A finite difference method, based on the generation of a discrete stream function, is proposed fo... more A finite difference method, based on the generation of a discrete stream function, is proposed for the solution of unsteady incompressible viscous flows. The discrete stream function is obtained by operating as at the continuum level, but directly on the discretized form of the Navier Stokes equations. The resulting numerical procedure allows the boundary conditions to be given in primitive variables and, at the same time, produces a set of velocities which exactly satisfy the mass conservation in discretized form, by eliminating the pressure as a variable to be computed. These features of the method are very appealing for free surface unsteady problems. At this purpose the extension of the method to curvilinear moving grids is outlined. The general properties of the method in comparison with others based on the continuum stream function are shortly discussed and illustrated with some computational results.
A decoupling of the pressure field from the velocity field is presently obtained by means of a no... more A decoupling of the pressure field from the velocity field is presently obtained by means of a novel approach for generating a zero-divergence velocity field on the basis of a direct operation on the discretized Navier-Stokes equations; an analysis is then conducted of the feasibility of treating three-dimensional flows and multiply-connected domains. The model used retains the classical vector potential
A weakly compressible SPH scheme has been used to describe the evolution of viscous ows around bl... more A weakly compressible SPH scheme has been used to describe the evolution of viscous ows around blunt bodies at Reynolds numbers ranging from 10 to 2400. The simulation of such a wide range, rarely addressed to in the SPH literature, has been possible thanks to the use of a proper ghost-uid technique and to an accurate enforcement of the boundary conditions along the solid boundaries. In this context, a new numerical technique based on previous works by Takeda et al. (1994), Marrone et al. (2011) and De Lee et al. (2011) has been proposed, along with a new method for the evaluation of the global loads on bodies. Particular care has been taken to study the inuence of the weakly-compressibility assumption and of dierent ghostuid techniques on the numerical results. An in-depth validation of the model has been performed by comparing the numerical outcome with experimental data from the literature and other numerical references. The inuence of the domain size has been discussed in order to avoid wall side eects and, at the same time, to limit the computational costs. The convergence of the numerical solutions has been checked on both global and local quantities by choosing appropriate Reynolds-cell number.
We review the basic ideas underlying two popular particle methods for fluids: smoothed-particle h... more We review the basic ideas underlying two popular particle methods for fluids: smoothed-particle hydrodynamics and the vortex method. We discuss convergence problems, numerical schemes, and examples of practical simulations. MSC2010: primary 35Q30, 35Q35, 76D17, 35Q31; secondary 35L60, 35Q70. 45 46 ANDREA COLAGROSSI, GIORGIO GRAZIANI AND MARIO PULVIRENTI
The present paper proposes a novel algorithm to detect the free-surface in particle simulations, ... more The present paper proposes a novel algorithm to detect the free-surface in particle simulations, both in two and three dimensions. Since the proposed algorithms are based on SPH interpolations their implementation does not require complex geometrical procedures. Thus the free-surface detection can be easily embedded in SPH solvers, without a significant increase of the CPU time. Throughout this procedure accurate normal vectors to the free-surface are made available. Then it is possible to define a level-set function algorithm which is presented in detail. The latter allows in-depth analyses of three-dimensional free-surface simulations by using standard visualization tools, including internal features of the flow. The algorithms proposed for detecting free-surface particles and defining the level-set function are validated on simple and complex two-and three-dimensional flow simulations. The usefulness of the proposed procedures to post-process and analyze complex flows are illustrated on realistic examples.
The diffusive weakly-compressible SPH scheme described in Antuono et al. (hereinafter denoted as ... more The diffusive weakly-compressible SPH scheme described in Antuono et al. (hereinafter denoted as δ-SPH model) has been challenged in the analysis of impacts against structures generated by dam-break flows. Specifically, the 3D SPHERIC benchmarks number 1 and 2 have been studied as well as a novel 2D test case characterized by complex solid boundary profiles.
SUMMARY. A novel technique based on ghost-fluid approach has been defined to enforce proper bound... more SUMMARY. A novel technique based on ghost-fluid approach has been defined to enforce proper boundary conditions along solid profiles in Smoothed Particle Hydrodynamics schemes (SPH). The present work extends the classic ghost fluid method (see, for example,[4]) used for inviscid flows to simulate viscous laminar flows. The main idea is to couple the technique proposed by De Leffe (2011)[7] where a proper ghost fluid field is defined for each SPH differential operator, to the mirroring technique proposed by [17]. ...
SUMMARY. An enhanced treatment of the solid boundaries is proposed within the two-dimensional SPH... more SUMMARY. An enhanced treatment of the solid boundaries is proposed within the two-dimensional SPH scheme. These are modeled by means of boundary particles which take the flow properties through interpolation nodes internal to the fluid. For what concerns the free surface, a fast and accurate algorithm for the free-surface detection is presented which can be easily extended to the three dimensional case.
Computer Methods in Applied Mechanics and Engineering, Jan 9, 2011
A smoothed particle hydrodynamics model with numerical diffusive terms, hereinafter referred to a... more A smoothed particle hydrodynamics model with numerical diffusive terms, hereinafter referred to as δ-SPH [1] is used to analyze violent water flows. The boundary conditions on solid surfaces of arbitrary shape are enforced with a new technique based on fixed ghost particles. The violent impacts studied result from dam-break water flows striking obstacles of different shapes. The numerical results are validated against experimental data from the literature and solutions from a Navier–Stokes Level-Set solver. Predicted impact ...
SUMMARY. An enhanced treatment of the solid boundaries is proposed within the two-dimensional SPH... more SUMMARY. An enhanced treatment of the solid boundaries is proposed within the two-dimensional SPH scheme. These are modeled by means of boundary particles which take the flow properties through interpolation nodes internal to the fluid. For what concerns the free surface, a fast and accurate algorithm for the free-surface detection is presented which can be easily extended to the three dimensional case.
A finite difference method, based on the generation of a discrete stream function, is proposed fo... more A finite difference method, based on the generation of a discrete stream function, is proposed for the solution of unsteady incompressible viscous flows. The discrete stream function is obtained by operating as at the continuum level, but directly on the discretized form of the Navier Stokes equations. The resulting numerical procedure allows the boundary conditions to be given in primitive variables and, at the same time, produces a set of velocities which exactly satisfy the mass conservation in discretized form, by eliminating the pressure as a variable to be computed. These features of the method are very appealing for free surface unsteady problems. At this purpose the extension of the method to curvilinear moving grids is outlined. The general properties of the method in comparison with others based on the continuum stream function are shortly discussed and illustrated with some computational results.
A decoupling of the pressure field from the velocity field is presently obtained by means of a no... more A decoupling of the pressure field from the velocity field is presently obtained by means of a novel approach for generating a zero-divergence velocity field on the basis of a direct operation on the discretized Navier-Stokes equations; an analysis is then conducted of the feasibility of treating three-dimensional flows and multiply-connected domains. The model used retains the classical vector potential
A weakly compressible SPH scheme has been used to describe the evolution of viscous ows around bl... more A weakly compressible SPH scheme has been used to describe the evolution of viscous ows around blunt bodies at Reynolds numbers ranging from 10 to 2400. The simulation of such a wide range, rarely addressed to in the SPH literature, has been possible thanks to the use of a proper ghost-uid technique and to an accurate enforcement of the boundary conditions along the solid boundaries. In this context, a new numerical technique based on previous works by Takeda et al. (1994), Marrone et al. (2011) and De Lee et al. (2011) has been proposed, along with a new method for the evaluation of the global loads on bodies. Particular care has been taken to study the inuence of the weakly-compressibility assumption and of dierent ghostuid techniques on the numerical results. An in-depth validation of the model has been performed by comparing the numerical outcome with experimental data from the literature and other numerical references. The inuence of the domain size has been discussed in order to avoid wall side eects and, at the same time, to limit the computational costs. The convergence of the numerical solutions has been checked on both global and local quantities by choosing appropriate Reynolds-cell number.
We review the basic ideas underlying two popular particle methods for fluids: smoothed-particle h... more We review the basic ideas underlying two popular particle methods for fluids: smoothed-particle hydrodynamics and the vortex method. We discuss convergence problems, numerical schemes, and examples of practical simulations. MSC2010: primary 35Q30, 35Q35, 76D17, 35Q31; secondary 35L60, 35Q70. 45 46 ANDREA COLAGROSSI, GIORGIO GRAZIANI AND MARIO PULVIRENTI
The present paper proposes a novel algorithm to detect the free-surface in particle simulations, ... more The present paper proposes a novel algorithm to detect the free-surface in particle simulations, both in two and three dimensions. Since the proposed algorithms are based on SPH interpolations their implementation does not require complex geometrical procedures. Thus the free-surface detection can be easily embedded in SPH solvers, without a significant increase of the CPU time. Throughout this procedure accurate normal vectors to the free-surface are made available. Then it is possible to define a level-set function algorithm which is presented in detail. The latter allows in-depth analyses of three-dimensional free-surface simulations by using standard visualization tools, including internal features of the flow. The algorithms proposed for detecting free-surface particles and defining the level-set function are validated on simple and complex two-and three-dimensional flow simulations. The usefulness of the proposed procedures to post-process and analyze complex flows are illustrated on realistic examples.
The diffusive weakly-compressible SPH scheme described in Antuono et al. (hereinafter denoted as ... more The diffusive weakly-compressible SPH scheme described in Antuono et al. (hereinafter denoted as δ-SPH model) has been challenged in the analysis of impacts against structures generated by dam-break flows. Specifically, the 3D SPHERIC benchmarks number 1 and 2 have been studied as well as a novel 2D test case characterized by complex solid boundary profiles.
SUMMARY. A novel technique based on ghost-fluid approach has been defined to enforce proper bound... more SUMMARY. A novel technique based on ghost-fluid approach has been defined to enforce proper boundary conditions along solid profiles in Smoothed Particle Hydrodynamics schemes (SPH). The present work extends the classic ghost fluid method (see, for example,[4]) used for inviscid flows to simulate viscous laminar flows. The main idea is to couple the technique proposed by De Leffe (2011)[7] where a proper ghost fluid field is defined for each SPH differential operator, to the mirroring technique proposed by [17]. ...
SUMMARY. An enhanced treatment of the solid boundaries is proposed within the two-dimensional SPH... more SUMMARY. An enhanced treatment of the solid boundaries is proposed within the two-dimensional SPH scheme. These are modeled by means of boundary particles which take the flow properties through interpolation nodes internal to the fluid. For what concerns the free surface, a fast and accurate algorithm for the free-surface detection is presented which can be easily extended to the three dimensional case.
Computer Methods in Applied Mechanics and Engineering, Jan 9, 2011
A smoothed particle hydrodynamics model with numerical diffusive terms, hereinafter referred to a... more A smoothed particle hydrodynamics model with numerical diffusive terms, hereinafter referred to as δ-SPH [1] is used to analyze violent water flows. The boundary conditions on solid surfaces of arbitrary shape are enforced with a new technique based on fixed ghost particles. The violent impacts studied result from dam-break water flows striking obstacles of different shapes. The numerical results are validated against experimental data from the literature and solutions from a Navier–Stokes Level-Set solver. Predicted impact ...
SUMMARY. An enhanced treatment of the solid boundaries is proposed within the two-dimensional SPH... more SUMMARY. An enhanced treatment of the solid boundaries is proposed within the two-dimensional SPH scheme. These are modeled by means of boundary particles which take the flow properties through interpolation nodes internal to the fluid. For what concerns the free surface, a fast and accurate algorithm for the free-surface detection is presented which can be easily extended to the three dimensional case.
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