3D staggered Lagrangian hydrodynamics scheme with cell‐centered Riemann solver‐based artificial viscosity

Loubère, Raphaël; Maire, Pierre‐Henri; Váchal, Pavel

doi:10.1002/fld.3730

Cited by 58 publications

(61 citation statements)

References 25 publications

(76 reference statements)

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“…This is a well-known test case for moving mesh schemes [110,87,92,85] that measures the preservation of spherical symmetry on non symmetric grid. An analytical solution based on selfsimilarity arguments is available, see Kamm et al [71].…”

Section: D Sedov Problemmentioning

confidence: 99%

“…Exhaustive 3D description of these tests can be found in the following references: the isentropic vortex problem [39], Sedov problem [85,20], Saltzman problem [25,22,92,20] and the triple point problem [42].…”

Section: D Test Problemsmentioning

confidence: 99%

“…Furthermore Lagrangian algorithms require a moving mesh framework, with the physical variables either located at the cell barycenter [33,107,90,91,89] or defined at different positions within each control volume [84,85]. The first approach leads to cell-centered Lagrangian schemes, while the latter is usually addressed as the staggered mesh approach, where the velocity is defined at the cell vertices or interfaces and the other variables at the cell center.…”

Section: Introductionmentioning

confidence: 99%

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

Boscheri

Loubère

Dumbser

2015

Journal of Computational Physics

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Section: D Sedov Problemmentioning

confidence: 99%

Section: D Test Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Boscheri

Loubère

Dumbser

2015

Journal of Computational Physics

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“…The Sedov problem consists in the evolution of a blast wave with spherical symmetry and is widely used in literature [61,62,67], hence we limit us to present here the numerical results, without providing the information for setting up this well-known test problem. The initial computational domain is the cube Ω(0) = [0; 1.2] × [0; 1.2] × [0; 1.2] and is discretized with a total number N E = 40000 of right tetrahedra, obtained starting from a Cartesian grid composed by 20 × 20 × 20 cubes and splitting each cube into five tetrahedra, as done in [10].…”

Section: The Sedov Problemmentioning

confidence: 99%

“…For this reason a lot of effort has been made in the last decades concerning the development and improvement of Lagrangian algorithms, see, for example, [4,15,16,65,68,75,87]. Lagrangian schemes are also classified in the literature according to the location of the physical variables on the mesh: in the cell-centered approach [21,[64][65][66]72] all variables are continuously defined inside the cell, whereas in the staggered mesh approach [60,61] the velocity is continuously defined on the dual cell, around the grid nodes, and the other variables on the primary cell.…”

Section: Introductionmentioning

confidence: 99%

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

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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

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A nodal Godunov method for Lagrangian shock hydrodynamics on unstructured tetrahedral grids

Waltz

Morgan

Canfield

et al. 2014

Numerical Methods in Fluids

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SUMMARYWe present a nodal Godunov method for Lagrangian shock hydrodynamics. The method is designed to operate on three‐dimensional unstructured grids composed of tetrahedral cells. A node‐centered finite element formulation avoids mesh stiffness, and an approximate Riemann solver in the fluid reference frame ensures a stable, upwind formulation. This choice leads to a non‐zero mass flux between control volumes, even though the mesh moves at the fluid velocity, but eliminates volume errors that arise due to the difference between the fluid velocity and the contact wave speed. A monotone piecewise linear reconstruction of primitive variables is used to compute interface unknowns and recover second‐order accuracy. The scheme has been tested on a variety of standard test problems and exhibits first‐order accuracy on shock problems and second‐order accuracy on smooth flows using meshes of up to O(106) tetrahedra. Copyright © 2014 John Wiley & Sons, Ltd.

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3D staggered Lagrangian hydrodynamics scheme with cell‐centered Riemann solver‐based artificial viscosity

Abstract: International audienc

Cited by 58 publications

References 25 publications

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

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

A nodal Godunov method for Lagrangian shock hydrodynamics on unstructured tetrahedral grids

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