Multi-material pressure relaxation methods for Lagrangian hydrodynamics

Yanilkin, Yury Vasilyevich; Goncharov, Evgeny; Kolobyanin, V. Yu.; Sadchikov, V. V.; Kamm, James R.; Shashkov, Mikhail; Rider, William J.

doi:10.1016/j.compfluid.2012.05.020

Cited by 39 publications

(32 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These methods have been tested on numerous problems, including those not included in this work (see [40,41]). It does not seem possible to present results of all such calculations, so the author confines himself to three one-dimensional and one two-dimensional problem having analytical solutions.…”

Section: Test Problems and Resultsmentioning

confidence: 99%

“…In this work, we use model 7, which, as shown in [40,41], is the most widely applicable with respect to modeling different kinds of flow. It follows from it that…”

Section: The Acm-2 Modelmentioning

confidence: 99%

“…When mixed cells are used for gas dynamics equations, additional closing relations are needed, which in fact define the interaction of materials inside the cell (the subcell interaction). Most of the known models manage with information about volume (or mass) fractions of the materials and their thermodynamic states [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Such models can be divided into two classes according to the number of computational stages involved.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Closure Models for Lagrangian Gas Dynamics and Elastoplasticity Equations in Multimaterial Cells

Yanilkin¹

2017

Lagrangian Mechanics

View full text Add to dashboard Cite

Mixed cells (multicomponent cells) emerging in the development of Lagrangian-Eulerian (ALE) or Eulerian numerical techniques for solving the gas dynamics and elastoplasticity equations in multicomponent media contain either interfaces between materials or a mixture of materials. There is a problem of correctly approximation of the equations in such cells and the ALE code accuracy and performance depend on how the problem is resolved. Many approximation methods use the equation splitting into two stages, one of which consists in solving a given equation in Lagrangian variables. If mixed cells are simulated, the system of equations describing the gas dynamics and elastoplasticity is unclosed and there is a need to introduce additional closure relations that will allow determining the thermodynamic parameters of components using the available data for the mixture of components, as a whole. The chapter presents a review of the equation closure methods and results of the methods verification using several test problems having exact solutions.

show abstract

Section: Test Problems and Resultsmentioning

confidence: 99%

“…In this work, we use model 7, which, as shown in [40,41], is the most widely applicable with respect to modeling different kinds of flow. It follows from it that…”

Section: The Acm-2 Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Closure Models for Lagrangian Gas Dynamics and Elastoplasticity Equations in Multimaterial Cells

Yanilkin¹

2017

Lagrangian Mechanics

View full text Add to dashboard Cite

show abstract

“…The ALE approach allows the mesh velocity to be chosen independently from the local fluid velocity, therefore the grid nodes can be arbitrarily moved. Such an approach is also suitable for solving multi-phase and multi-material flow problems [58,127,21,108,67,98,112]. All the Lagrangian schemes listed so far achieve at most second order of accuracy in space and time.…”

Section: Introductionmentioning

confidence: 97%

Direct Arbitrary-Lagrangian–Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws

Boscheri

Loubère

Dumbser

2015

Journal of Computational Physics

View full text Add to dashboard Cite

“…In the ALE framework the mesh velocity does not necessarily have to coincide with the local fluid velocity, hence allowing the grid nodes to be arbitrarily moved. Such an approach is also suitable for solving multi-phase and multimaterial flow problems [14,45,48,71,73,75,88]. At most second order of accuracy in space and time is achieved by all the Lagrangian finite volume schemes mentioned so far.…”

Section: Introductionmentioning

confidence: 98%

An Efficient Quadrature-Free Formulation for High Order Arbitrary-Lagrangian–Eulerian ADER-WENO Finite Volume Schemes on Unstructured Meshes

Boscheri

Dumbser

2015

J Sci Comput

View full text Add to dashboard Cite

In this paper we present a new and efficient quadrature-free formulation for the family of cell-centered high order accurate direct arbitrary-Lagrangian-Eulerian one-step ADER-WENO finite volume schemes on unstructured triangular and tetrahedral meshes that has been developed by the authors in a recent series of papers (Boscheri et al. in J Comput ). High order of accuracy in time is obtained by using a local space-time Galerkin predictor on moving curved meshes, while a high order accurate nonlinear WENO method is adopted to produce high order essentially non-oscillatory reconstruction polynomials in space. The mesh is moved at each time step according to the solution of a node solver algorithm that assigns a unique velocity vector to each node of the mesh. A rezoning procedure can also be applied when mesh distortions and deformations become too severe. The space-time mesh is then constructed by straight edges connecting the vertex positions at the old time level t n with the new ones at the next time level t n+1 , yielding closed space-time control volumes, on the boundary of which the numerical flux must be integrated. This is done here with a new and efficient quadrature-free approach: the space-time boundaries are split into simplex sub-elements, i.e. either triangles in 2D or tetrahedra in 3D. This leads to space-time normal vectors as well as Jacobian matrices that are constant within each sub-element. Within the space-time Galerkin predictor stage that solves the Cauchy problem inside each element in the small, the discrete solution and the flux tensor are approximated using a nodal space-time basis. Since these space-time basis functions are defined on a reference element and do not change, their integrals over the simplex sub-surfaces of the space-time reference control volume can be integrated once and for all analytically during a preprocessing step. The resulting integrals are then used together B M. Dumbser 123 J Sci Comput with the space-time degrees of freedom of the predictor in order to compute the numerical flux that is needed in the finite volume scheme. We apply the high order algorithm presented in this paper to the equations of hydrodynamics obtaining convergence rates up to fourth order of accuracy in space and time. A set of classical Lagrangian test problems has been solved and the results have been compared with the ones given by the original formulation of the algorithm (Boscheri and Dumbser 2013, 2014). The efficiency has been monitored and measured for each test case and the new quadrature-free schemes were up to 3.7 times faster than the ones based on Gaussian quadrature.Keywords Arbitrary-Lagrangian-Eulerian (ALE) · Finite volume schemes · Quadraturefree flux integration · WENO reconstruction on moving unstructured meshes · High order of accuracy in space and time · Local rezoning · Hydrodynamics

show abstract

Multi-material pressure relaxation methods for Lagrangian hydrodynamics

Cited by 39 publications

References 6 publications

Closure Models for Lagrangian Gas Dynamics and Elastoplasticity Equations in Multimaterial Cells

Closure Models for Lagrangian Gas Dynamics and Elastoplasticity Equations in Multimaterial Cells

Direct Arbitrary-Lagrangian–Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws

An Efficient Quadrature-Free Formulation for High Order Arbitrary-Lagrangian–Eulerian ADER-WENO Finite Volume Schemes on Unstructured Meshes

Contact Info

Product

Resources

About