Mesh Optimization Research Articles

Numerical study of microalgae cultivation process in a batch liquid foam-bed photobioreactor using CFD approach

Microalgae have different uses as feedstock of beneficial chemicals such as polysaccharides, carotenoids, and polyunsaturated fatty acids. Furthermore, they have been applied in the renewable energy, food, agriculture and feed industries, and in wastewater treatment. The growth and cultivation of microalgae are highly regarded by researchers worldwide. So, a variety of systems and designs have been used to cultivate microalgae. A research team recently proposed a new experimental design of photobioreactors based on a liquid foam flow at Wageningen University in the Netherlands. In this study, a numerical study of hydrodynamics and mass transfer of this novel system was conducted using computational fluid dynamics (CFD). This method is based on the simultaneous solution of transfer equations including hydrodynamic equations, mass transfer, cell growth, and radiation transport equation. The simulation was performed in an unsteady and three-dimensional state in COMSOL 5.5 software. The flow regime was considered laminar and mixture model and transport dilution species physics were used to model the behavior of two-phase fluid. Manual geometry grid generation was performed after defining the velocity and concentration boundaries. The number of optimal meshes was determined to be approximately 1.2 × 105 using the mesh independence test. The simulation results were validated according to the concentration-time curve. The cell density, 22 g l−1, is minimal in the center. The maximum biomass is 30.9 g l−1 at the bed wall after 80 h at 1446 μmol photon. m−2. s−1 light flux for the minimal cell density.

Development of a Silicone Rubber Mold with an Innovative Waterfall Cooling Channel.

A conformal cooling channel (CCC) follows the mold core or cavity profile to carry out uniform cooling in the cooling stage. However, the significant pressure drop along the cooling channels is a distinct disadvantage of the CCC. In this study, an innovative waterfall cooling channel (WCC) was proposed and implemented. The WCC cools the injected products via surface contact, replacing the conventional line contact to cool the injected products. The WCC was optimized using numerical simulation software. Silicone rubber molds with two kinds of cooling channels were designed and implemented. The cooling time of the molded part was evaluated using a low-pressure wax injection molding machine. The experimental results of the cooling time of the molded part were compared with the simulation results from numerical simulation software. The results showed that the optimal mesh element count was about 1,550,000 with a mesh size of 1 mm. The simulation software predicted the filling time of the water cup injection-molded product to be approximately 2.008 s. The cooling efficiency for a silicone rubber mold with a WCC is better than that of the silicone rubber mold with a CCC since the core and cavity cooling efficiency is close to 50%. The pressure drop of the WCC is smaller than that of the CCC, which reduces the pressure drop by about 56%. Taking a water cup with a mouth diameter of 70 mm, a height of 60 mm, and a thickness of 2 mm as an example, the experimental results confirmed that the use of the WCC can save the cooling time of the product by about 265 s compared with the CCC. This shows how a WCC can increase cooling efficiency by approximately 17.47%.

Mesh Independence Study on CFD for Cryo-CO2 Cooling Strategy

This study conducts comprehensive mesh independence tests to identify the optimum mesh independence parameters that offer the most feasible Computational Fluid Dynamic (CFD) analysis on cryo-CO2 temperature variations and its heat transfer performance under cryo-CO2 cooling strategy in metal cutting. ANSYS Fluent was used to conduct the CFD study with its mesh control parameters (relevance center and smoothing) designed using Response Surface Methodology (RSM) under Central Composite Design (CCD). An Analysis of Variance (ANOVA) was applied to analyse how the controlled factors influenced the cryo-CO2 flow temperature when it flowed from the nozzle to the tooltip. The analysis found that the relevance centre was more significant in influencing the accuracy of the response value. For optimization, the combination of medium relevance center and smoothing meshes was suggested to develop the lowest cryo-CO2 flow temperature at 256.85 K. This is crucial since most machining outputs are heat dependent. Experimental data sets were used to validate the predicted result. Distances between 3.6 to 18 mm showed an acceptable deviation of ~0.4 – 0.6% and ~0.4 – 4.2% for simulated and experimented work, respectively. This value is acceptable, and the generated quadratic model equation can be applied for prediction. The heat transfer performance of the cryo-CO2 flow at tool-chip and tool-workpiece interfaces under high-speed machining was also discussed. Moreover, further analysis using the optimal solution has led to a better understanding of heat transfer in cryogenic carbon dioxide (CO2), resulting in enhanced cooling of the cutting zone and improved machining processes.

Concrete crack segmentation combined with linear guidance and mesh optimization

Concrete crack segmentation combined with linear guidance and mesh optimization

THE MATHEMATICAL MODEL OF TWO-DIMENSIONAL ELECTROMAGNETHIC FIELD

The purpose of this work is to develop a mathematical model of two-dimensional electromagnetic field, i.e. to construct a system of axioms (assumptions) that we unconditionally accept, although they do not correspond to the real electromagnetic field, but approximate it quite well. A mathematical model of two-dimensional electromagnetic field is constructed based on four assumptions: 1. Boundedness: we assume that on an infinite plane there is a bounded convex domain, outside which the field is zero. 2. Existence of nodes: we assume that in the domain there is a finite set of points, called nodes. All calculations of potential values are carried out only at internal nodes․ 3. Existence of neighbors: we assume that all pairs of nodes are divided into two types: neighboring and non-neighboring, and only neighboring nodes interact. 4. Discretization: we assume that the magnetic permeability of the medium is discrete, i.e. is a piecewise constant function. It is shown that within our mathematical model, from Assumptions 1 – 4, it follows that the electromagnetic potential is necessarily a piecewise linear function. It is shown that within our mathematical model, minimization of the energy functional leads to a system of nonlinear equations, the number of equations is equal to the number of internal nodes. It is proved that within our mathematical model, from Assumptions 1 – 4, it follows that for the numerical solution of the resulting system of equations, the optimal mesh is the Delaunay triangulation. The results are illustrated by an example of numerical solution of a field problem for electromagnetic systems with magnetorheological fluid using the FEMM tool. It is shown that the FEMM application package corresponds to our model.

A revisited verification and validation analysis for URANS simulation of planing hulls in calm water

Verification and Validation (V&V) is the foremost analysis which is carried out for evaluation of the accuracy level and dependability of computational fluid dynamic (CFD) simulations. The present study investigates the V&V of CFD models in predicting the dynamic trim and hull resistance of high-speed planing hulls with an aim to provide a deeper understanding of V&V analysis in this specific field of application. Two different planing hulls, namely the C05 stepped hull and the C1 interceptor hull, are analyzed with four different grids and time-steps using two mesh motion techniques, namely overset and morphing approach. The discretization (grid) and time-step uncertainties for each CFD simulation are estimated using the least squares method. The results indicate that the overset mesh approach performs better than the morphing grid method in terms of numerical uncertainty and validation achieved for both hulls. The error of both techniques in the prediction of resistance and trim angle of the boat shows an acceptable range of accuracy. The findings provide valuable insights for simulation-based designing and optimizing high-speed planing hulls, specifically by identifying the optimal mesh technique, cell number, and time-step for accurate prediction of wetted surface shape, ventilation formation, running attitude, and resistance.

Optimal Mesh Size in Three-Dimensional Arbitrary Lagrangian-Eulerian Method of Free-air Explosions

Optimal Mesh Size in Three-Dimensional Arbitrary Lagrangian-Eulerian Method of Free-air Explosions

Advances in Numerical Data Visualization of Flow around a Square Cylinder

In this work, we present a grid study oriented to capture 3D flow simulations around smooth and wrinkled cylinders that could have practical applications in various engineering areas. The study considers three Reynolds numbers, namely, a benchmark Re =2.14×104 and two orders of magnitude above and below it. The main contributions of the paper relate to the optimization of the computational mesh for the spanwise direction of the wind flow that results from the computational-mathematical framework employed, in addition to a novel visualization technique that unfolds features in the recording data that could otherwise be hidden when using traditional plots. We compare our benchmark results with those reported by other authors to conclude that the intermediate resolution grids employed with the widest spanwise provide acceptable results. Furthermore, the new visualization technique offers significant advantages compared to traditional pressure maps, regarding clarity for observing and interpreting local flow disturbances, making variations with Re clearer, and by enabling the detection of asymmetries.

A reinforcement learning strategy for p-adaptation in high order solvers

Reinforcement learning (RL) has emerged as a promising approach to automating decision processes. This paper explores the application of RL techniques to optimise the polynomial order in the computational mesh when using high-order solvers. Mesh adaptation plays a crucial role in improving the efficiency of numerical simulations by increasing accuracy while reducing the cost. Here, actor-critic RL models based on Proximal Policy Optimization offer an approach for agents to learn optimal mesh modifications based on evolving conditions.The paper provides a strategy for p-adaptation in high-order solvers and includes insights into the main aspects of RL-based mesh adaptation, including the formulation of appropriate reward structures and the interaction between the RL agent and the simulation environment. The proposed strategy does not require a high-fidelity solution during the training process and the formulation is general for any computational mesh and partial differential equation (PDE), solved in a discontinuous Galerkin solver. We discuss the impact of RL-based mesh p-adaptation on computational efficiency and accuracy. We apply the RL p-adaptation strategy to a one-dimensional inviscid Burgers' equation, focusing our analysis on smooth solutions of the equation to showcase its effectiveness. The RL strategy reduces the computational cost and improves accuracy over uniform adaptation, while minimising human intervention.

Studying the Influence of Finite Element Mesh Size on the Accuracy of Ventricular Tachycardia Simulation.

Ventricular tachycardia (VT) is a life-threatening heart condition commonly seen in patients with myocardial infarction (MI). Although personalized computational modeling has been used to understand VT and its treatment noninvasively, this approach can be computationally intensive and time consuming. Therefore, finding a balance between mesh size and computational efficiency is important. This study aimed to find an optimal mesh resolution that minimizes the need for computational resources while maintaining numerical accuracy and to investigate the effect of mesh resolution variation on the simulation results. We constructed ventricular models from contrast-enhanced magnetic resonance imaging data from six patients with MI. We created seven different models for each patient, with average edge lengths ranging from 315 to 645 µm using commercial software, Mimics. Programmed electrical stimulation was used to assess VT inducibility from 19 sites in each heart model. The simulation results in the slab model with adaptive tetrahedral mesh (same as in the patient-specific model) showed that the absolute and relative differences in conduction velocity (CV) were 6.1 cm/s and 7.8% between average mesh sizes of 142 and 600 µm, respectively. However, the simulation results in the six patient-specific models showed that average mesh sizes with 350 µm yielded over 85% accuracy for clinically relevant VT. Although average mesh sizes of 417 and 478 µm could also achieve approximately 80% accuracy for clinically relevant VT, the percentage of incorrectly predicted VTs increases. When conductivity was modified to match the CV in the model with the finest mesh size, the overall ratio of positively predicted VT increased. The proposed personalized heart model could achieve an optimal balance between simulation time and VT prediction accuracy when discretized with adaptive tetrahedral meshes with an average edge length about 350 µm.

An ANN-BCMO Approach for Material Distribution Optimization of Bi-Directional Functionally Graded Nanocomposite Plates with Geometrically Nonlinear Behaviors

This study commences with the application of an efficient artificial neural network (ANN)-balancing composite motion optimization (BCMO) approach for finding the optimal material distribution of bi-directional functional graded nanocomposite (FGN) thin plates considering geometrically nonlinear behaviors. To this regard, an ANN-based surrogate model of the high-fidelity isogeometric analysis (IGA) of the geometrically nonlinear Kirchhoff–Love plates based on the Von Kármán nonlinearity theory is first constructed and then employed to predict the values of objectives and constraints required in the BCMO framework. The multi-mesh design approach is utilized to form two separate nonuniform rational B-spline meshes for optimal material distribution and analysis meshes. The unknown control point values of the design mesh are herein selected as the continuous design variables. This allows a possibility to fully explore the complex distribution of optimal material profiles without requiring a significant number of variables. Selected numerical examples with different plate geometries and loading conditions are presented to illustrate the merit features of the proposed approach. Obtained results reveal not only its high accuracy and significant efficiency compared with the conventional approach coupling the BCMO with IGA direct analysis but also the stable ability of the BCMO in finding global optimum material distributions in comparison with two commonly used metaheuristics algorithms, i.e., particle swarm optimization and genetic algorithm.

Differentiable Rendering of Parametric Geometry

We propose an efficient method for differentiable rendering of parametric surfaces and curves, which enables their use in inverse graphics problems. Our central observation is that a representative triangle mesh can be extracted from a continuous parametric object in a differentiable and efficient way. We derive differentiable meshing operators for surfaces and curves that provide varying levels of approximation granularity. With triangle mesh approximations, we can readily leverage existing machinery for differentiable mesh rendering to handle parametric geometry. Naively combining differentiable tessellation with inverse graphics settings lacks robustness and is prone to reaching undesirable local minima. To this end, we draw a connection between our setting and the optimization of triangle meshes in inverse graphics and present a set of optimization techniques, including regularizations and coarse-to-fine schemes. We show the viability and efficiency of our method in a set of image-based computer-aided design applications.

Roboticassisted incisional hernia surgery-Retromuscular techniques

The trend to minimally invasive surgery has also made its way into the surgical treatment of incisional hernias. Unlike other areas of visceral surgery, recent years have seen aresurgence of open sublay repair in incisional hernia procedures, primarily due to the recognition of the retromuscular layer as the optimal mesh placement site. Additionally, with the growing availability of robotic systems in visceral surgery, these procedures are increasingly being offered in the form of minimally invasive procedures. These methods can be categorized based on the access routes: robotic-assisted transperitoneal procedures (e.g., r‑Rives, r‑TARUP, r‑TAR) and total extraperitoneal hernia repair (e.g., r‑eTEP, r‑eTAR). Notably, the introduction of transversus abdominis muscle release enables the robotic-assisted treatment of larger and more complex hernia cases with complete fascial closure. With respect to the comparison with open surgery required in retromuscular hernia treatment, the currently available literature on incisional hernia repair seems to show initial advantages of robotic-assisted surgery in the perioperative course. New technologies create new possibilities. In the context of surgical training the use of surgical robot systems with double consoles opens up completely new perspectives. Furthermore, the robot enables the implementation of models of artificial intelligence and augmented reality and could therefore open up novel dimensions in surgery.

A Globalized and Preconditioned Newton-CG Solver for Metric-Aware Curved High-Order Mesh Optimization

We present a specific-purpose globalized and preconditioned Newton-CG solver to minimize a metric-aware curved high-order mesh distortion. The solver is specially devised to optimize curved high-order meshes for high polynomial degrees with a target metric featuring non-uniform sizing, high stretching ratios, and curved alignment — exactly the features that stiffen the optimization problem. To this end, we consider two ingredients: a specific-purpose globalization and a specific-purpose Jacobi-iLDLT(0) preconditioning with varying accuracy and curvature tolerances (dynamic forcing terms) for the CG method. These improvements are critical in stiff problems because, without them, the large number of non-linear and linear iterations makes curved optimization impractical. First, to enhance the global convergence of the non-linear solver, the globalization strategy modifies Newton’s direction to a feasible step. In particular, our specific-purpose globalization strategy memorizes the length of the feasible step (step-length continuation) between the optimization iterations while ensuring sufficient decrease and progress. Second, to compute Newton’s direction in second-order optimization problems, we consider a conjugate-gradient iterative solver with specific-purpose preconditioning and dynamic forcing terms. To account for the metric stretching and alignment, the preconditioner uses specific orderings for the mesh nodes and the degrees of freedom. We also present a preconditioner switch between Jacobi and iLDLT(0) preconditioners to control the numerical ill-conditioning of the preconditioner. In addition, the dynamic forcing terms determine the required accuracy for the Newton direction approximation. Specifically, they control the residual tolerance and enforce sufficient positive curvature for the conjugate-gradients method. Finally, to analyze the performance of our method, the results compare the specific-purpose solver with standard optimization methods. For this, we measure the matrix–vector products indicating the solver computational cost and the line-search iterations indicating the total amount of objective function evaluations. When we combine the globalization and the linear solver ingredients, we conclude that the specific-purpose Newton-CG solver reduces the total number of matrix–vector products by one order of magnitude. Moreover, the number of non-linear and line-search iterations is mainly smaller but of similar magnitude.

Comparison of percutaneous vertebroplasty and conservative treatment for one level thoracolumbar osteoporotic compression fracture in a 3-year study

The efficacy of Mesh optimized versus standard percutaneous vertebroplasty (PVP) for osteoporotic vertebral compression fractures. Grid optimization (102 cases; 38 men, 64 women aged 67.3 ± 8.5) and traditional PVP groups (94 cases) were identified from 196 PVP patients treated from May 2016 to 2019. The optimal puncture site and angle forced bone cement into both groups before surgery. The main indexes were operation time, X-ray fluoroscopy times, bone cement injection volume, leakage, VAS, and injured vertebrae height. Preoperative general data were equivalent between groups (P > 0.05). All patients survived surgery without spinal cord injury, incision infection, pulmonary embolism, or death. The mesh optimization group had improved operation time (34.8 ± 6.5 min), fluoroscopy times (29.5 ± 5.5), bone cement injection volume (5.3 ± 2.1 ml), and bone cement permeability greater (3.9 percent; 4/98) than the standard PVP group (P < 0.05). Similarly, the grid optimization group had superior VAS scores (1.1 ± 0.6; 1.0 ± 0.3; and 0.9 ± 0.2) than the standard PVP group at 3 days, 3 months, and the last follow-up visit (P < 0.05). On day three after surgery, both had similar heights of injured vertebra's anterior and middle edges (P > 0.05). However, in the mesh optimization group, measurements improved to 1.8 ± 0.4 mm and (1.8 ± 0.3) mm by month three and to 1.7 ± 0.3 mm at last follow-up (P < 0.05). Mesh-optimized PVP with a mesh locator treats osteoporotic vertebral compression fractures more safely and effectively than regular PVP.

R-Adaptive deep learning method for solving partial differential equations

We introduce a Deep Neural Network (DNN) method for solving Partial Differential Equations (PDEs) that simultaneously: (a) constructs an optimal r-adapted mesh, i.e., given an initial mesh, it provides optimal node locations, and (b) solves the PDE over the constructed r-adaptive mesh. The node locations are optimized over a set of 1D boundary nodes, and the corresponding 2D quadrilateral meshes are built using tensor product. The method supports the definition of fixed interfaces to create conforming meshes and allows nodes to jump across them, permitting topological variations. To numerically illustrate the performance of our novel r-adaptive deep learning method, we apply it in combination with other numerical methods including collocation, Least Squares, and the Deep Ritz method. We solve one- and two-dimensional problems whose solutions are smooth, singular, and/or exhibit strong gradients. Results consistently show the outperformance of employing r-adaptivity, while in some cases the improvement is limited by the tensor-product structure of the mesh.

SolidWorks Flow Simulation: Selecting the optimal mesh for conducting CFD analysis on a centrifugal fan

The accuracy of mesh use determines the suitability of simulation results with experimental test results, therefore it is necessary to study the type and number of mesh used for flow simulation. This study aims to investigate the type of mesh and the number of cells that are appropriately used in the simulation of centrifugal fans using the Solidworks Flow Simulation module. The research was conducted by comparing the simulation results with the experimental results on centrifugal fans that have been carried out by previous studies. In this research, the type of mesh used is global mesh. The parameter of determining the number of cells is done by varying the mesh level because the mesh level affects the number of cells. In this simulation study, the boundary condition is set to one flow volume of 5 m3/h and a rotation speed of 92.362 rad/s. In this study, the total pressure and efficiency of the centrifugal fan are the things that are seen from the comparison of flow simulation with the experiment. Based on the simulation results that have been carried out, mesh levels 1 to 4 show results that differ significantly from the experimental results. At machine levels 5 to 7, the results are close to the experimental results, but the closest total pressure and efficiency values are at mesh level 5. The results of this study can be a reference for research that simulates centrifugal fans.

Modeling Dynamics of Laterally Impacted Piles in Gravel Using Erosion Method

Understanding the dynamic interaction between piles and the surrounding soil under vehicular impacts is essential for effectively designing and optimizing soil-embedded vehicle barrier systems. The complex behavior of pile–soil systems under impact loading, attributed to the soil’s nonlinear behavior and large deformation experienced by both components, presents significant simulation challenges. Popular computation techniques, such as the updated Lagrangian finite element method (UL-FEM), encounter difficulties in scenarios marked by large soil deformation, e.g., impacts involving rigid piles. While mesh-free particle and discrete element methods offer another option, their computational demands for field-scale pile–soil impact simulations are considerable. We introduce the erosion method to bridge this gap by integrating UL-FEM with an erosion algorithm for simulating large soil deformations during vehicular impacts. Validation against established physical impact tests confirmed the method’s effectiveness for flexible and rigid pile failure mechanisms. Additionally, this method was used to examine the effects of soil mesh density, soil domain sizes, and boundary conditions on the dynamic impact response of pile–soil systems. Our findings provide guidelines for optimal soil domain size, mesh density, and boundary conditions. This investigation sets the stage for improved, computationally efficient techniques for the pile–soil impact problem, leading to better pile designs for vehicular impacts.

An accurate and efficient multiphysics 3D model for the design and operation analysis of production-scale solid oxide cell stacks

A rapid and reliable numerical model to predict solid oxide cell (SOC) stack behaviors is essential for technology advancement. This work reports the development of an accurate and efficient multiphysics model for production-scale SOC stacks. An analytical model is constructed to consider the ohmic resistance of current conduction in thin electrodes, simplifying modeling process. The model demonstrates good agreement with experimental I–V curves. A detailed mesh optimization is performed for all components of SOC stacks to ensure grid independence in flow, electrochemistry, and thermal fields. Moreover, a well-designed simulation strategy is presented, contributing equally to the computational efficiency as mesh optimization. A multiphysics simulation of a 5 kW SOEC stack takes only 50 min on a 2-CPU/24-core workstation, demonstrating the applicability of the model. The fuel uniformity of a H2O-SOEC (H2-SOFC) stack is found to increase (decrease) with increased fuel utilization, with underlying mechanism revealed through a representative 2D flow model.

Local element operations for curved simplex meshes

SummaryMesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post‐processing step in mesh generation procedures and in applications such as fluid simulations with severely deforming domains. In order to perform high‐order mesh optimization, these ingredients must also be extended to high‐order (curved) meshes. In this work, we present a method to perform local element operations on curved meshes. The mesh operations discussed in this work are edge/face swaps, edge collapses, and edge splitting (more generally refinement) for triangular and tetrahedral meshes. These local operations are performed by first identifying the patch of elements which contain the edge/face being acted on, performing the operation as a “straight‐sided one" by placing the high‐order nodes via an isoparametric mapping from the master element, and smoothing the high‐order nodes on the elements in the patch by minimizing a Jacobian‐based high‐order mesh distortion measure. Since the initial “straight‐sided guess” from the placement of the nodes via the isoparametric mapping frequently results in invalid elements, the distortion measure must be regularized which allows for mesh untangling for the optimization to succeed. We present several examples in 2D and 3D to demonstrate these local operations and how they can be combined with a high‐order node smoothing procedure to maintain mesh quality when faced with severe deformations.