Mesh generation

Many science and engineering applications use high-resolution unstructured hexahedral meshes to model solid 3D shapes for finite element simulations. These simulations frequently dump the mesh and associated fields to disk for subsequent analysis, which involves the transfer of huge volumes of data. To reduce requirements on disk space and bandwidth, we propose efficient schemes for lossless online compression of hexahedral mesh geometry and connectivity. Our approach is to use hash-based value predictors to transform the mesh connectivity list into a more compact byte-aligned stream of symbols that can then be efficiently compressed using conventional text compressors such as gzip. Our scheme is memory efficient, fast, and simple to implement, and yields 1-3 orders of magnitude reduction on a set of benchmark meshes. For geometry and field coding, we derive a set of local spectral predictors optimized for each possible configuration of previously encoded and thus available vertices within a hexahedron. Combined with lossless floating-point residual coding, this approach improves considerably upon prior predictive geometry coding schemes.

An overset mesh approach is useful for unsteady flow problems which involve components moving relative to each other. Since the generation of a single mesh around all components is prone to mesh stretching due to the relative motion of bodies, using the overset grid methodology, an individual mesh can be generated for each component. In this study, a parallel overset grid assembler was developed to establish connectivity across component meshes. Connectivity information was transferred to the developed parallel flow solver. The assembler uses multiple methods such as alternating digital tree and stencil walking to reduce the time spent on domain connectivity. Both the assembler and solver were partitioned spatially so that overlapping mesh blocks reside in the same partitions. Spatial partitioning was performed using a 3D space partitioning structure, namely octree, to which mesh blocks are registered. The octree was refined adaptively until bins of octree could be evenly distribute...

A more accurate formulation of the mass source/sink is derived for the immersed-boundary method developed by Kim et al. (2001). Two flow problems (the decaying vortex problem and uniform flow past a circular cylinder) are simulated. The results indicate that the errors are reduced and the immersed boundary is smoothly represented by the present method. Recently the immersed-boundary (IB) method using momentum forcing and a Cartesian grid Navier-Stokes (N-S) solver has received much attention due to its ability to simulate viscous flows over or inside complex geometries. Many interpolation schemes for the momentum forcing have been developed in previous studies to simulate an IB of arbitrary shape. However, these schemes do not properly account for mass conservation of the cells crossed by the IB. Thus in practice the non-physical solution inside the solid region influences the physical solution in the fluid region. This problem can be avoided by using the Cartesian grid method (Ye et al. ( )), which is also known as the cut-cell method. However, the reshaping procedure introduces substantial complexities in terms of the modifications to the N-S solver. In addition, the velocity field must be solved by iteration at each time step, which substantially increases the computation time. Another approach to accounting for mass conservation of the cells crossed by the IB, proposed by Kim et al. (2001) (referred to as the KKC method hereafter), is to introduce a mass source/sink into the continuity equation. In practice, the only modification of the original N-S solver that was required was the addition of a source term to the right hand side of the pressure Poisson equation. This greatly simplified the manipulation and increased the computation time only slightly. Importantly, using this approach the velocity field can be solved without iteration at each time step. When the mass source/sink term was employed, Kim et al. (2001) found that the quality of the solution was improved and non-physical solution was corrected. However, they formulated the mass source/sink term in an approximate manner, i.e. the grid points fall on the IB. This approximation degrades the quality of the solution. In the present study, a more accurate mass

Se generaliza el esquema de indexación para una región circular concéntrica plana a la superficie de una esfera. Se define una estructura discreta con anillos latitudinales cuyo número de nodos crece linealmente desde los polos hasta el ecuador, y se establece una biyección explícita entre un índice lineal global m y coordenadas discretas (i,j), donde i denota la capa latitudinal y j la posición azimutal. Se derivan fórmulas cerradas para la función directa y, de manera particular, para la función inversa en el hemisferio sur, usando la función suelo, la función techo y una raíz cuadrada. Para el caso n = 2, se ilustra la distribución completa de los 38 nodos y se muestran ejemplos detallados de la correspondencia entre índices globales y coordenadas discretas. Se proporciona la correspondencia con coordenadas esféricas continuas y se analizan las propiedades topológicas de la malla inducida (vértices, aristas y caras triangulares).

Se generaliza el esquema de indexación para una región circular concéntrica plana a la superficie de una esfera. Se define una estructura discreta con anillos latitudinales cuyo número de nodos crece linealmente desde los polos hasta el ecuador, y se establece una biyección explícita entre un índice lineal global m y coordenadas discretas (i,j), donde i denota la capa latitudinal y j la posición azimutal. Se derivan fórmulas cerradas para la función directa y, de manera particular, para la función inversa en el hemisferio sur, usando la función suelo, la función techo y una raíz cuadrada. Para el caso n = 2, se ilustra la distribución completa de los 38 nodos y se muestran ejemplos detallados de la correspondencia entre índices globales y coordenadas discretas. Se proporciona la correspondencia con coordenadas esféricas continuas y se analizan las propiedades topológicas de la malla inducida (vértices, aristas y caras triangulares).

Se presenta un esquema de indexación para una región circular discreta formada por n circunferencias concéntricas. Se define una biyección explícita entre un índice lineal m y coordenadas discretas (i, j), donde i denota la capa concéntrica y j la posición angular. Para el caso n = 4, se ilustra la distribución completa de los 41 nodos y se muestran ejemplos de la correspondencia entre índices globales y coordenadas discretas. Se deriva una fórmula cerrada para la función inversa, permitiendo recuperar (i, j) a partir de m mediante una expresión que involucra la función suelo y una raíz cuadrada. Se analizan las propiedades topológicas de la malla inducida, estableciendo fórmulas cerradas para el número de aristas (E = 6n^2 +2n) y triángulos (T = 4n^2), y se verifica la característica de Euler V-E+T = 1 para dominios planos con frontera. Finalmente, se proporciona la correspondencia con coordenadas polares continuas, útil para aplicaciones numéricas y geométricas.

The article explores the phenomenon of applied computer science “information field of applied systems”. A new information model in computer science is the information field. The information field can be global and local or private. The global information field reflects reality or a picture of the world. The local information field reflects the subject area or area associated with the use of a system. Application systems serve as the implementation of complex systems in the information field. Application systems have their own information field, which is associated with the subject area and scope of the application system. The article reveals the content of the information field of the application system. A comparative analysis of an applied system and a complex system is given. Application systems in the information field can have the property of self-development. The preparation of information for application systems is described. It is shown that fact-fixing models have the property of emergence. The importance of information reception when working with application systems is shown. The necessity of cognitive modeling in preparing models for an applied system is shown. the activity and operation of application systems is described. The place of applied systems in the general theory of complex systems is shown.

This academic paper investigates the deep geometric properties, rigorous analytical proofs, and advanced structural applications of the Simson Line Theorem, a highly captivating topic in advanced Euclidean geometry that is unfortunately rarely covered within standard secondary school mathematics curricula. The fundamental essence of the theorem states that if perpendicular lines are dropped from any arbitrary point situated on the circumcircle of a given triangle to its three respective sides, the three resulting feet of these perpendiculars will always be strictly collinear. In this comprehensive study, we present a complete, highly structured, and elegant geometric proof of this unique collinearity property by utilizing the intrinsic cyclic properties of quadrilaterals and the sophisticated interplay of inscribed angles within a circle. Additionally, we actively explore the dynamic and fluid behavior of the Simson line using modern geometric visualization methodologies and explicitly demonstrate its high utility in solving some of the most challenging mathematical Olympiad problems across the globe. Through this multi-layered analysis, this independent research aims to foster higher-order analytical reasoning, advanced spatial awareness, and independent scientific research capabilities among high school students pursuing future STEM disciplines.

Generalized finite difference methods require that a properly posed set of nodes exists around each node in the mesh, so that the solution for the corresponding multivariate interpolation problem be unique. In this paper we first show that the construction of these meshes can be computerized using a relatively simple algorithm based on the concept of a Coatmèlec lattice. Then, we present a generalized finite difference method which provides a numerical solution of a partial differential equation over an arbitrary domain, using the generated meshes. The accuracy and mesh adaptivity of the method is evaluated using elliptical equations in several domains.

Geometr ía discreta, topolog ía combinatoria y construcci ón de mallas Triangulaciones como gramática topológica: las operaciones (1, 3) y (1, 2) del disco a las superficies con borde Una lectura formal y operativa de cómo los movimientos locales revelan la característica de Euler

Here, perfect truncated-distance codes (PTDC's) in the n-dimensional grid Λ n of Z n (0 < n ∈ Z) and its quotient toroidal grids are obtained via the truncated distance ρ (u, v) for all i ∈ {1, . . . , n}, and as n + 1, otherwise. While this ρ is related to the ℓ p metrics, the construction of PTDC's associated with lattice tilings of Z n is obtained as that of rainbow perfect dominating sets in previous work. In this work, that construction is extended to that of ternary compounds Γ n obtained by glueing, or locking, ternary n-cubes along their codimension 1 ternary subcubes. We ascertain the existence of an isolated PTDC of radius 2 in Γ n for n = 2 and conjecture that to hold for n > 2 with radius n. Finally, we ask whether there exists a suitable notion replacing that of quotient toroidal grids of Λ n for the case of Γ n . Lee spheres , perfect dominating sets (PDS's) , perfect-distance dominating sets (PDDS's) [1] and efficient dominating sets . Let 0 < n ∈ Z. The aforementioned codes or dominating sets are generally realized in lattice tilings of Z n whose tiles are translates of a common generalized Lee sphere. A natural follow-up here would be to consider lattice tilings of Z n with two different generalized Lee spheres. Focus on such follow-up for n > 3 is only possible by modifying the notion of the Lee distance d to that of a truncated distance ρ, defined in the next paragraph (not a standard distance, but see Remark 6) and subsequently applied in Section 2 that restates results of ). Furthermore, new graphs Γ n built as compounds of ternary n-cubes, presented below in Remark 1 and Sections 3-4 that generalize the lattice graph of Z n , extend those applications. Recall that the Hamming distance h(u, v) between vectors u is the number of positions i ∈ [n] = {1, . . . , n} for which u i = v i . Now, let ρ : Z n × Z n → Z be given by:

In this work we present an optimization of a mesh generation technique for pipe connections. Several stress analyses are made on these types of connections using a commercial finite element code with meshes supplied by the user. To facilitate the generation of these meshes a program was developed that generates a basic parameterized mesh composed of quadrilateral superelements, which are refined for each analysis. The user must specify the number of subdivisions in each superelement direction for each superelement. To optimize this process, minimizing user interventions, we employ isotropic and anisotropic refinement indicators. In the oil industry an important point is the analysis of the contact pressures at the connections. In the numerical examples presented we can appreciate the importance of the mesh refinement procedure to obtain accurate values of these pressures.

In this work we present an optimization of a mesh generation technique for pipe connections. Several stress analyses are made on these types of connections using a commercial finite element code with meshes supplied by the user. To facilitate the generation of these meshes a program was developed that generates a basic parameterized mesh composed of quadrilateral superelements, which are refined for each analysis. The user must specify the number of subdivisions in each superelement direction for each superelement. To optimize this process, minimizing user interventions, we employ isotropic and anisotropic refinement indicators. In the oil industry an important point is the analysis of the contact pressures at the connections. In the numerical examples presented we can appreciate the importance of the mesh refinement procedure to obtain accurate values of these pressures.

Low-order Whitney forms are widely used for electromagnetic field problems. Higher-order ones are increasingly applied, but their development is hampered by the complexity of the generation of element basis functions and of the localisation of the corresponding degrees of freedom on the mesh volumes. The paper aims to give a geometrical localisation of the degrees of freedom associated with Whitney forms of a polynomial degree higher than one. A conveniently implementable basis is provided for these elements on simplicial meshes. As for Whitney forms of degree one, the basis is expressed only in terms of the barycentric co-ordinates of the simplex.

Damages due to pitting corrosion of metals cost industry billions of dollars per year and can put human lives at risk. The design and implementation of an adaptive moving mesh method is provided for a moving boundary problem related to pitting corrosion. The adaptive mesh is generated automatically by solving a mesh PDE coupled to the nonlinear potential problem. The moving mesh approach is shown to enable initial mesh generation, provide mesh recovery and is able to smoothly tackle changing pit geometry. Materials with varying crystallography are considered. Changing mesh topology due to the merging of pits is also handled. The evolution of the pit shape, the pit depth and the pit width are computed and compared to existing results in the literature.

An enhanced higher-order 3-D ADI-FDTD algorithm for the accurate and unconditionally stable modeling of complex curvilinear EMC problems, is introduced in this paper. The new technique launches a topologically-consistent family of non-standard concepts which eliminate the serious dispersion errors of the usual ADI-FDTD scheme as time-step increases, and cancel its strong dependence on cell shape or mesh resolution. Thus, temporal increments can greatly exceed the Courant limit with superior stability and convergence levels. To optimize computing, higherorder curvilinear PML absorbers are also developed. Theoretical analysis, along with the numerical verification of diverse structures reveal that the proposed method is highly precise, subdues the vector-parasitic mechanisms of the ADI approach and achieves significant computational savings.

An enhanced higher-order 3-D ADI-FDTD algorithm for the accurate and unconditionally stable modeling of complex curvilinear EMC problems, is introduced in this paper. The new technique launches a topologically-consistent family of non-standard concepts which eliminate the serious dispersion errors of the usual ADI-FDTD scheme as time-step increases, and cancel its strong dependence on cell shape or mesh resolution. Thus, temporal increments can greatly exceed the Courant limit with superior stability and convergence levels. To optimize computing, higherorder curvilinear PML absorbers are also developed. Theoretical analysis, along with the numerical verification of diverse structures reveal that the proposed method is highly precise, subdues the vector-parasitic mechanisms of the ADI approach and achieves significant computational savings.

An algorithm to generate volume meshes by extrusion from surface meshes of arbitrary topology is presented. The algorithm utilizes a three-step, advancing layer scheme to extrude a smooth volume mesh starting from an initial surface mesh. First, a locally orthogonal reference mesh is algebraically generated for the layer. The reference mesh is then smoothed using a locally three-dimensional Poisson-type mesh generation equation that is generalized to smooth extruded meshes of arbitrary surface topology. By using the Poisson equation, control functions developed for elliptic grid generation may be employed to improve mesh quality. The Poisson smoother is modified in concave regions to enhance the robustness of the advancing layer scheme. Several preliminary examples are included to demonstrate the efficacy of the approach.

We describe a new geometric representation scheme suitable for finite element mesh generation. The representation is by boundaries (i.e., brep) and relations between boundaries are stored as a directed acyclic graph. The geometry itself is based on NURBS curves and surfaces. The new geometry proposal has been been adopted by the Cornell-Mississippi State joint ITR project. We describe why the geometric representation scheme is well-suited for mesh generation and engineering analysis.

In the domain of flow simulation, avoiding the manual conception and numerisation of the domain can lead to the saving of a certain amount of time. Some processes, using heavy devices like LASER metrology, allow the numerical reconstruction of a real object. The aim of this paper is to propose a more simple tool requiring a commercial digital camera (like a smartphone), to transform a digital picture into a ready to use mesh. Besides simplicity, the tool has to be precise enough to bring accurate simulation results. Then, image processing object detection and reconstruction are used to generate a 2D mesh that can be integrated in a finite volume transient CFD simulation. Cars and airfoils are chosen as objects and the DNS fluid flow Gerris solver performs the simulations. After a validation on a circular shape object, simulations, conducted at different Reynolds number, provide accurate results plotting the Von Karman alley regime.

This work introduces a methodology for selfadaptive numerical procedures, which relies on the various components of an integrated, object-oriented, computational environment involving pre-, analysis, and post-processing modules. A basic platform for numerical experiments and further development is provided, which allows implementation of new elements/error estimators and sensitivity analysis. A general implementation of the Superconvergent Patch Recovery (SPR) and the recently proposed Recovery by Equilibrium in Patches (REP) is presented. Both SPR and REP are compared and used for error estimation and for guiding the adaptive remeshing process. Moreover, the SPR is extended for calculating sensitivity quantities of ®rst and higher orders. The mesh (re-)generation process is accomplished by means of modern methods combining quadtree and Delaunay triangulation techniques. Surface mesh generation in arbitrary domains is performed automatically (i.e. with no user intervention) during the self-adaptive analysis using either quadrilateral or triangular elements. These ideas are implemented in the Finite Element System Technology in Adaptivity (FESTA) software. The effectiveness and ver-satility of FESTA are demonstrated by representative numerical examples illustrating the interconnections among ®nite element analysis, recovery procedures, error estimation/adaptivity and automatic mesh generation.

This work describes the implementation of a plug-in that adds finite element pre-and post-processing capabilities to gOcad. The gFEM plug-in implements an algorithm for generating unstructured tetrahedral finite element meshes in arbitrarily shaped three-...

This work describes a techni que for generating two-dimensional triangular meshes using distributed memory parallel computers, based on a master/slaves model. This techni que uses a coarse quadtree to decompo se the domain and a serial advancing front techni que to generate the mesh in each subdomain concurrently. In order to advance the front to a neighboring subdomain, each subdomain suffers a shift to a Cartesian direction, and the same advancing front approach is performed on the shi fted subdomain. This shift-and-remesh procedure is repeatedly applied until no more mesh can be generated, shifting the subdomains to different directions each turn. A finer quadtree is also employed in this work to help estimate the processing load associated with each subdomain. This load estimati on technique produces results that accurately represent the numbe r of elements to be generated in each subdomain, leading to proper runtime prediction and to a well-balanced algorithm. The meshes generated with the parallel technique have the same quality as those generated serially, within acceptable limits. Although the presented approach is two-dimensional, the idea can be easily extended to three dimensions.

Aerodynamic shape optimization based on computational fluid dynamics (CFD) requires three steps: updating the geometry based on the design variables, updating the CFD surface mesh for the new geometry, and updating the CFD volume mesh based on the new surface mesh. While there are many tools available for the first and third steps, the methods available for the second step are insufficient for geometries that have intersecting components. For these geometries, the CFD surface mesh needs to be updated near component intersections to conform to the component geometries and the updated intersection curves. To address this need, we introduce a method that can deform the CFD surface mesh nodes near component intersections. The method can handle arbitrary design changes for each intersecting component as long as the geometric topology is unchanged. Furthermore, the method is suitable for gradient-based optimization because it smoothly deforms every CFD surface node without introducing topological changes in the CFD surface mesh. In this paper, we detail each step of the proposed method and visualize the range of design changes that can be achieved with this approach. Finally, we use the proposed method in an aerodynamic shape optimization problem to optimize the wing-body intersection of the DLR-F6 configuration. These results demonstrate the effectiveness of the proposed method in a high-fidelity design optimization framework. The method applies to both structured and unstructured CFD meshes and makes it possible to use computer-aided design and conceptual design geometry tools within high-fidelity design optimization.

The visualization of 3D groundwater flow is a challenging task. Previous versions of our software STRING [1] solely focused on intuitive visualization of complex flow scenarios for non-professional audiences. STRING, developed by Fraunhofer ITWM (Kaiserslautern, Germany) and delta h Ingenieurgesellschaft mbH (Witten, Germany), provides the necessary means for visualization of both 2D and 3D data on planar and curved surfaces. In this contribution we discuss how to extend this approach to a full 3D tool and its challenges in continuation of Michel et al. [2]. This elevates STRING from a post-production to an exploration tool for experts.

A new multi-phase model for low speed gas/liquid mixtures is presented; it does not require ad-hoc closure models for the variation of mixture density with pressure and yields thermodynamically correct acoustic propagation for multi-phase mixtures. The solution procedure has an interface-capturing scheme that incorporates an additional scalar transport equation for the gas void fraction. Cavitation is modeled via a finite rate source term that initiates phase change when liquid pressure drops below its saturation value. The numerical procedure has been implemented within a multi-element unstructured framework CRUNCH that permits the grid to be locally refined in the interface region. The solution technique incorporates a parallel, domain decomposition strategy for efficient 3D computations. Detailed results are presented for sheet cavitation over a cylindrical head form and a NACA 66 hydrofoil.

We give an expected-case analysis of Delaunay triangulations. To avoid edge effects we consider a unit-intensity Poisson process in Euclidean d-space, and then limit attention to the portion of the triangulation within a cube of side n 1/d . For d equal to two, we calculate the expected maximum edge length, the expected minimum and maximum angles, and the average aspect ratio of a triangle. We also show that in any fixed dimension the expected maximum vertex degree is Θ(log n/ log log n). Altogether our results provide some measure of the suitability of the Delaunay triangulation for certain applications, such as interpolation and mesh generation.

We show how to triangulate an n-vertex polygonal region-adding extra vertices as necessary-with triangles of guaranteed quality. Using only O(n) triangles, we can guarantee that the smallest height (shortest dimension) of a triangle is approximately aa large as possible. Using O(n log n) triangles, we can also guarantee that the largest angle is no greater than 150°. Finally we give a nonobtuse triangulation algorithm for convex polygons that uses O(nl 85) triangles. 1.

We study several versions of the problem of generating triangular meshes for nite element methods. We show how to triangulate a planar point set or polygonally bounded domain with triangles of bounded aspect ratio; how to triangulate a planar point set with triangles having no obtuse angles; how to triangulate a point set in arbitrary dimension with simplices of bounded aspect ratio; and how to produce a linear-size Delaunay triangulation of a multi-dimensional point set by adding a linear number of extra points. All our triangulations have size (number of triangles) within a constant factor of optimal, and run in optimal time O(n logn+k) with input of size n and output of size k. No previous work on mesh generation simultaneously guarantees well-shaped elements and small total size.

We describe efficient PRAM algorithms for constructing unbalanced quadtrees, balanced quadtrees, and quadtree-based finite element meshes. Our algorithms take time O(log n) for point set input and O(log n log k) time for planar straight-line graphs, using O(n + k/ log n) processors, where n measures input size and k output size.

We survey the computational geometry relevant to nite element mesh generation. We especially focus on optimal triangulations of geometric domains in two-and three-dimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some criterion that measures the size, shape, or number of triangles. We discuss algorithms both for the optimization of triangulations on a xed set of vertices and for the placement of new vertices Steiner points. We brie y survey the heuristic algorithms used in some practical mesh generators.

In this paper we present a new parallel multi-frontal direct solver, dedicated for hp Finite Element Method (hp-FEM). The self-adaptive hp FEM generates in a fully automatic mode a sequence of hp meshes delivering exponential convergence of the error with respect to the number of degrees of freedom (d.o.f.) as well as the CPU time, by performing a sequence of hp refinements starting from an arbitrary initial mesh. The solver constructs initial elimination tree for an arbitrary initial mesh, and expands the elimination tree each time the mesh is refined. This allows to keep track of the order of elimination for the solver. The solver also minimizes the memory usage, by de-allocating partial LU factorizations computed during the elimination stage of the solver, and recomputes them for the backward substitution stage, by utilizing only about 10% of the computational time necessary for the original computations. The solver has been tested on 3D Direct Current (DC) borehole resistivity measurement simulations problems. We measure the execution time and memory usage of the solver over large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive hp-FEM, with finite elements of various size and polynomial orders of approximation varying from p = 1 to p = 9. From the presented experiments it follows that the parallel solver scales well up to the maximum number of utilized processors. The limit for the solver scalability is the maximum sequential part of the algorithm: the computations of the partial LU factorizatons over the longest path, comming from the root of the elimination tree down to the deepest leaf.

This work presents a numerical method for the analysis of fully nonlinear aeroelastic problems. The aeroelastic model consisted of a Navier-Stokes flow solver, a nonlinear structural model, and a solution methodology that assured synchronous interaction between the nonlinear structure and the fluid flow. The flow around the deforming wing was modeled as unsteady, compressible and viscous using the Reynolds-averaged Navier-Stokes (RANS) equations. To reduce the computational time, a three-level multigrid algorithm was implemented and the flow solver was parallelized. The message-passing interface (MPI) standard libraries were used for the parallel interprocessor communication. The computational domain was divided into topologically identical layers that spanned from the root to past the tip of the wing. A novel mesh deformation algorithm was developed to deform the mesh as the structure of the wing was being displaced. The mesh deformation algorithm was able to handle wing tip deformations of up to 60 % of the wing semi-span. Besides being robust, the mesh deforming algorithm was computationally more efficient than regriding, since deforming an existing mesh was computationally less expensive than generating a new mesh for each wing position. Results are presented for the validation and verification of both the flow solver and the aeroelastic solver. The flow solver was validated using: (1) the flow over a flat plate, to validate the turbulent model implementation, and (2) the flow over the NACA 0012 airfoil and over the F-5 wing, to validate the implementation of I would also like to thank my fellow graduate students Brian Richardson, Tom Brenner, and those who already graduated, Chetan Nichkawde, Steven Chambers, Kyusup Kim, Celerino Resendiz, and Tao Yuan. Special thanks to my classmates and friends at the Aerospace Department and to the fine department faculty and staff, who assisted me during my studies at Texas A&M University. Finally, I would like to thank my parents, Angel and Marta, my brother Matias, and my beloved girlfriend Lisa, for their love, support, and encouragement. Special thanks to my friends and family in Argentina who despite the distance kept a close contact with me and shared the exciting experience of living in College Station and Texas. vi TABLE OF CONTENTS CHAPTER

A standard use of triangulation in GIS is to model terrain surface using TIN. In many simulation models of physical phenomena, triangulation is often used to depict the entire spatial domain, which may include buildings, landmarks and other surface objects in addition to the terrain surface. Creating a seamless surface of complex building structures together with the terrain is challenging and existing approaches are laborious, time-consuming and error-prone. We propose an efficient and robust procedure using computational geometry techniques to derive triangulated building surfaces from 2D polygon data with a height attribute. We also propose a new method to merge the resultant building surfaces with the triangulated terrain surface to produce a seamless surface for the entire study area. Using Oklahoma City data, we demonstrate the proposed method. The resultant surface is used as the input data for a simulated transport and dispersion event in Oklahoma City. The proposed method can produce the seamless surface data to be used for various types of physical models in a fraction of the time required by previous methods.

This report has been reproduced directly from the best available copy. Available to DOE and DOE contractors from the Office of Scientific and Technical Information, P. 0. Box 62, Oak Ridge, TN 3783 1; prices available from (423) 576-8401, FTS 626-8401.

The Liquid Composite Molding is a processing technique has the capability of manufacturing polymer composites with large size and complex shapes. A good control of process leads to improve the process performance hence the productivity and quality of manufactured parts and that requires knowing all or some process states, but it is often difficult to access these states. However, in many cases, due to cost considerations and physical constraints, the use of sensors is still very limited. In this paper, we overcame the need to use of mechanical sensors by using an observer. This paper proposes an observer for determine the observability for liquid composite molding process. The system observability is analysed by the rank condition, then a nonlinear state observer is designed using a Lyapunov theory and a linear matrix inequalities technique. The observer is formally shown that all variables converge to their true values. The effectiveness of the proposed scheme is demonstrated through computer simulations in the MATLAB/SIMULINK environment.

In Computational Fluid Dynamics (CFD), coarse mesh simulations offer computational efficiency but often lack precision. Applying conventional super-resolution to these simulations poses a significant challenge due to the fundamental contrast between downsampling high-resolution images and authentically emulating lowresolution physics. The former method conserves more of the underlying physics, surpassing the usual constraints of real-world scenarios. We propose a novel definition of super-resolution tailored for PDE-based problems. Instead of simply downsampling from a high-resolution dataset, we use coarse-grid simulated data as our input and predict fine-grid simulated outcomes. Employing a physics-infused UNet upscaling method, we demonstrate its efficacy across various 2D-CFD problems such as discontinuity detection in Burger's equation, Methane combustion, and fouling in Industrial heat exchangers. Our method enables the generation of fine-mesh solutions bypassing traditional simulation, ensuring considerable computational saving and fidelity to the original ground truth outcomes. Through diverse boundary conditions during training, we further establish the robustness of our method, paving the way for its broad applications in engineering and scientific CFD solvers.

This paper presents a new algorithm to generate hexahedral meshes in extrusion geometries. Several algorithms have been devised to generate hexahedral meshes by projecting the cap surfaces along a sweep path. In all of these algorithms the crucial step is the placement of the inner layer of nodes. That is, the projection of the source surface mesh along the sweep path. From the computational point of view, sweep methods based on a leastsquares approximation of an affine mapping are the fastest alternative to compute these projections. Several functionals have been introduced to perform the least-squares approximation. However, for very simple and typical geometrical configurations they may generate low-quality projected meshes. For instance, they may induce skewness and flattening effects on the projected discretizations. In addition, for these configurations the minimization of these functionals may lead to a set of normal equations with singular system matrix. In this work we analyze previously defined functionals. Based on this analysis we propose a new functional and show that its minimization overcomes these drawbacks. Finally, we present several examples to assess the properties of the proposed functional.

Sweep method is one of the most robust techniques to generate hexahedral meshes in extrusion volumes. One of the main issues to be dealt by any sweep algorithm is the projection of a source surface mesh onto the target surface. This paper presents a new algorithm to map a given mesh over the source surface onto the target surface. This projection is carried out by means of a least-squares approximation of an affine mapping defined between the parametric spaces of the surfaces. Once the new mesh is obtained on the parametric space of the target surface, it is mapped up according to the target surface parameterization. Therefore, the developed algorithm does not require to solve any root finding problem to ensure that the projected nodes are on the target surface. Afterwards, this projection algorithm is extended to three dimensional cases and it is used to generate the inner layers of elements in the physical space.

This paper presents a new algorithm to generate hexahedral meshes in extrusion geometries. Several algorithms have been devised to generate hexahedral meshes by projecting the cap surfaces along a sweep path. In all of these algorithms the crucial step is the placement of the inner layer of nodes. That is, the projection of the source surface mesh along the sweep path. From the computational point of view, sweep methods based on a leastsquares approximation of an affine mapping are the fastest alternative to compute these projections. Several functionals have been introduced to perform the least-squares approximation. However, for very simple and typical geometrical configurations they may generate low-quality projected meshes. For instance, they may induce skewness and flattening effects on the projected discretizations. In addition, for these configurations the minimization of these functionals may lead to a set of normal equations with singular system matrix. In this work we analyze previously defined functionals. Based on this analysis we propose a new functional and show that its minimization overcomes these drawbacks. Finally, we present several examples to assess the properties of the proposed functional.