Implicit integrations for SPH in semi-Lagrangian approach: Application to the accretion disc modeling in a microquasar

Lanzafame, G.

doi:10.1016/j.cpc.2012.11.001

Cited by 4 publications

(3 citation statements)

References 58 publications

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“…For the examples taken in this article, the ideal gas equation of state is adopted for (5), which is expressed as follows:…”

Section: Governing Equationsmentioning

confidence: 99%

“…The Lagrangian method is also a heart part of the arbitrary Lagrangian-Eulerian method. The Lagrangian method has received many researches, [1][2][3][4][5][6][7][8] and can be categorized as the cell-centered hydrodynamic (CCH) method, [9][10][11][12] the point-centered hydrodynamic (PCH) method, [13][14][15] and the staggered-grid hydrodynamic (SGH) method. [16][17][18][19][20] In CCH, the thermodynamic variables (pressure, density, and internal energy) and kinematic variables (velocity and kinetic energy) are defined at each element's center.…”

Section: Introductionmentioning

confidence: 99%

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Study on a matter flux method for staggered essentially Lagrangian hydrodynamics on triangular grids

Zhao

Xiao

Wang

et al. 2022

Numerical Methods in Fluids

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A classical Lagrangian staggered-grid hydrodynamic (SGH) method on triangular grids is prone to cell-to-cell oscillations. The causes of these oscillations can be divided into two categories. One is dissipation and the other is fluid deformation. For dissipation, when the kinematic energy stored on nodes are dissipated into internal energy in cells (shock wave is the most typical case), the dissipated energy may be unevenly assigned among cells, thus causes oscillations. This kind of oscillations can be controlled to a small level through a carefully designed viscous stress tensor or artificial heat flux, as studied widely in references. For fluid deformation, as the grid composed of straight lines cannot deform as flexibly as a continuous fluid, the volume of a grid cell would not accurately represent that of a fluid element, and this volume error will lead to oscillations too. In this article, we study in the SGH framework a matter-flow method, whose design principle is representing the under-grid bending motion of fluid elements by matter transport through grid edges. We first derive governing equations of the matter flow velocity defined at each edge of a grid, then derive formulas for the mass, energy, and momentum fluxes on the edge with the matter flow velocity. We test the matter-flow method in largely deforming fluids problems on triangular meshes. It is shown that serious oscillations arise in the regular SGH simulations, while they are well controlled after implementing the matter-flow method. In order to get a knowledge about the adaptability of the matter-flow method, we also test it in shock problems that do not fall within its design goal. For this purpose, an artificial heat flow is introduced in the SGH scheme to play a major role in stabilizing the shock capture. The test results show that the matter-flow method can help improve the shock simulations. The source code can be downloaded from the GitHub repository: https:// github.com/zhaoli0321/Matterflow.

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“…For the examples taken in this article, the ideal gas equation of state is adopted for (5), which is expressed as follows:…”

Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Study on a matter flux method for staggered essentially Lagrangian hydrodynamics on triangular grids

Zhao

Xiao

Wang

et al. 2022

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

“…In this case, if working in SPH, the mass of the ith SPH particle should be recalculated each time step as m i = ρ i n −1 i , being the numerical density n i of the same particle directly obtained by eq. 11 for SPH-like codes, taking care that the smoothing interpolated n i = ρ i m −1 i since the starting initial conditions [39].…”

Section: Some Remarks On the Basic Hypothesesmentioning

confidence: 99%

A general tool for LTE thermochemistry for adiabatic non-diffusive reactive fluid dynamics: Applications to 2D planar discontinuity flows in SPH

Lanzafame

2018

Journal of Computational Science

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Applications of semi-Lagrangian methods in the geosciences

Fletcher

2020

Semi-Lagrangian Advection Methods and Their Applications in Geoscience

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Implicit integrations for SPH in semi-Lagrangian approach: Application to the accretion disc modeling in a microquasar

Cited by 4 publications

References 58 publications

Study on a matter flux method for staggered essentially Lagrangian hydrodynamics on triangular grids

Study on a matter flux method for staggered essentially Lagrangian hydrodynamics on triangular grids

A general tool for LTE thermochemistry for adiabatic non-diffusive reactive fluid dynamics: Applications to 2D planar discontinuity flows in SPH

Applications of semi-Lagrangian methods in the geosciences

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