Numerical modelling of two-dimensional gas-dynamic flows on a variable-structure mesh

Михайлова, Н.В.; Тишкин, В. Ф.; Tyurina, N. N.; Favorskii, A. P.; Shashkov, Mikhail

doi:10.1016/0041-5553(86)90043-1

Cited by 12 publications

(11 citation statements)

References 3 publications

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“…First, we note that SOM can be applied to a grid of any structure ± e.g., logically rectangular, triangular, the Voronoi mesh, etc. In particular, the application of SOM to discretizations for free-Lagrange methods, using Voronoi tesselations to de®ne the cells, is described in [28].…”

Section: Discussionmentioning

confidence: 99%

A discrete operator calculus for finite difference approximations

Margolin

2000

Computer Methods in Applied Mechanics and Engineering

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In this article we describe two areas of recent progress in the construction of accurate and robust ®nite di erence algorithms for continuum dynamics. The support operators method (SOM) provides a conceptual framework for deriving a discrete operator calculus, based on mimicking selected properties of the di erential operators. In this paper, we choose to preserve the fundamental conservation laws of a continuum in the discretization. A strength of SOM is its applicability to irregular unstructured meshes. We describe the construction of an operator calculus suitable for gas dynamics and for solid dynamics, derive general formulae for the operators, and exhibit their realization in 2D cylindrical coordinates. The multidimensional positive de®nite advection transport algorithm (MPDATA) provides a framework for constructing accurate nonoscillatory advection schemes. In particular, the nonoscillatory property is important in the remapping stage of arbitrary-Lagrangian±Eulerian (ALE) programs. MPDATA is based on the sign-preserving property of upstream di erencing, and is fully multidimensional. We describe the basic second-order-accurate method, and review its generalizations. We show examples of the application of MPDATA to an advection problem, and also to a complex¯uid ow. We also provide an example to demonstrate the blending of the SOM and MPDATA approaches. Ó

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Section: Discussionmentioning

confidence: 99%

A discrete operator calculus for finite difference approximations

Margolin

2000

Computer Methods in Applied Mechanics and Engineering

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“…For a Lagrangian method the boundary of parcel has to move in Lagrangian fashion too. Unfortunately, for "pure" free-Lagrange it is not the case because parcels are Voronoi cells and the vertices of the Voronoi cell are not moved independently in a Lagrangian way but defined from positions of the particles in a very nonlinear way [90]. It is well known [52,21,117] that a Voronoi cell is not a Lagrangian object and it is rigorously proven in [114] that for "pure" free-Lagrangian methods discrete continuity equation is not consistent (order of approximation is zero) with continuous continuity equation; it also means that the socalled Geometric Conservation Law (GCL), [50,83], which can affect stability of the method, [50], is not fulfilled.…”

Section: Introductionmentioning

confidence: 99%

“…We start our analysis with methods, which we will call pure free-Lagrangian methods, [90,118,51,110,109,103,9]. In these methods, the fluid is represented by point particles surrounded by parcels.…”

Section: Introductionmentioning

confidence: 99%

“…In "pure" freeLagrange, one approximates some form of Lagrangian equations. Several discretization approaches are possible, for example, mimetic finite difference [90], or Godunov type methods [9]. The energy equation can be approximated in conservative form [9], or in non-conservative form as in [90].…”

Section: Introductionmentioning

confidence: 99%

“…There are several approaches which intend to mitigate non-Lagrangian behavior of Voronoi cells. For example, in [90,110] special type of artificial viscosity was introduced which helps to regularize the particle positions and do not allow particles to be to close to each other. In [9] some corrections to velocity of generators are introduced and in [65] special artificial forces are introduced to correct shape of parcels.…”

Section: Introductionmentioning

confidence: 99%

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ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method

Loubère

Maire

Shashkov

et al. 2010

Journal of Computational Physics

182

130

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We present a new reconnection-based Arbitrary Lagrangian Eulerian (ALE) method. The main elements in a standard ALE simulation are an explicit Lagrangian phase in which the solution and grid are updated, a rezoning phase in which a new grid is defined, and a remapping phase in which the Lagrangian solution is transferred (conservatively interpolated) onto the new grid. In standard ALE methods the new mesh from the rezone phase is obtained by moving grid nodes without changing connectivity of the mesh. Such rezone strategy has its limitation due to the fixed topology of the mesh. In our new method we allow connectivity of the mesh to change in rezone phase, which leads to general polygonal mesh and allows to follow Lagrangian features of the mesh much better than for standard ALE methods. Rezone strategy with reconnection is based on using Voronoi tessellation. We demonstrate performance of our new method on series of numerical examples and show it superiority in comparison with standard ALE methods without reconnection.

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Moving least-squares particle hydrodynamics II: conservation and boundaries

Dilts

2000

Int. J. Numer. Meth. Engng.

199

129

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Previous work by the author has shown that the consistency of the SPH method can be improved to acceptable levels by substituting MLS interpolants for SPH interpolants, that the SPH inconsistency drives the tension instability and that imposition of consistency via MLS severely retards tension instability growth. The new method however was not conservative, and made no provision for boundary conditions. Conservation is an essential property in simulations where large localized mass, momentum or energy transfer occurs such as high‐velocity impact or explosion modeling. A new locally conservative MLS variant of SPH that naturally incorporates realistic boundary conditions is described. In order to provide for the boundary fluxes one must identify the boundary particles. A new, purely geometric boundary detection technique for assemblies of spherical particles is described. A comparison with SPH on a ball‐and‐plate impact simulation shows qualitative improvement. Copyright © 2000 John Wiley & Sons, Ltd.

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Numerical modelling of two-dimensional gas-dynamic flows on a variable-structure mesh

Cited by 12 publications

References 3 publications

A discrete operator calculus for finite difference approximations

A discrete operator calculus for finite difference approximations

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method

Moving least-squares particle hydrodynamics II: conservation and boundaries

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