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• Modeling bed erosion in free surface flows by the particle finite element method

  E. Oñate, M. Celigueta, S. Idelsohn

  Acta Geotechnica (2006). Vol. 1 (4), pp. 237-252

  
  

  Abstract

  We present a general formulation for modeling bed erosion in free surface flows using the particle finite element method (PFEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in domains containing fluid and solid subdomains. Nodes are viewed as material points (called particles) which can freely move and even separate from the fluid and solid subdomains representing, for instance, the effect of water drops or soil/rock particles. A mesh connects the nodes defining the discretized domain in the fluid and solid regions where the governing equations, expressed in an integral form, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the nonlinear transient coupled fluid-structure problem is described. The erosion mechanism is modeled by releasing the material adjacent to the bed surface according to the frictional work generated by the fluid shear stresses. The released bed material is subsequently transported by the fluid flow. Examples of application of the PFEM to solve a number of bed erosion problems involving large motions of the free surface and splashing of waves are presented.

  Abstract
  We present a general formulation for modeling bed erosion in free surface flows using the particle finite element method (PFEM). The key feature of the PFEM is the use of [...]

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• A multiresolution strategy for solving landslides using the Particle Finite Element Method

  P. Becker, S. Idelsohn

  Acta Geotechnica (2016). Vol. 11 (3), pp. 643-657

  
  

  Abstract

  We present an approach for the simulation of landslides using the Particle Finite Element Method of the second generation. In this work, the multiphase nature (granular phase and water) of the phenomenon is considered in a staggered fashion using a single, indeformable Finite Element mesh. A fractional step and a monolithic strategy are used for the water flow and granular phase, respectively. In this way, the maximum accuracy with minimal computational times is reached. The method is completed by adding the interaction terms due to drag and pressure forces, together with a moving mesh strategy to reduce the size of the computational domain.

  Abstract
  We present an approach for the simulation of landslides using the Particle Finite Element Method of the second generation. In this work, the multiphase nature (granular phase [...]

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• Numerical Simulation of the 3D Laminar Viscous Flow on a Horizontal-axis Wind Turbine Blade

  R. Prado, M. Storti, S. Idelsohn

  Int. J. Computational Fluid Dynamics (2002). Vol. 16 (4), pp. 283-295

  
  

  Abstract

  The aim of this paper is to describe the methodology followed in order to determine the viscous effects of a uniform wind on the blades of small horizontal-axis wind turbines that rotate at a constant angular speed. The numerical calculation of the development of the three-dimensional boundary layer on the surface of the blades is carried out under laminar conditions and considering flow rotation, airfoil curvature and blade twist effects. The adopted geometry for the twisted blades is given by cambered thin blade sections conformed by circular are airfoils with constant chords. The blade is working under stationary conditions at a given tip speed ratio, so that an extensive laminar boundary layer without flow separation is expected. The boundary layer growth is determined on a non-orthogonal curvilinear coordinate system related to the geometry of the blade surface. Since the thickness of the boundary layer grows from the leading edge of the blade and also from the tip to the blade root, a domain transformation is proposed in order to solve the discretized equations in a regular computational 3D domain. The non-linear system of partial differential coupled equations that governs the boundary layer development is numerically solved applying a finite difference technique using the Krause zig-zag scheme. The resulting coupled equations of motion are linearized, leading to a tridiagonal system of equations that is iteratively solved for the velocity components inside the viscous layer applying the Thomas algorithm, procedure that allows the subsequent numerical determination of the shear stress distribution on the blade surface.

  Abstract
  The aim of this paper is to describe the methodology followed in order to determine the viscous effects of a uniform wind on the blades of small horizontal-axis wind turbines [...]

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• A Panel-Fourier Method for Free-Surface Flows

  J. D'ELIA, M. Storti, S. Idelsohn

  Journal of Fluids Engineering (1999). Vol. 122 (2), 309-317

  
  

  Abstract

  A panel Fourier method for ship-wave flow problems is considered here. It is based on a three-dimensional potential flow model with a linearized free surface condition, and it is implemented by means of a low order panel method coupled to a Fourier series. The wave resistance is computed by pressure integration over the static wet hull and the wave pattern is obtained by a post-processing procedure. The strategy avoids the use of numerical viscosity, in contrast with the Dawson-like methods, widely used in naval panel codes, therefore a second centered scheme can be used for the discrete operator on the free surface. Numerical results including the wave pattern for a ferry along fifteen ship lengths are presented.

  Abstract
  A panel Fourier method for ship-wave flow problems is considered here. It is based on a three-dimensional potential flow model with a linearized free surface condition, and [...]

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• An unstructured grid-based, parallel free surface solver

  R. Löhner, C. Yang, E. Oñate, S. Idelsohn

  Applied Numerical Mathematics (1999). Vol. 31 (3), pp. 271-293

  
  

  Abstract

  An unstructured grid-based, parallel-free surface solver is presented. The overall scheme combines a finite-element, equal-order, projection-type 3-D incompressible flow solver with a finite element, 2-D advection equation solver for the free surface equation. For steady-state applications, the mesh is not moved every timestep, in order to reduce the cost of geometry recalculations and surface repositioning. A number of modifications required for efficient processing on shared-memory, cache-based parallel machines are discussed, and timings are shown that indicate scalability to a modest number of processors. The results show good quantitative comparison with experiments and the results of other techniques. The present combination of unstructured grids (enhanced geometrical flexibility) and good parallel performance (rapid turnaround) should make the present approach attractive to hydrodynamic design simulations.

  Abstract
  An unstructured grid-based, parallel-free surface solver is presented. The overall scheme combines a finite-element, equal-order, projection-type 3-D incompressible flow solver [...]

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• A second-order in time and space particle-based method to solve flow problems on arbitrary meshes

  J. Gimenez, H. Aguerre, S. Idelsohn, N. Nigro

  Journal of Computational Physics (2018). Vol. 380, pp. 295-310

  
  

  Abstract

    This work presents a novel proposal of a second-order accurate (in time and space) particle-based method for solving transport equations including incompressible flows problems within a mixed Lagrangian–Eulerian formulation. This methodology consists of a symmetrical operator splitting, the use of high-order operators to transfer data between the particles and the background mesh, and an improved version of the eXplicit Integration Following the Streamlines (X–IVS) method. In the case of incompressible flows, a large time-step iterative solver is employed where the momentum equation is split to improve the numerical approximation of the convective term. New interpolation and projection operators are evaluated and quadratically accurate solutions of scalar transport tests are presented. Then, incompressible flow problems are solved where the rate of convergence of the method is assessed using both structured and unstructured background grids. The method is implemented in the open source platform OpenFOAM®allowing employing arbitrary meshes and obtaining reliable computing time comparisons with standardized solvers. The results obtained reveal that the current method is able to obtain a lower level of error than a fast Eulerian alternative, without increasing the total computing time.

  Abstract
    This work presents a novel proposal of a second-order accurate (in time and space) particle-based method for solving transport equations including incompressible [...]

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• Algebraic Discrete Nonlocal (DNL) Absorbing Boundary Condition for the Ship Wave Resistance Problem

  M. Storti, J. D'ELIA, S. Idelsohn

  Journal of Computational Physics (1998). Vol. 146 (2), pp 570-602

  
  

  Abstract

  An absorbing boundary condition for the ship wave resistance problem is presented. In contrast to the Dawson-like methods, it avoids the use of numerical viscosities in the discretization, so that a centered scheme can be used for the free surface operator. The absorbing boundary condition is “completely absorbing,” in the sense that the solution is independent of the position of the downstream boundary and is derived from straightforward analysis of the resulting constant-coefficients difference equations, assuming that the mesh is 1D-structured (in the longitudinal direction) and requires the eigen-decomposition of a matrix one dimension lower than the system matrix. The use of a centered scheme for the free surface operator allows a full finite element discretization. The drag is computed by a momentum flux balance. This method is more accurate and guarantees positive resistances.

  Abstract
  An absorbing boundary condition for the ship wave resistance problem is presented. In contrast to the Dawson-like methods, it avoids the use of numerical viscosities in the [...]

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• Applied hydrodynamic wave-resistance computation by Fourier transform

  J. D'ELIA, M. Storti, S. Idelsohn

  Ocean Engng. (2002). Vol. 29 (3), p. 261-278

  
  

  Abstract

  An applied Fourier transform computation for the hydrodynamic wave-resistance coefficient is shown, oriented to potential flows with a free surface and infinity depth. The presence of a ship-like body is simulated by its equivalent pressure disturbance imposed on the un-perturbed free surface, where a linearized free surface condition is used. The wave-resistance coefficient is obtained from the wave-height downstream. Two examples with closed solutions are considered: a submerged dipole, as a test-case, and a parabolic pressure distribution of compact support. In the three dimensional case, a dispersion relation is included which is a key resource for an inexpensive computation of the wave pattern far downstream like fifteen ship-lengths.

  Abstract
  An applied Fourier transform computation for the hydrodynamic wave-resistance coefficient is shown, oriented to potential flows with a free surface and infinity depth. The [...]

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• Buckling of circular, annular plates of non-uniform thickness

  P. Laura, R. Gutiérrez, V. Sonzogni, S. Idelsohn

  Ocean Engng. (1997). Vol. 24 (1), pp. 51-62

  
  

  Abstract

  This paper deals with the solution of the title problem in the case where the outer boundary is subjected to uniform, hydrostatic pressure while the inner edge of the plate is free. It is assumed that the plate thickness varies (a) in a discontinuous fashion and (b) linearly. An approximate approach is proposed using polynomial coordinate functions which identically satisfy the boundary conditions at the outer edge, only. The eigenvalues are determined using the optimized Rayleigh-Ritz method and good engineering agreement is shown to exist with buckling parameters obtained by means of a finite element code.

  Abstract
  This paper deals with the solution of the title problem in the case where the outer boundary is subjected to uniform, hydrostatic pressure while the inner edge of the plate [...]

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• CVBEM Formulation for Multiple Profiles and Cascades

  M. Storti, J. D'ELIA, S. Idelsohn

  Appl. Mech. Rev. (1995). Vol. 48 (11), pp. 203-210

  
  

  Abstract

  A numerical algorithm based on the CVBEM (from Complex Variable Boundary Element Method) for plane incompressible potential flow around aerofoils and cascades is described. The method is based on the representation of the complex disturbance velocity by means of a Cauchy-type integral around the foil. The Cauchy density function is approximated piecewise linearly and a linear system on the nodal values is obtained by collocation at the nodes. The Kutta condition is imposed via a Lagrange multiplier, in contrast with the least-squares formulation used in a previous work. For cascades, the problem is conformally mapped by a simple hyperbolic function (exponential or hyperbolic tangent) to a related problem with only one profile and one or two poles. Thus, the cascade problem is accurately solved with minor modifications to the single profile code and at the same cost of a single profile computation. Finally, several numerical examples are shown: single Joukowski and NACA profiles, interference coefficients for the flat plate cascade and a plane cascade at the external cylindrical section of an industrial fan.

  Abstract
  A numerical algorithm based on the CVBEM (from Complex Variable Boundary Element Method) for plane incompressible potential flow around aerofoils and cascades is described. [...]

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