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We present an isogeometric analysis (IGA) framework for structural vibrations involving complex geometries. The framework is based on the Complex-Geometry IGA Mesh Generation (CGIMG) method. The CGIMG process is flexible and can accommodate, without a major effort, challenging complex-geometry applications in computational mechanics. To demonstrate how the new IGA framework significantly increases the computational effectiveness, in a set of structural-vibration test computations, we compare the accuracies attained by the IGA and finite element (FE) method as the number of degrees-of-freedom is increased. The results show that the NURBS meshes lead to faster convergence and higher accuracy compared to both linear and quadratic FE meshes. The clearly defined IGA mesh generation process and significant per-degree-of-freedom accuracy advantages of IGA over FE discretization make IGA more accessible, reliable, and attractive in applications of both academic and industrial interest. We note that the accuracy of a structural mechanics discretization, which may be assessed through eigenfrequency analysis, plays an important role in the overall accuracy of fluid–structure interaction computations.

The NURBS Surface-to-Volume Guided Mesh Generation (NSVGMG) is a general-purpose mesh generation method, introduced to increase the scope of isogeometric analysis in computing complex-geometry problems. In the NSVGMG, NURBS patch surface meshes serve as guides in generating the patch volume meshes. The interior control points are determined independent of each other, with only a small subset of the surface control points playing a role in determining each interior point. In the updated version of the NSVGMG we are introducing in this article, in the process of determining the location of an interior point in a parametric direction, more weight is given to the closer guides, with the closeness measured along the guides in the other parametric directions. Tests with 2D and 3D shapes show the effectiveness of the NSVGMG in generating good quality meshes, and the robustness of the updated NSVGMG even in mesh generation for complex shapes with distorted boundaries.

We present computational flow analysis of a vertical-axis wind turbine (VAWT) that has been proposed to also serve as a tsunami shelter. In addition to the three-blade rotor, the turbine has four support columns at the periphery. The columns support the turbine rotor and the shelter. Computational challenges encountered in flow analysis of wind turbines in general include accurate representation of the turbine geometry, multiscale unsteady flow, and moving-boundary flow associated with the rotor motion. The tsunami-shelter VAWT, because of its rather high geometric complexity, poses the additional challenge of reaching high accuracy in turbine-geometry representation and flow solution when the geometry is so complex. We address the challenges with a space–time (ST) computational method that integrates three special ST methods around the core, ST Variational Multiscale (ST-VMS) method, and mesh generation and improvement methods. The three special methods are the ST Slip Interface (ST-SI) method, ST Isogeometric Analysis (ST-IGA), and the ST/NURBS Mesh Update Method (STNMUM). The ST-discretization feature of the integrated method provides higher-order accuracy compared to standard discretization methods. The VMS feature addresses the computational challenges associated with the multiscale nature of the unsteady flow. The moving-mesh feature of the ST framework enables high-resolution computation near the blades. The ST-SI enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA enables more accurate representation of the blade and other turbine geometries and increased accuracy in the flow solution. The STNMUM enables exact representation of the mesh rotation. A general-purpose NURBS mesh generation method makes it easier to deal with the complex turbine geometry. The quality of the mesh generated with this method is improved with a mesh relaxation method based on fiber-reinforced hyperelasticity and optimized zero-stress state. We present computations for the 2D and 3D cases. The computations show the effectiveness of our ST and mesh generation and relaxation methods in flow analysis of the tsunami-shelter VAWT.

A recently introduced NURBS mesh generation method for complex-geometry Isogeometric Analysis (IGA) is applied to building a high-quality mesh for a gas turbine. The compressible flow in the turbine is computed using the IGA and a stabilized method with improved discontinuity-capturing, weakly-enforced no-slip boundary-condition, and sliding-interface operators. The IGA results are compared with the results from the stabilized finite element simulation to reveal superior performance of the NURBS-based approach. Free-vibration analysis of the turbine rotor using the structural mechanics NURBS mesh is also carried out and shows that the NURBS mesh generation method can be used also in structural mechanics analysis. With the flow field from the NURBS-based turbine flow simulation, the Courant number is computed based on the NURBS mesh local length scale in the flow direction to show some of the other positive features of the mesh generation framework. The work presented further advances the IGA as a fully-integrated and robust design-to-analysis framework, and the IGA-based complex-geometry flow computation with moving boundaries and interfaces represents the first of its kind for compressible flows.

We present a space–time (ST) isogeometric analysis framework for car and tire aerodynamics with road contact and tire deformation and rotation. The geometries of the computational models for the car body and tires are close to the actual geometries. The computational challenges include i) the complexities of these geometries, ii) the tire rotation, iii) maintaining accurate representation of the boundary layers near the tire while being able to deal with the flow-domain topology change created by the road contact, iv) the turbulent nature of the flow, v) the aerodynamic interaction between the car body and the tires, and vi) NURBS mesh generation for the complex geometries. The computational framework is made of the ST Variational Multiscale (ST-VMS) method, ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods, ST Isogeometric Analysis (ST-IGA), integrated combinations of these ST methods, NURBS Surface-to-Volume Guided Mesh Generation (NSVGMG) method, and the element-based mesh relaxation (EBMR). The ST context provides higher-order accuracy in general, the VMS feature of the ST-VMS addresses the challenge created by the turbulent nature of the flow, and the moving-mesh feature of the ST context enables high-resolution flow computation near the moving fluid–solid interfaces. The ST-SI enables moving-mesh computation with the tire rotating. The mesh covering the tire rotates with it, and the SI between the rotating mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-TC enables moving-mesh computation even with the TC created by the contact between the tire and the road. It deals with the contact while maintaining high-resolution flow representation near the tire. Integration of the ST-SI and ST-TC enables high-resolution representation even though parts of the SI are coinciding with the tire and road surfaces. It also enables dealing with the tire–road contact location change and contact sliding. By integrating the ST-IGA with the ST-SI and ST-TC, in addition to having a more accurate representation of the tire geometry and increased accuracy in the flow solution, the element density in the tire grooves and in the narrow spaces near the contact areas is kept at a reasonable level. The NSVGMG enables NURBS mesh generation for the complex car and tire geometries, and the EBMR improves the quality of the meshes. The car and tire aerodynamics computation we present shows the effectiveness of the analysis framework we have built.

We present the Space–Time Isogeometric Analysis (ST-IGA) of wind turbine rotor and tower aerodynamics, with the rotor geometry of the NREL 5MW offshore baseline wind turbine. The computation is with a given wind speed and a specified rotor speed. The computational challenges include accurate representation of the rotor geometry, multiscale nature of the unsteady flow, the fast, rotational relative motion between the rotor and tower, and the IGA mesh generation for the complex geometry. In addressing the computational challenges, the ST-IGA is used together with the ST Variational Multiscale (ST-VMS) method, which is a core computational method, and the ST Slip Interface (ST-SI) and Complex-Geometry IGA Mesh Generation (CGIMG) methods, which are complementary general-purpose methods. These are the methods of the ST Computational Flow Analysis in this case. The ST-discretization feature provides higher-order accuracy compared to standard discretization methods. The VMS feature addresses the computational challenges associated with the multiscale nature of the unsteady flow. The moving-mesh feature of the ST framework enables high-resolution computation near the blades. The ST-SI enables high-fidelity moving-mesh computations even over meshes made of patches with nonmatching meshes at the interfaces between those patches. The mesh covering the rotor rotates with it, and the SI between the rotating mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA, with IGA basis functions in space, enables more accurate representation of the rotor geometry and increased accuracy in the flow solution. With IGA basis functions in time, it enables more accurate representation of the rotor and mesh rotations. The CGIMG makes it easier in IGA mesh generation to deal with the complex geometry. The computation presented shows that the ST-IGA and the accompanying methods are successful in addressing the challenges and bringing high-fidelity computational analysis to wind turbine rotor and tower aerodynamics.

A parallel structured mesh generation method is proposed for FDTD (Finite Difference Time Domain) simulation in this paper by MPI (Message Passing Interface) implementation. This parallel method is based on serial projection and ray tracing. It completely implements the process from surface triangles recorded in a STL (STereoLithography) file to solid hexahedral grids. Furthermore, the parallel method realizes the balanced task allocation for processes which provides almost linear parallelism. Experimental results show that the running time of the MPI program increases in a nearly linear way. As the number of processes increases, the efficiency of the parallel program consistently remains above 80%.

This paper presents a uniformly accurate difference approximation for a system of singularly perturbed reaction-diffusion equations with delay. The proposed method utilizes an appropriate combination of exponential and cubic spline difference schemes. It employs grid equidistribution to address the challenges posed by the multiscale nature of these systems, which often feature sharp gradients and boundary layers. The grid is generated based on the equidistribution of a positive monitor function, a linear combination of a constant floor and a power of the second derivative of the solution. By using adaptive mesh generation and a spline difference method, the approach enhances the accuracy of the numerical solutions while maintaining computational efficiency. Numerical experiments validate the uniform convergence and theoretical findings, demonstrating the method’s robustness irrespective of the perturbation parameter size.

Block-structured meshes are favoured in various computational simulations due to their superior computational efficiency and accuracy. While cross-field methods have demonstrated promising capabilities in generating high-quality quadrilateral meshes, they often face challenges such as non-uniform mesh distribution, limit cycles, and complex block structures. Additionally, the effectiveness of these methods heavily relies on the quality and density of the underlying background mesh. To address these limitations, this paper introduces a novel approach that synergizes medial-axis and cross-field methodologies. Our proposed method diverges from traditional four-sided block decompositions, opting instead for a flexible N-sided subdomain strategy guided by both a cross-field and its corresponding distance field. This innovation not only simplifies the decomposition structure but also lessens the dependency on the background mesh’s density, enhancing the method’s robustness and applicability. The paper details the development and validation of this technique, showcasing its efficiency in handling complex geometries compared to existing methods.

PurposeTo present the detailed implementation processes of the IDEAL algorithm for two-dimensional compressible flows based on Delaunay triangular mesh, and compare the performance of the SIMPLE and IDEAL algorithms for solving compressible problems. What’s more, the implementation processes of Delaunay mesh generation and derivation of the pressure correction equation are also introduced.Design/methodology/approachProgramming completely in C++.FindingsFive compressible examples are used to test the SIMPLE and IDEAL algorithms, and the comparison with measurement data shows good agreement. The IDEAL algorithm has much better performance in both convergence rate and stability over the SIMPLE algorithm.Originality/valueThe detail solution procedure of implementing the IDEAL algorithm for compressible flows based on Delaunay triangular mesh is presented in this work, seemingly first in the literature.