A Lagrangian staggered grid Godunov-like approach for hydrodynamics

Morgan, Nathaniel R.; Lipnikov, Konstantin; Burton, Donald E.; Kenamond, Mark A.

doi:10.1016/j.jcp.2013.12.013

Cited by 60 publications

(35 citation statements)

References 28 publications

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“…The interface fix is applied on all interfaces and the artificial energy flux is again turned off at the interfaces. The result at time t = 2.7 as in [29] is shown in Fig. 15.…”

Section: Triple-point Problemmentioning

confidence: 99%

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Some cell-centered Lagrangian Lax–Wendroff HLL hybrid schemes

Fridrich

Liska

Wendroff

2016

Journal of Computational Physics

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“…The interface fix is applied on all interfaces and the artificial energy flux is again turned off at the interfaces. The result at time t = 2.7 as in [29] is shown in Fig. 15.…”

Section: Triple-point Problemmentioning

confidence: 99%

“…There are multiple versions of this problem, differing by the choice of γ for each state. We present here the version from [29] with γ = 1.4 in all three states. The interface fix is applied on all interfaces and the artificial energy flux is again turned off at the interfaces.…”

Section: Triple-point Problemmentioning

confidence: 99%

Some cell-centered Lagrangian Lax–Wendroff HLL hybrid schemes

Fridrich

Liska

Wendroff

2016

Journal of Computational Physics

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“…The aforementioned Riemann jump relation modifies the one used in [10,11,13,30] by using Eq. The first relation is where u ´i s the Riemann velocity at the cell center, the subscript c.p/ is the cell corner between node p and cell´, is the shock impedance, and a is a unit vector in the approximate direction of the shock.…”

Section: Riemann Calculationmentioning

confidence: 99%

“…The final test problem is the triple-point shock problem, which has significant vorticity [11,21,30,39,40]. The initial conditions are three ideal gas regions.…”

Section: Triple Pointmentioning

confidence: 99%

“…The multidimensional Riemann-like problems were first proposed for Lagrangian CCH [10][11][12]26]; since then, researchers have extended these Riemann problems to finite volume SGH [27][28][29][30] and edge-based finite element PCH [16,21]. The multidimensional Riemann-like problems were first proposed for Lagrangian CCH [10][11][12]26]; since then, researchers have extended these Riemann problems to finite volume SGH [27][28][29][30] and edge-based finite element PCH [16,21].…”

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confidence: 99%

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A 3D finite element ALE method using an approximate Riemann solution

Chiravalle

Morgan

2016

Numerical Methods in Fluids

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Summary Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann‐like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann‐like problem. Two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well‐known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problem results are presented. Copyright © 2016 John Wiley & Sons, Ltd.

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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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A Lagrangian staggered grid Godunov-like approach for hydrodynamics

Cited by 60 publications

References 28 publications

Some cell-centered Lagrangian Lax–Wendroff HLL hybrid schemes

Some cell-centered Lagrangian Lax–Wendroff HLL hybrid schemes

A 3D finite element ALE method using an approximate Riemann solution

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

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