An Implicit Lagrangian Method for Solving One- and Two-Dimensional Gasdynamic Equations

Liu, F.; McIntosh, Andy C.; Brindley, J.

doi:10.1006/jcph.1994.1009

Cited by 6 publications

(7 citation statements)

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“…One-dimension pressure wave propagation [34]. In this example, the initial pressure pulse will break into two propagating waves in the positive and negative directions.…”

Section: Numerical Examplesmentioning

confidence: 98%

“…In this example, the initial pressure pulse will break into two propagating waves in the positive and negative directions. We select the initial conditions in the region x ∈ [0; 1] [34]. This scheme can maintain these strong gradients.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The ÿrst one is the typical Riemann problem, namely the shock tube problem of Lax. The second one is the propagation of a planar pressure pulse [34]. The third one simulates the response of a planar ame to a harmonic pressure wave [34].…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The second one is the propagation of a planar pressure pulse [34]. The third one simulates the response of a planar ame to a harmonic pressure wave [34]. The last problem is two-dimensional Sod's problem containing shock waves 1.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…An implicit scheme with entropy modiÿcation [34] We consider isentropic ows: the entropy of each computational element is written as…”

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confidence: 99%

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An implicit Lagrangian lattice Boltzmann method for the compressible flows

Yan

Dong

Liu

2006

Int. J. Numer. Meth. Fluids

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SUMMARYIn this paper, we propose a new Lagrangian lattice Boltzmann method (LBM) for simulating the compressible ows. The new scheme simulates uid ows based on the displacement distribution functions. The compressible ows, such as shock waves and contact discontinuities are modelled by using Lagrangian LBM. In this model, we select the element in the Lagrangian coordinate to satisfy the basic uid laws. This model is a simpler version than the corresponding Eulerian coordinates, because the convection term of the Euler equations disappears. The numerical simulations conform to classical results.

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“…One-dimension pressure wave propagation [34]. In this example, the initial pressure pulse will break into two propagating waves in the positive and negative directions.…”

Section: Numerical Examplesmentioning

confidence: 98%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

“…An implicit scheme with entropy modiÿcation [34] We consider isentropic ows: the entropy of each computational element is written as…”

mentioning

confidence: 99%

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An implicit Lagrangian lattice Boltzmann method for the compressible flows

Yan

Dong

Liu

2006

Int. J. Numer. Meth. Fluids

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A Free-Lagrange method for unsteady compressible flow: simulation of a confined cylindrical blast wave

Ball

1996

Shock Waves

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Abstract.A Free-Lagrange numerical procedure for the simulation of two-dimensional inviscid compressible flow is described in detail. The unsteady Euler equations are solved on an unstructured Lagrangian grid based on a density-weighted Voronoi mesh. The flow solver is of the Godunov type, utilising either the HLLE (2 wave) approximate Riemann solver or the more recent HLLC (3 wave) variant, each adapted to the Lagrangian frame. Within each mesh cell, conserved properties are treated as piece-wise linear, and a slope limiter of the MUSCL type is used to give non-oscillatory behaviour with nominal second order accuracy in space. The solver is first order accurate in time. Modifications to the slope limiter to minimise grid and coordinate dependent effects are described. The performances of the HLLE and HLLC solvers are compared for two test problems; a one-dimensional shock tube and a two-dimensional blast wave confined within a rigid cylinder. The blast wave is initiated by impulsive heating of a gas column whose centreline is parallel to, and one half of the cylinder radius from, the axis of the cylinder. For the shock tube problem, both solvers predict shock and expansion waves in good agreement with theory. For the HLLE solver, contact resolution is poor, especially in the blast wave problem. The HLLC solver achieves near-exact contact capture in both problems.

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A lagrangian lattice boltzmann method for euler equations

Yan

1998

Acta Mech Sinica

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A Lagrangian lattice Boltzmann method for solving Euler equations is proposed. The key step in formulating this method is the introduction of the displacement distribution function. The equilibrium distribution function consists of macroscopic Lagrangian variables at time steps n and n + 1. It is different from the standard lattice Boltzmann method. In this method the element, instead of each particle, is required to satisfy the basic law, The element is considered as one large particle, which results in simpler version than the corresponding Eulerian one, because the advection term disappears here. Our numerical examples successfully reproduce the classical results.

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An Implicit Lagrangian Method for Solving One- and Two-Dimensional Gasdynamic Equations

Cited by 6 publications

References 0 publications

An implicit Lagrangian lattice Boltzmann method for the compressible flows

An implicit Lagrangian lattice Boltzmann method for the compressible flows

A Free-Lagrange method for unsteady compressible flow: simulation of a confined cylindrical blast wave

A lagrangian lattice boltzmann method for euler equations

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