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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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• A general algorithm for compressible and incompressible flow. Stability analysis and explicit time integration

  N. Nigro, M. Storti, S. Idelsohn

  Int. J. of Num. Meths. for Heat and Fluid Flow (1997). Vol. 7 (2/3), pp. 141-168

  
  

  Abstract

  Addresses two difficulties which arise when using a compressible code with equal order interpolation (non‐staggered grids in the finite‐difference nomenclature) to capture a steady‐state solution in the incompressible limit, i.e. at low Mach numbers. Explains that, first, numerical instabilities in the form of spurious oscillations in pressure pollute the solution and, second, the convergence to the steady state becomes extremely slow owing to bad conditioning of the different speeds of propagation. By using a stabilized method, allows the use of equal‐order interpolations in a consistent (weighted‐residual) formulation which stabilizes both the convection and the continuity terms at the same time. On the other hand, by using specially devised preconditioning, assures a rate of convergence independent of Mach number.

  Abstract
  Addresses two difficulties which arise when using a compressible code with equal order interpolation (non‐staggered grids in the finite‐difference nomenclature) to capture [...]

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• An improved enrichment method for weak discontinuities for thermal problems

  J. Marti, E. Ortega, S. Idelsohn

  Int. J. of Num. Meths. for Heat and Fluid Flow (2017). Vol. 27 (8), pp.1748-1764

  
  

  Abstract

  Purpose   The purpose of this paper is to propose a new elemental enrichment technique to improve the accuracy of the simulations of thermal problems containing weak discontinuities. Design/methodology/approach   The enrichment is introduced in the elements cut by the materials interface by means of adding additional shape functions. The weak form of the problem is obtained using Galerkin approach and subsequently integrating the diffusion term by parts. To enforce the continuity of the fluxes in the “cut” elements, a contour integral must be added. These contour integrals named here the “inter-elemental heat fluxes” are usually neglected in the existing enrichment approaches. The proposed approach takes these fluxes into account. Findings   It has been shown that the inter-elemental heat fluxes cannot be generally neglected and must be included. The corresponding method can be easily implemented in any existing finite element method (FEM) code, as the new degrees of freedom corresponding to the enrichment are local to the elements. This allows for their static condensation, thus not affecting the size and structure of the global system of governing equations. The resulting elements have exactly the same number of unknowns as the non-enriched finite element (FE). Originality/value   It is the first work where the necessity of including inter-elemental heat fluxes has been demonstrated. Moreover, numerical tests solved have proven the importance of these findings. It has been shown that the proposed enrichment leads to an improved accuracy in comparison with the former approaches where inter-elemental heat fluxes were neglected.

  Abstract
  Purpose   The purpose of this paper is to propose a new elemental enrichment technique to improve the accuracy of the simulations of thermal problems [...]

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• Variational Framework for FIC Formulations in Continuum Mechanics: High Order Tensor-Derivative Transformations and Invariants

  C. Felippa, E. Oñate, S. Idelsohn

  Archives of Comp. Meths. Engng. (2018). Vol. 25 (4), pp. 919–963

  
  

  Abstract

  This is part of an article series on a variational framework for continuum mechanics based on the Finite Increment Calculus (FIC). The formulation utilizes high order derivatives of the classical fields of continuum mechanics integrated over control regions to construct stabilizing modification terms. Fields may include displacements, body forces, strains, stresses, pressure and volumetric strains. To support observer-invariant FIC formulations, we have catalogued field transformation equations as well as sets of linear and quadratic invariants of fields and of their derivatives up to appropriate order. Attention is focused on the two-dimensional case of a body in plane strain under the drilling-rotation transformation group. Results are presented for displacement and body-force derivatives of orders up to 4, and for stress, strain, pressure and volumetric strain derivatives of order up to 3. The material assembled here is self-contained because this catalog is believed to be useful beyond FIC applications; for example gradient-based, nonlocal constitutive models of multiscale mechanics and physics that involve finite characteristic dimensions analogous to FIC steplengths.

  Abstract
  This is part of an article series on a variational framework for continuum mechanics based on the Finite Increment Calculus (FIC). The formulation utilizes high order derivatives [...]

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• Numerical methods in phase-change problems

  S. Idelsohn, M. Storti, L. Crivelli

  Archives of Comp. Meths. Engng. (1994). Vol. 1 (1), pp. 49-74

  
  

  Abstract

  This paper summarizes the state of the art of the numerical solution of phase-change problems. After describing the governing equations, a review of the existing methods is presented. The emphasis is put mainly on fixed domain techniques, but a brief description of the main front-tracking methods is included. A special section is devoted to the Newton-Raphson resolution with quadratic convergence of the non-linear system of equations.

  Abstract
  This paper summarizes the state of the art of the numerical solution of phase-change problems. After describing the governing equations, a review of the existing methods is [...]

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• A discrete non‐local (DNL) outgoing boundary condition for diffraction of surface waves

  R. Bonet Chaple, N. Nigro, M. Storti, S. Idelsohn

  Commun. Numer. Meth. Engng (1998). Vol. 14 (9), pp. 849-861

  
  

  Abstract

  A discrete non‐local (DNL) boundary condition is used to solve the water waves propagation problem over variable depth. This condition is obtained by means of full solution of the discrete Helmholtz operator in a structured network. We consider a simulation of wave propagation around a circular island located on either a paraboloidal shoal or constant depth bathymetry. Such examples confirm the important improvement in accuracy for the DNL method over standard conditions in the near field.

  Abstract
  A discrete non‐local (DNL) boundary condition is used to solve the water waves propagation problem over variable depth. This condition is obtained by means of full solution [...]

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• Computing ship wave resistance from wave amplitude with a non‐local absorbing boundary condition

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

  Commun. Numer. Meth. Engng (1998). Vol. 14 (11), pp. 997-1012

  
  

  Abstract

  A method for computing ship wave resistance from a momentum flux balance is presented. It is based on computing the momentum flux carried by the gravity waves that exit the computational domain through the outlet plane. It can be shown that this method ensures a non‐negative wave‐resistance, in contrast with straightforward integration of the normal pressure forces. However, this calculation should be performed on a transverse plane located far behind the ship. Traditional Dawson‐like methods add a numerical viscosity that dampens the wave pattern so that some amount of momentum flux is lost, and resulting in an error in the momentum balance. The flow field is computed, then, with a centred scheme with absorbing boundary conditions.

  Abstract
  A method for computing ship wave resistance from a momentum flux balance is presented. It is based on computing the momentum flux carried by the gravity waves that exit the [...]

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