E. Ruiz-Gironés - Academia.edu (original) (raw)
Papers by E. Ruiz-Gironés
Una de las técnicas utilizadas para generar mallas estructuradas de cuadriláteros es el método de... more Una de las técnicas utilizadas para generar mallas estructuradas de cuadriláteros es el método de submapping. Este método descompone la geometría en piezas lógicamente equivalente a un cuadrilátero y después malla cada una de ellas por separado manteniendo la compatibilidad de la malla mediante la resolución de un problema lineal entero. El algoritmo de submapping tiene dos limitaciones principales. La primera de ellas es que sólo se puede aplicar en geometrías tales que el ángulo entre dos aristas consecutivas es, aproximadamente, un múltiplo entero de |-|/2. La segunda limitación es que la geometría tiene que ser simplemente conexa. Con el objetivo de mitigar estas restricciones, en este artículo se presentan dos modificaciones originales que permiten reducir el efecto de dichas limitaciones. Finalmente, se presentan diversos ejemplos numéricos que ponen de manifiesto la robustez y la aplicabilidad de los algoritmos desarrollados
Proceedings of the Sixth International Conference on Engineering Computational Technology, 2008
E. Ruiz-Gironés, X. Roca and J. Sarrate 1 Laboratori de Càlcul Numèric (LaCàN), Departament de Ma... more E. Ruiz-Gironés, X. Roca and J. Sarrate 1 Laboratori de Càlcul Numèric (LaCàN), Departament de Matemàtica Aplicada III (MA III), Universitat Politècnica de Catalunya (UPC), Campus Nord UPC, 08034 Barcelona, Spain. {eloi.ruiz, jose.sarrate}@upc.edu 2 Aerospace Computational Design Laboratory, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. xeviroca@mit.edu
During the last years, unstructured high-order methods are gaining popularity in those applicatio... more During the last years, unstructured high-order methods are gaining popularity in those applications of computational methods where high-fidelity simulations on curved domains are required. For these applications, it is required to generate meshes composed by highorder elements that are curved to match the boundaries of the domain. The existent techniques to generate curved meshes are based on a posteriori approach. Specifically, an unstructured linear mesh is first generated. Then, the linear mesh is converted to a high-order mesh, and curved to match the domain boundary. Finally, the boundary nodes are fixed, to preserve the curved boundary mesh, and the inner nodes are relocated to obtain a valid and high-quality mesh.
International Journal of Computational Fluid Dynamics
We develop a high-order hybridizable discontinuous Galerkin (HDG) formulation to solve the immisc... more We develop a high-order hybridizable discontinuous Galerkin (HDG) formulation to solve the immiscible and incompressible two-phase flow problem in a heterogeneous porous media. The HDG method is locally conservative, has fewer degrees of freedom than other discontinuous Galerkin methods due to the hybridization procedure, provides built-in stabilization for arbitrary polynomial degrees and, if the error of the temporal discretization is low enough, the pressure, the saturation and their fluxes converge with order P + 1 in L 2-norm, being P the polynomial degree. In addition, an element-wise post-process can be applied to obtain a convergence rate of P + 2 in L 2-norm for the scalar variables. All of these advantages make the HDG method suitable for solving multiphase flow trough porous media. We show numerical evidence of the convergences rates. Finally, to assess the capabilities of the proposed formulation, we apply it to several cases of water-flooding technique for oil recovery.
Computational Technology Reviews, 2014
Discretization techniques such the finite element method, the finite volume method or the discont... more Discretization techniques such the finite element method, the finite volume method or the discontinuous Galerkin method are the most used simulation techniques in applied sciences and technology. These methods rely on a spatial discretization adapted to the geometry and to the prescribed distribution of element size. Several fast and robust algorithms have been developed to generate triangular and tetrahedral meshes. In these methods local connectivity modifications are a crucial step. Nevertheless, in hexahedral meshes the connectivity modifications propagate through the mesh. In this sense, hexahedral meshes are more constrained and therefore, more difficult to generate. However, in many applications such as boundary layers in computational fluid dynamics or composite material in structural analysis hexahedral meshes are preferred. In this work we present a survey of developed methods for generating structured and unstructured hexahedral meshes.
Proceedings of the Seventh International Conference on Engineering Computational Technology, 2010
One of the most used algorithms to generate hexahedral meshes for extrusion volumes is the multi-... more One of the most used algorithms to generate hexahedral meshes for extrusion volumes is the multi-sweeping method. The algorithm decomposes the geometry into many-to-one sub-volumes and then meshes each sub-volume separately.
Advances in Engineering Software, 2015
In this work, we present a simultaneous untangling and smoothing technique for quadrilateral and ... more In this work, we present a simultaneous untangling and smoothing technique for quadrilateral and hexahedral meshes. The algorithm iteratively improves a quadrilateral or hexahedral mesh by minimizing an objective function defined in terms of a regularized algebraic distortion measure of the elements. We propose several techniques to improve the robustness and the computational efficiency of the optimization algorithm. In addition, we have adopted an object-oriented paradigm to create a common framework to smooth meshes composed by any type of elements, and using different minimization techniques. Finally, we present several examples to show that the proposed technique obtains valid meshes composed by high-quality quadrilaterals and hexahedra, even when the initial meshes contain a large number of tangled elements.
Una de las técnicas más utilizadas para generar mallas estructuradas de cuadriláteros es el métod... more Una de las técnicas más utilizadas para generar mallas estructuradas de cuadriláteros es el método de submapping. Este método descompone la geometría en piezas lógicamente equivalentes a un cuadrilátero y después malla cada una de ellas por separado manteniendo la compatibilidad de la malla mediante la resolución de un problema lineal entero. El algoritmo de submapping tiene dos limitaciones principales. La primera de ellas es que sólo se puede aplicar en geometrías tales que elángulo entre dos aristas consecutivas es, aproximadamente, un múltiplo entero de π/2. La segunda limitación es que la geometría tiene que ser simplemente conexa. Con el objetivo de mitigar estas restricciones, en este artículo se presentan dos modificaciones originales que permiten reducir el efecto de dichas limitaciones. Finalmente, se presentan diversos ejemplos numéricos que ponen de manifiesto la robustez y la aplicabilidad de los algoritmos desarrollados.
Procedia Engineering, 2014
Mesh untangling and smoothing is an important part of the meshing process to obtain high-quality ... more Mesh untangling and smoothing is an important part of the meshing process to obtain high-quality discretizations. The usual approach consists on moving the position of the interior nodes while considering fixed the position of the boundary ones. However, the boundary nodes may constrain the quality of the whole mesh, and high-quality elements may not be generated. Specifically, thin regions in the geometry or special configurations of the boundary edges may induce low-quality elements. To overcome this drawback, we present a smoothing and untangling procedure that moves the interior nodes as well as the boundary ones, via an optimization process. The objective function is defined as a regularized distortion of the elements, and takes the nodal Cartesian coordinates as input arguments. When dealing with surface and edge nodes, the objective function uses the nodal parametric coordinates in order to avoid projecting them to the boundary. The novelty of the approach is that we consider a single target objective function (mesh distortion) where all the nodes, except the vertex nodes, are free to move on the corresponding CAD entity. Although the objective function is defined globally, for implementation purposes we propose to perform a node-by-node process. To minimize the objective function, we consider a block iterated non-linear Gauss-Seidel method using a hierarchical approach. That is, we first smooth the edge nodes, then the face nodes, and finally the inner nodes. This process is iterated using a node-by-node Gauss-Seidel approach until convergence is achieved.
Proceedings of the 22nd International Meshing Roundtable, 2014
One of the most widely used algorithms to generate hexahedral meshes in extrusion volumes with se... more One of the most widely used algorithms to generate hexahedral meshes in extrusion volumes with several source and target surfaces is the multi-sweeping method. However, the multi-sweeping method is highly dependent on the final location of the nodes created during the decomposition process. Moreover, inaccurate location of inner nodes may generate erroneous imprints of the geometry surfaces such that a final mesh could not be generated. In this work, we present a new procedure to decompose the geometry in many-to-one sweepable volumes. The decomposition is based on a least-squares approximation of affine mappings defined between the loops of nodes that bound the sweep levels. In addition, we introduce the concept of computational domain, in which every sweep level is planar. We use this planar representation for two purposes. On the one hand, we use it to perform all the imprints between surfaces. Since the computational domain is planar, the robustness of the imprinting process is increased. On the other hand, the computational domain is also used to compute the projection onto source surfaces. Finally, the location of the inner nodes created during the decomposition process is computed by averaging the locations computed projecting from target and source surfaces.
Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based ... more Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high quality elements in the inner part of the domain using an inside-outside approach. On the other hand, advancing front methods generate high quality hexahedra near the boundary using an outside-inside approach.
Una de las técnicas utilizadas para generar mallas estructuradas de cuadriláteros es el método de... more Una de las técnicas utilizadas para generar mallas estructuradas de cuadriláteros es el método de submapping. Este método descompone la geometría en piezas lógicamente equivalente a un cuadrilátero y después malla cada una de ellas por separado manteniendo la compatibilidad de la malla mediante la resolución de un problema lineal entero. El algoritmo de submapping tiene dos limitaciones principales. La primera de ellas es que sólo se puede aplicar en geometrías tales que el ángulo entre dos aristas consecutivas es, aproximadamente, un múltiplo entero de |-|/2. La segunda limitación es que la geometría tiene que ser simplemente conexa. Con el objetivo de mitigar estas restricciones, en este artículo se presentan dos modificaciones originales que permiten reducir el efecto de dichas limitaciones. Finalmente, se presentan diversos ejemplos numéricos que ponen de manifiesto la robustez y la aplicabilidad de los algoritmos desarrollados
Proceedings of the Sixth International Conference on Engineering Computational Technology, 2008
E. Ruiz-Gironés, X. Roca and J. Sarrate 1 Laboratori de Càlcul Numèric (LaCàN), Departament de Ma... more E. Ruiz-Gironés, X. Roca and J. Sarrate 1 Laboratori de Càlcul Numèric (LaCàN), Departament de Matemàtica Aplicada III (MA III), Universitat Politècnica de Catalunya (UPC), Campus Nord UPC, 08034 Barcelona, Spain. {eloi.ruiz, jose.sarrate}@upc.edu 2 Aerospace Computational Design Laboratory, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. xeviroca@mit.edu
During the last years, unstructured high-order methods are gaining popularity in those applicatio... more During the last years, unstructured high-order methods are gaining popularity in those applications of computational methods where high-fidelity simulations on curved domains are required. For these applications, it is required to generate meshes composed by highorder elements that are curved to match the boundaries of the domain. The existent techniques to generate curved meshes are based on a posteriori approach. Specifically, an unstructured linear mesh is first generated. Then, the linear mesh is converted to a high-order mesh, and curved to match the domain boundary. Finally, the boundary nodes are fixed, to preserve the curved boundary mesh, and the inner nodes are relocated to obtain a valid and high-quality mesh.
International Journal of Computational Fluid Dynamics
We develop a high-order hybridizable discontinuous Galerkin (HDG) formulation to solve the immisc... more We develop a high-order hybridizable discontinuous Galerkin (HDG) formulation to solve the immiscible and incompressible two-phase flow problem in a heterogeneous porous media. The HDG method is locally conservative, has fewer degrees of freedom than other discontinuous Galerkin methods due to the hybridization procedure, provides built-in stabilization for arbitrary polynomial degrees and, if the error of the temporal discretization is low enough, the pressure, the saturation and their fluxes converge with order P + 1 in L 2-norm, being P the polynomial degree. In addition, an element-wise post-process can be applied to obtain a convergence rate of P + 2 in L 2-norm for the scalar variables. All of these advantages make the HDG method suitable for solving multiphase flow trough porous media. We show numerical evidence of the convergences rates. Finally, to assess the capabilities of the proposed formulation, we apply it to several cases of water-flooding technique for oil recovery.
Computational Technology Reviews, 2014
Discretization techniques such the finite element method, the finite volume method or the discont... more Discretization techniques such the finite element method, the finite volume method or the discontinuous Galerkin method are the most used simulation techniques in applied sciences and technology. These methods rely on a spatial discretization adapted to the geometry and to the prescribed distribution of element size. Several fast and robust algorithms have been developed to generate triangular and tetrahedral meshes. In these methods local connectivity modifications are a crucial step. Nevertheless, in hexahedral meshes the connectivity modifications propagate through the mesh. In this sense, hexahedral meshes are more constrained and therefore, more difficult to generate. However, in many applications such as boundary layers in computational fluid dynamics or composite material in structural analysis hexahedral meshes are preferred. In this work we present a survey of developed methods for generating structured and unstructured hexahedral meshes.
Proceedings of the Seventh International Conference on Engineering Computational Technology, 2010
One of the most used algorithms to generate hexahedral meshes for extrusion volumes is the multi-... more One of the most used algorithms to generate hexahedral meshes for extrusion volumes is the multi-sweeping method. The algorithm decomposes the geometry into many-to-one sub-volumes and then meshes each sub-volume separately.
Advances in Engineering Software, 2015
In this work, we present a simultaneous untangling and smoothing technique for quadrilateral and ... more In this work, we present a simultaneous untangling and smoothing technique for quadrilateral and hexahedral meshes. The algorithm iteratively improves a quadrilateral or hexahedral mesh by minimizing an objective function defined in terms of a regularized algebraic distortion measure of the elements. We propose several techniques to improve the robustness and the computational efficiency of the optimization algorithm. In addition, we have adopted an object-oriented paradigm to create a common framework to smooth meshes composed by any type of elements, and using different minimization techniques. Finally, we present several examples to show that the proposed technique obtains valid meshes composed by high-quality quadrilaterals and hexahedra, even when the initial meshes contain a large number of tangled elements.
Una de las técnicas más utilizadas para generar mallas estructuradas de cuadriláteros es el métod... more Una de las técnicas más utilizadas para generar mallas estructuradas de cuadriláteros es el método de submapping. Este método descompone la geometría en piezas lógicamente equivalentes a un cuadrilátero y después malla cada una de ellas por separado manteniendo la compatibilidad de la malla mediante la resolución de un problema lineal entero. El algoritmo de submapping tiene dos limitaciones principales. La primera de ellas es que sólo se puede aplicar en geometrías tales que elángulo entre dos aristas consecutivas es, aproximadamente, un múltiplo entero de π/2. La segunda limitación es que la geometría tiene que ser simplemente conexa. Con el objetivo de mitigar estas restricciones, en este artículo se presentan dos modificaciones originales que permiten reducir el efecto de dichas limitaciones. Finalmente, se presentan diversos ejemplos numéricos que ponen de manifiesto la robustez y la aplicabilidad de los algoritmos desarrollados.
Procedia Engineering, 2014
Mesh untangling and smoothing is an important part of the meshing process to obtain high-quality ... more Mesh untangling and smoothing is an important part of the meshing process to obtain high-quality discretizations. The usual approach consists on moving the position of the interior nodes while considering fixed the position of the boundary ones. However, the boundary nodes may constrain the quality of the whole mesh, and high-quality elements may not be generated. Specifically, thin regions in the geometry or special configurations of the boundary edges may induce low-quality elements. To overcome this drawback, we present a smoothing and untangling procedure that moves the interior nodes as well as the boundary ones, via an optimization process. The objective function is defined as a regularized distortion of the elements, and takes the nodal Cartesian coordinates as input arguments. When dealing with surface and edge nodes, the objective function uses the nodal parametric coordinates in order to avoid projecting them to the boundary. The novelty of the approach is that we consider a single target objective function (mesh distortion) where all the nodes, except the vertex nodes, are free to move on the corresponding CAD entity. Although the objective function is defined globally, for implementation purposes we propose to perform a node-by-node process. To minimize the objective function, we consider a block iterated non-linear Gauss-Seidel method using a hierarchical approach. That is, we first smooth the edge nodes, then the face nodes, and finally the inner nodes. This process is iterated using a node-by-node Gauss-Seidel approach until convergence is achieved.
Proceedings of the 22nd International Meshing Roundtable, 2014
One of the most widely used algorithms to generate hexahedral meshes in extrusion volumes with se... more One of the most widely used algorithms to generate hexahedral meshes in extrusion volumes with several source and target surfaces is the multi-sweeping method. However, the multi-sweeping method is highly dependent on the final location of the nodes created during the decomposition process. Moreover, inaccurate location of inner nodes may generate erroneous imprints of the geometry surfaces such that a final mesh could not be generated. In this work, we present a new procedure to decompose the geometry in many-to-one sweepable volumes. The decomposition is based on a least-squares approximation of affine mappings defined between the loops of nodes that bound the sweep levels. In addition, we introduce the concept of computational domain, in which every sweep level is planar. We use this planar representation for two purposes. On the one hand, we use it to perform all the imprints between surfaces. Since the computational domain is planar, the robustness of the imprinting process is increased. On the other hand, the computational domain is also used to compute the projection onto source surfaces. Finally, the location of the inner nodes created during the decomposition process is computed by averaging the locations computed projecting from target and source surfaces.
Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based ... more Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high quality elements in the inner part of the domain using an inside-outside approach. On the other hand, advancing front methods generate high quality hexahedra near the boundary using an outside-inside approach.