Convergence of SPH Method for Scalar Nonlinear Conservation Laws

Moussa, B.; Vila, Jean‐Paul

doi:10.1137/s0036142996307119

Cited by 64 publications

(36 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here, we do not want to challenge the SPH particle resolution required (commonly about 30−50 neighbours per particle in 3D simulations), but only to indicate that a problem exists in the astrophysical context of inviscid low compressibility modelling, when thermal energies are of the order of gravitational energies (generally of any binding energies) or larger. From a strictly mathematical point of view, the minimum condition of at least 3 non-coplanar neighbours SPH particles is statistically satisfied even in our "starting" inviscid disc model, following Ben Moussa & Vila (2000). See the neighbours histograms in Fig.…”

Section: Sph Accuracymentioning

confidence: 83%

Low compressibility accretion disc formation in close binaries: the role of physical viscosity

Lanzafame

Belvedère

Molteni

2006

A&A

View full text Add to dashboard Cite

Aims. Physical viscosity naturally hampers gas dynamics (rarefaction or compression). Such a role should support accretion disc development inside the primary gravitation potential well in a close binary system, even for low compressibility modelling. Therefore, from the astrophysical point of view, highly viscous accretion discs could exist even in the low compressibility regime showing strong thermal differences to high compressibility ones Methods. We performed simulations of stationary Smooth Particle Hydrodynamics (SPH) low compressibility accretion disc models for the same close binary system. Artificial viscosity operates in all models. The absence of physical viscosity and a supersonic high mass transfer characterize the first model. Physical viscosity and the same supersonic high mass transfer characterize the second model, whilst physical viscosity and a subsonic low mass transfer characterize the third model. The same binary system parameters, such as stellar masses and their separation, have been adopted, as well as the same polytropic index γ = 5/3. Thus we investigated the role of physical viscosity in mass and angular momentum transport in the two viscid models and compare them to the inviscid model. An initial value of the parameter α = 1 has been considered for the physically viscous models, according to the well-known Shakura and Sunjaev formulation, but simulations were carried out also for α = 0.1 and α = 0.5 in the case of a supersonic mass transfer. Physical viscosity is represented by the viscous force contribution expressed by the divergence of the symmetric viscous stress tensor in the Navier-Stokes equation, while the viscous energy contribution is given by a symmetric combination of the symmetric shear tensor times the particle velocity. Results. The results show that physical viscosity supports and favours accretion disc formation despite the very low compressibility assumed. On the contrary, in the inviscid case no evident disc structure appears. In all models neither shock fronts nor extended clear spirals in the radial flow develop.

show abstract

Section: Sph Accuracymentioning

confidence: 83%

Low compressibility accretion disc formation in close binaries: the role of physical viscosity

Lanzafame

Belvedère

Molteni

2006

A&A

View full text Add to dashboard Cite

show abstract

“…Encouraging preliminary steps in this direction have already been put forward very recently by Ben Moussa [119], who proved convergence of their meshless scheme for non-linear scalar conservation laws; see also [120]. This theoretical result appears to be the first of its kind in the context of meshless methods.…”

Section: Introductionmentioning

confidence: 70%

Brief Review of Numerical Simulation Applied to Solve Oil Extraction Problems

Onofre-Ramos¹,

Castañeda²,

Austria-Aguilar³

et al. 2015

IJG

View full text Add to dashboard Cite

In the last decades, the numerical analysis has abridged the time and cost of oil extractive operations, and thus their implementation has been promoted so much that today is used to solve a large number of phenomena that occur during the extraction of hydrocarbons, not only economizing the operation, but also shedding light to the phenomenon, and helping to have a better understanding. Nevertheless in spite of the success of the applications of numerical simulations, it has been until today, looking for their optimization, because the discretization methods of the domain and the model are through meshes, which require modifying the physics of the problem so that this matches the numerical method, and not in backwards.

show abstract

“…Encouraging preliminary steps in this direction have already been put forward very recently by Ben Moussa [38], who proved convergence of their meshless scheme for non-linear scalar conservation laws; see also [39]. This theoretical result appears to be the first of its kind in the context of meshless methods.…”

Section: Introductionmentioning

confidence: 70%

Review of Development of the Smooth Particle Hydrodynamics (SPH) Method

Vignjević

Campbell

2009

Predictive Modeling of Dynamic Processes

View full text Add to dashboard Cite

The paper gives an overview of developments of the SPH method. Especial attention is given to the main shortcomings of the original form of the method namely consistency, tensile instability and zero energy modes. An example of derivation of correction necessary to assure first order consistency is given. The origin of the tensile instability and few proposed solutions to this problem are described. Similar consideration is given with respect to the zero energy modes typical for the collocational SPH method.

show abstract

Convergence of SPH Method for Scalar Nonlinear Conservation Laws

Cited by 64 publications

References 20 publications

Low compressibility accretion disc formation in close binaries: the role of physical viscosity

Low compressibility accretion disc formation in close binaries: the role of physical viscosity

Brief Review of Numerical Simulation Applied to Solve Oil Extraction Problems

Review of Development of the Smooth Particle Hydrodynamics (SPH) Method

Contact Info

Product

Resources

About