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Papers by Ignasi Colominas
Computer Methods in Applied Mechanics and Engineering, Sep 1, 2007
This paper introduces the use of Moving Least-Squares (MLS) approximations for the development of... more This paper introduces the use of Moving Least-Squares (MLS) approximations for the development of high order upwind schemes on unstructured grids, applied to the numerical solution of the compressible Navier-Stokes equations. This meshfree interpolation technique is designed to reproduce arbitrary functions and their succesive derivatives from scattered, pointwise data, which is precisely the case of unstructured-grid finite volume discretizations. The Navier-Stokes solver presented in this study follows the ideas of the generalized Godunov scheme, using Roe's approximate Riemann solver for the inviscid fluxes. Linear, quadratic and cubic polynomial reconstructions are developed using MLS to compute high order derivatives of the field variables. The diffusive fluxes are computed using MLS as a global reconstruction procedure. Various examples of inviscid and viscous flow are presented and discussed.
International Journal for Numerical Methods in Engineering, Jun 25, 2009
This paper presents a comparison between two high-order methods. The first one is a high-order fi... more This paper presents a comparison between two high-order methods. The first one is a high-order finite volume (FV) discretization on unstructured grids that uses a meshfree method (moving least squares (MLS)) in order to construct a piecewise polynomial reconstruction and evaluate the viscous fluxes. The second method is a discontinuous Galerkin (DG) scheme. Numerical examples of inviscid and viscous flows are presented and the solutions are compared. The accuracy of both methods, for the same grid resolution, is similar, although the DG scheme requires a larger number of degrees of freedom than the FV-MLS method.
Applied Mathematics and Computation, Apr 1, 2023
Nowadays, in CFD there is a need of high accuracy methods for problems in which is essential to c... more Nowadays, in CFD there is a need of high accuracy methods for problems in which is essential to capture the fine features of the flow. Pseudospectral methods and finite differences schemes are commonly used in such high-accuracy demanding applications, as computational aeroacoustics or the simulation of turbulent flows. These methods are unbeatable, both in terms of accuracy and efficiency, by unstructured-grid approaches. For rather complex geometries, however, even though the use of multiblock grids allows the use of structured grid procedures, unstructured-grids methods are a reasonable option. But this kind of methods presents several problems for its application to real problems, some of them suffer a great increase of the computational resources and many others have difficulties for the evaluation of high order derivatives of the variables.-",,-.". 8th Wo rld 5th Euro pean Congress Con gr es s on on Computational Co mpu t a t io nal Methods in Applied Mechanics Sciences and Engineering
Computer Methods in Applied Mechanics and Engineering, Mar 1, 2020
A new very high-order technique for solving conservation laws with curved boundary domains is pro... more A new very high-order technique for solving conservation laws with curved boundary domains is proposed. A Finite Difference scheme on Cartesian grids is coupled with an original ghost cell method that provide accurate approximations for smooth solutions. The technology is based on a specific least square method with restrictions that enables to handle general Robin conditions. Several examples in two-dimensional geometries are presented for the unsteady Convection-Diffusion equation and the Euler equations. A fifth-order WENO scheme is employed with matching fifth-order reconstruction at the boundaries. Arbitrary high-order reconstruction for smooth flows is achievable independently of the underlying differential equation since the method works as a black-box dedicated to boundary condition treatment. c
WIT Transactions on the Built Environment, Sep 1, 2005
This paper presents a Galerkin based SPH formulation with moving least-squares meshless approxima... more This paper presents a Galerkin based SPH formulation with moving least-squares meshless approximation, applied to free surface flows. The Galerkin scheme provides a clear framework to analyze several procedures widely used in the classical SPH literature, suggesting that some of them should be reformulated in order to develop consistent algorithms. The performance of the methodology proposed is tested through various dynamic simulations, demonstrating the attractive ability of particle methods to handle severe distortions and complex phenomena.
European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2004, Jyva... more European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2004, Jyvaskiyla, Finland, 24–28 July 2004
Electric Power Systems Research, Feb 1, 2022
Engineering With Computers, May 7, 2020
This paper presents a computer software for the optimization of power transmission structures. Th... more This paper presents a computer software for the optimization of power transmission structures. The software employs a modified version of the Simulated Annealing algorithm that has been proven effective in large engineering problems. The target structures are three-dimensional steel trusses to be used as supporting towers of electrical lines. A mixed formulation merging continuous and discrete design variables is proposed for optimizing the size and shape of the trusses, including a first-order sensitivity analysis that reduces the computational cost. The implementation can be adapted to any kind of transmission tower and allows to quickly create a model to be analyzed and optimized in a few sequential steps. Despite its simplicity of use, the tools provided by the proposed framework allow to perform a full analysis of the design and provide an entire comprehension of its structural behavior. The software also includes a post-process and visualization tool set in a user-friendly graphical interface.
Applied Mathematics and Computation
WIT Transactions on the Built Environment, 2005
Besides the computational cost of solving advective-diffusive problems in convection dominated si... more Besides the computational cost of solving advective-diffusive problems in convection dominated situations, the standard statement for this phenomenon leads to the result that mass can propagate at an infinite speed. This paradoxical result occurs as a consequence of using Fick’s law [1] and it is related to the appearance of boundary layers on outflow borders when convection dominates diffusion. For these reasons we propose to use Cattaneo’s law [2] instead of Fick’s law as the constitutive equation of the problem. This approach leads to a totally hyperbolic system of partial differential equations. A finite diffusive velocity can be defined by using this approach. Several problems have been solved to show that the proposed formulation leads to stable results in convection dominated situations.
Organic Process Research & Development, 2001
Integral methods -such as the Finite Element Method (FEM) and the Boundary Element Method (BEL1)a... more Integral methods -such as the Finite Element Method (FEM) and the Boundary Element Method (BEL1)are frequently used in structural optimization problems to solve systems of partial differential equations. Therefore: one must take into account the large computational requirements of these sophisticated techniques at the time of choosing a suitable Mathematical Programming (MP) algorithm for this kind of problems. Among the currently available M P algorithms, Sequential Linear Programming (SLP) seems t o be one of the most adequate to structural optimization. Basically, SLP consist in constructing succesive linear approximations to the original non linear optimization problem within each step. However, the application of SLP may involve important malfunctions. Thus, the solution to the approximated linear problems can fail to exist, or may lead to a highly unfeasible point of the original non linear problem; also, large oscillations often occur near the optimum, precluding the algorith...
European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona 11-14 s... more European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona 11-14 september 2000
Computer Methods in Applied Mechanics and Engineering, Sep 1, 2007
This paper introduces the use of Moving Least-Squares (MLS) approximations for the development of... more This paper introduces the use of Moving Least-Squares (MLS) approximations for the development of high order upwind schemes on unstructured grids, applied to the numerical solution of the compressible Navier-Stokes equations. This meshfree interpolation technique is designed to reproduce arbitrary functions and their succesive derivatives from scattered, pointwise data, which is precisely the case of unstructured-grid finite volume discretizations. The Navier-Stokes solver presented in this study follows the ideas of the generalized Godunov scheme, using Roe's approximate Riemann solver for the inviscid fluxes. Linear, quadratic and cubic polynomial reconstructions are developed using MLS to compute high order derivatives of the field variables. The diffusive fluxes are computed using MLS as a global reconstruction procedure. Various examples of inviscid and viscous flow are presented and discussed.
International Journal for Numerical Methods in Engineering, Jun 25, 2009
This paper presents a comparison between two high-order methods. The first one is a high-order fi... more This paper presents a comparison between two high-order methods. The first one is a high-order finite volume (FV) discretization on unstructured grids that uses a meshfree method (moving least squares (MLS)) in order to construct a piecewise polynomial reconstruction and evaluate the viscous fluxes. The second method is a discontinuous Galerkin (DG) scheme. Numerical examples of inviscid and viscous flows are presented and the solutions are compared. The accuracy of both methods, for the same grid resolution, is similar, although the DG scheme requires a larger number of degrees of freedom than the FV-MLS method.
Applied Mathematics and Computation, Apr 1, 2023
Nowadays, in CFD there is a need of high accuracy methods for problems in which is essential to c... more Nowadays, in CFD there is a need of high accuracy methods for problems in which is essential to capture the fine features of the flow. Pseudospectral methods and finite differences schemes are commonly used in such high-accuracy demanding applications, as computational aeroacoustics or the simulation of turbulent flows. These methods are unbeatable, both in terms of accuracy and efficiency, by unstructured-grid approaches. For rather complex geometries, however, even though the use of multiblock grids allows the use of structured grid procedures, unstructured-grids methods are a reasonable option. But this kind of methods presents several problems for its application to real problems, some of them suffer a great increase of the computational resources and many others have difficulties for the evaluation of high order derivatives of the variables.-",,-.". 8th Wo rld 5th Euro pean Congress Con gr es s on on Computational Co mpu t a t io nal Methods in Applied Mechanics Sciences and Engineering
Computer Methods in Applied Mechanics and Engineering, Mar 1, 2020
A new very high-order technique for solving conservation laws with curved boundary domains is pro... more A new very high-order technique for solving conservation laws with curved boundary domains is proposed. A Finite Difference scheme on Cartesian grids is coupled with an original ghost cell method that provide accurate approximations for smooth solutions. The technology is based on a specific least square method with restrictions that enables to handle general Robin conditions. Several examples in two-dimensional geometries are presented for the unsteady Convection-Diffusion equation and the Euler equations. A fifth-order WENO scheme is employed with matching fifth-order reconstruction at the boundaries. Arbitrary high-order reconstruction for smooth flows is achievable independently of the underlying differential equation since the method works as a black-box dedicated to boundary condition treatment. c
WIT Transactions on the Built Environment, Sep 1, 2005
This paper presents a Galerkin based SPH formulation with moving least-squares meshless approxima... more This paper presents a Galerkin based SPH formulation with moving least-squares meshless approximation, applied to free surface flows. The Galerkin scheme provides a clear framework to analyze several procedures widely used in the classical SPH literature, suggesting that some of them should be reformulated in order to develop consistent algorithms. The performance of the methodology proposed is tested through various dynamic simulations, demonstrating the attractive ability of particle methods to handle severe distortions and complex phenomena.
European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2004, Jyva... more European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2004, Jyvaskiyla, Finland, 24–28 July 2004
Electric Power Systems Research, Feb 1, 2022
Engineering With Computers, May 7, 2020
This paper presents a computer software for the optimization of power transmission structures. Th... more This paper presents a computer software for the optimization of power transmission structures. The software employs a modified version of the Simulated Annealing algorithm that has been proven effective in large engineering problems. The target structures are three-dimensional steel trusses to be used as supporting towers of electrical lines. A mixed formulation merging continuous and discrete design variables is proposed for optimizing the size and shape of the trusses, including a first-order sensitivity analysis that reduces the computational cost. The implementation can be adapted to any kind of transmission tower and allows to quickly create a model to be analyzed and optimized in a few sequential steps. Despite its simplicity of use, the tools provided by the proposed framework allow to perform a full analysis of the design and provide an entire comprehension of its structural behavior. The software also includes a post-process and visualization tool set in a user-friendly graphical interface.
Applied Mathematics and Computation
WIT Transactions on the Built Environment, 2005
Besides the computational cost of solving advective-diffusive problems in convection dominated si... more Besides the computational cost of solving advective-diffusive problems in convection dominated situations, the standard statement for this phenomenon leads to the result that mass can propagate at an infinite speed. This paradoxical result occurs as a consequence of using Fick’s law [1] and it is related to the appearance of boundary layers on outflow borders when convection dominates diffusion. For these reasons we propose to use Cattaneo’s law [2] instead of Fick’s law as the constitutive equation of the problem. This approach leads to a totally hyperbolic system of partial differential equations. A finite diffusive velocity can be defined by using this approach. Several problems have been solved to show that the proposed formulation leads to stable results in convection dominated situations.
Organic Process Research & Development, 2001
Integral methods -such as the Finite Element Method (FEM) and the Boundary Element Method (BEL1)a... more Integral methods -such as the Finite Element Method (FEM) and the Boundary Element Method (BEL1)are frequently used in structural optimization problems to solve systems of partial differential equations. Therefore: one must take into account the large computational requirements of these sophisticated techniques at the time of choosing a suitable Mathematical Programming (MP) algorithm for this kind of problems. Among the currently available M P algorithms, Sequential Linear Programming (SLP) seems t o be one of the most adequate to structural optimization. Basically, SLP consist in constructing succesive linear approximations to the original non linear optimization problem within each step. However, the application of SLP may involve important malfunctions. Thus, the solution to the approximated linear problems can fail to exist, or may lead to a highly unfeasible point of the original non linear problem; also, large oscillations often occur near the optimum, precluding the algorith...
European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona 11-14 s... more European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona 11-14 september 2000