The preconditioned Navier–Stokes equations for all Mach numbers are employed and the structural equations are tightly coupled with the fluid equations by discretizing their time derivative term in the same pseudo time-stepping method. A modified mesh deformation method based on reduced control points radial basis functions (RBF) is utilized, and a RBF based mapping algorithm is introduced for data exchange on the interaction interface. To evaluate the methodology, the flutter boundary and the limit cycle oscillation of Isogai wing and the flutter boundary of AGARD 445.6 wing are analyzed and validated.