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Volume 10 (2019): Issue 2 (January 2019)
Special Issue on Mathematical Models and Methods in Biology, Medicine and Physiology. Guest Editors: Michele Piana, Luigi Preziosi

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Special Issue on Mathematical modelling for complex systems: multi-agents methods. Guest Editor: Elena De Angelis

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Volume 7 (2016): Issue 3 (September 2016)
"Special Issue on New Trends in Semi-Lagrangian Methods, Guest Editors: Luca Bonaventura, Maurizio Falcone and Roberto Ferretti

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Special Issue on Constitutive Equations for Heat Conduction in Nanosystems and Non-equilibrium Processes. Guest Editors: Vito Antonio Cimmelli and David Jou

Volume 7 (2016): Issue 1 (January 2016)
Open Issue

Journal Details
Format
Journal
eISSN
2038-0909
First Published
15 Dec 2014
Publication timeframe
1 time per year
Languages
English

Search

Volume 7 (2016): Issue 1 (January 2016)
Open Issue

Journal Details
Format
Journal
eISSN
2038-0909
First Published
15 Dec 2014
Publication timeframe
1 time per year
Languages
English

Search

4 Articles

Editorial

access type Open Access

A note from the Editor

Published Online: 20 May 2016
Page range: 1 - 3

Abstract

Research Papers

access type Open Access

A study of the interactions between uniform and pointwise vortices in an inviscid fluid

Published Online: 20 May 2016
Page range: 4 - 22

Abstract

Abstract

The planar interactions between pair of vortices in an inviscid fluid are analytically investigated, by assuming one of the two vortices pointwise and the other one uniform. A novel approach using the Schwarz function of the boundary of the uniform vortex is adopted. It is based on a new integral relation between the (complex) velocity induced by the uniform vortex and its Schwarz function and on the time evolution equation of this function. They lead to a singular integrodifferential problem. Even if this problem is strongly nonlinear, its nonlinearities are confined inside two terms, only. As a consequence, its solution can be analytically approached by means of successive approximations. The ones at 0th (nonlinear terms neglected) and 1st (nonlinear terms evaluated on the 0-order solution) orders are calculated and compared with contour dynamics simulations of the vortex motion. A satisfactory agreement is keept for times which are small with respect to the turn-over time of the vortex pair.

Keywords

  • inviscid two-dimensional vortex dynamics
  • uniform vortex
  • point vortex
  • contour dynamics
  • Schwarz function
  • nonlinear singular integral equation
access type Open Access

Sequential quadrature methods for RDO

Published Online: 20 May 2016
Page range: 23 - 47

Abstract

Abstract

This paper presents a comparative study between a large number of different existing sequential quadrature schemes suitable for Robust Design Optimization (RDO), with the inclusion of two partly original approaches. Efficiency of the different integration strategies is evaluated in terms of accuracy and computational effort: main goal of this paper is the identification of an integration strategy able to provide the integral value with a prescribed accuracy using a limited number of function samples. Identification of the different qualities of the various integration schemes is obtained utilizing both algebraic and practical test cases. Differences in the computational effort needed by the different schemes is evidenced, and the implications on their application to practical RDO problems is highlighted.

Keywords

  • Quadrature schemes
  • Robust Design Optimization
  • Industrial Design
access type Open Access

Dynamics of a bubble rising in gravitational field

Published Online: 20 May 2016
Page range: 48 - 67

Abstract

Abstract

The rising motion in free space of a pulsating spherical bubble of gas and vapour driven by the gravitational force, in an isochoric, inviscid liquid is investigated. The liquid is at rest at the initial time, so that the subsequent flow is irrotational. For this reason, the velocity field due to the bubble motion is described by means of a potential, which is represented through an expansion based on Legendre polynomials. A system of two coupled, ordinary and nonlinear differential equations is derived for the vertical position of the bubble center of mass and for its radius. This latter equation is a modified form of the Rayleigh-Plesset equation, including a term proportional to the kinetic energy associated to the translational motion of the bubble.

Keywords

  • cavitation
  • bubble dynamics
  • Rayleigh-Plesset equation
4 Articles

Editorial

access type Open Access

A note from the Editor

Published Online: 20 May 2016
Page range: 1 - 3

Abstract

Research Papers

access type Open Access

A study of the interactions between uniform and pointwise vortices in an inviscid fluid

Published Online: 20 May 2016
Page range: 4 - 22

Abstract

Abstract

The planar interactions between pair of vortices in an inviscid fluid are analytically investigated, by assuming one of the two vortices pointwise and the other one uniform. A novel approach using the Schwarz function of the boundary of the uniform vortex is adopted. It is based on a new integral relation between the (complex) velocity induced by the uniform vortex and its Schwarz function and on the time evolution equation of this function. They lead to a singular integrodifferential problem. Even if this problem is strongly nonlinear, its nonlinearities are confined inside two terms, only. As a consequence, its solution can be analytically approached by means of successive approximations. The ones at 0th (nonlinear terms neglected) and 1st (nonlinear terms evaluated on the 0-order solution) orders are calculated and compared with contour dynamics simulations of the vortex motion. A satisfactory agreement is keept for times which are small with respect to the turn-over time of the vortex pair.

Keywords

  • inviscid two-dimensional vortex dynamics
  • uniform vortex
  • point vortex
  • contour dynamics
  • Schwarz function
  • nonlinear singular integral equation
access type Open Access

Sequential quadrature methods for RDO

Published Online: 20 May 2016
Page range: 23 - 47

Abstract

Abstract

This paper presents a comparative study between a large number of different existing sequential quadrature schemes suitable for Robust Design Optimization (RDO), with the inclusion of two partly original approaches. Efficiency of the different integration strategies is evaluated in terms of accuracy and computational effort: main goal of this paper is the identification of an integration strategy able to provide the integral value with a prescribed accuracy using a limited number of function samples. Identification of the different qualities of the various integration schemes is obtained utilizing both algebraic and practical test cases. Differences in the computational effort needed by the different schemes is evidenced, and the implications on their application to practical RDO problems is highlighted.

Keywords

  • Quadrature schemes
  • Robust Design Optimization
  • Industrial Design
access type Open Access

Dynamics of a bubble rising in gravitational field

Published Online: 20 May 2016
Page range: 48 - 67

Abstract

Abstract

The rising motion in free space of a pulsating spherical bubble of gas and vapour driven by the gravitational force, in an isochoric, inviscid liquid is investigated. The liquid is at rest at the initial time, so that the subsequent flow is irrotational. For this reason, the velocity field due to the bubble motion is described by means of a potential, which is represented through an expansion based on Legendre polynomials. A system of two coupled, ordinary and nonlinear differential equations is derived for the vertical position of the bubble center of mass and for its radius. This latter equation is a modified form of the Rayleigh-Plesset equation, including a term proportional to the kinetic energy associated to the translational motion of the bubble.

Keywords

  • cavitation
  • bubble dynamics
  • Rayleigh-Plesset equation

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