Some cell-centered Lagrangian Lax–Wendroff HLL hybrid schemes

Fridrich, David; Liska, R.; Wendroff, Burton

doi:10.1016/j.jcp.2016.09.022

Cited by 10 publications

(13 citation statements)

References 29 publications

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“…where the summation goes over c(p), which is the set of all cells sharing the vertex p. In the original paper [13] the conservative cell quantities in the first term on the right hand side of (7) were weighted by the Cartesian subzonal masses m pc , giving the standard Lax-Friedrichs (LF) approximation. Here, being inspired by Wendroff and White [17], we weight them by the inverses of the subzonal volumes 1/V pc .…”

Section: Predictormentioning

confidence: 99%

“…Our recently introduced Lax-Wendroff HLL hybrid scheme [13] is also a cell-centered method. The artificial dissipation, in the form of dissipative part of the HLL approximate Riemann solver flux [14], is added to the momentum and energy equations.…”

Section: Introductionmentioning

confidence: 99%

“…The original method is improved by applying another weighting in the predictor. The original paper [13] has presented numerical results only on logical rectangular, quadrilateral meshes. Here we present results on unstructured meshes, including uniform triangular and hexagonal meshes and non-uniform triangular and polygonal meshes.…”

Section: Introductionmentioning

confidence: 99%

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Cell-Centered Lagrangian Lax-Wendroff HLL Hybrid Scheme on Unstructured Meshes

et al. 2021

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We have recently introduced a new cell-centered Lax-Wendroff HLL hybrid scheme for Lagrangian hydrodynamics [Fridrich et al. J. Comp. Phys. 326 (2016) 878-892] with results presented only on logical rectangular quadrilateral meshes. In this study we present an improved version on unstructured meshes, including uniform triangular and hexagonal meshes and non-uniform triangular and polygonal meshes. The performance of the scheme is verified on Noh and Sedov problems and its second-order convergence is verified on a smooth expansion test.Finally the choice of the scalar parameter controlling the amount of added artificial dissipation is studied.

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Section: Predictormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cell-Centered Lagrangian Lax-Wendroff HLL Hybrid Scheme on Unstructured Meshes

et al. 2021

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“…The density-dependent adiabatic bulk modulus factor in the last term in the left-hand side of Eq. 28is the only term in the system (27), (28) that accounts for a particular choice of EOS.…”

Section: Self-similar Solutions Of the Noh Problem For Cylindricamentioning

confidence: 99%

Solution of the Noh problem with an arbitrary equation of state

Velikovich

Giuliani

2018

Phys. Rev. E

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The classic self-similar solutions of the nonstationary compressible Euler equations obtained for a blast-wave propagation (Sedov, Taylor, and von Neumann), a shock-wave implosion (Guderley, Landau, and Stanyukovich), or an impulsive loading of a planar target (von Hoerner, Häfele, and Zel'dovich) have all been derived for a polytropic ideal gas. None of them can be generalized for a fluid with an arbitrary equation of state (EOS), such as the van der Waals EOS of a non-ideal-gas or a three-term EOS of a condensed material. We demonstrate here that the Noh accretion-shock problem is an exception. Its self-similar solutions exist in cylindrical and spherical geometry for fluids and materials with an arbitrary EOS. Such solutions for finite accretion-shock strength and nonuniform inflow velocity are constructed semianalytically with a model three-term equation of state that includes cold, thermal ion (lattice), and thermal electron contributions to the pressure and internal energy. Examples are presented for aluminum and copper. Other material- and EOS-specific semianalytic solutions of the Noh problem can be easily constructed using the same method for any material that in the pressure range of interest can be approximated as a dissipation-free fluid with an arbitrary equation of state.

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“…Lax-Wendroff scheme is a numerical method for the solution of hyperbolic partial differential equations, based on finite differences [11]. This method was applied in Lagrangian coordinates in one dimension [12]. The one step Lax-Wendroff scheme was applied to tidal wave propagation with uneven bottom test problem.…”

Section: One Step Lax-wendroff Schemementioning

confidence: 99%

Deficiency of finite difference methods for capturing shock waves and wave propagation over uneven bottom seabed

Ahmad¹,

Suliman²,

2018

IJET

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The implementation of finite difference method is used to solve shallow water equations under the extreme conditions. The cases such as dam break and wave propagation over uneven bottom seabed are selected to test the ordinary schemes of Lax-Friederichs and Lax-Wendroff numerical schemes. The test cases include the source term for wave propagation and exclude the source term for dam break. The main aim of this paper is to revisit the application of Lax-Friederichs and Lax-Wendroff numerical schemes at simulating dam break and wave propagation over uneven bottom seabed. For the case of the dam break, the two steps of Lax-Friederichs scheme produce nonoscillation numerical results, however, suffering from some of dissipation. Moreover, the two steps of Lax-Wendroff scheme suffers a very bad oscillation. It seems that these numerical schemes cannot solve the problem at discontinuities which leads to oscillation and dissipation. For wave propagation case, those numerical schemes produce inaccurate information of free surface and velocity due to the uneven seabed profile. Therefore, finite difference is unable to model shallow water equations under uneven bottom seabed with high accuracy compared to the analytical solution.

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Some cell-centered Lagrangian Lax–Wendroff HLL hybrid schemes

Cited by 10 publications

References 29 publications

Cell-Centered Lagrangian Lax-Wendroff HLL Hybrid Scheme on Unstructured Meshes

Cell-Centered Lagrangian Lax-Wendroff HLL Hybrid Scheme on Unstructured Meshes

Solution of the Noh problem with an arbitrary equation of state

Deficiency of finite difference methods for capturing shock waves and wave propagation over uneven bottom seabed

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