Remark on the generalized Riemann problem method for compressible fluid flows

Li, Jiequan; Sun, Zhongfeng

doi:10.1016/j.jcp.2006.08.017

Cited by 16 publications

(12 citation statements)

References 15 publications

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“…The distinct feature of that original GRP scheme is the analytic resolution of curved rarefaction waves, and is based on the relevant Lagrangian scheme. In order to avoid the Lagrangian version and treat complicated sonic cases, we introduced Riemann invariants in [8,21] to resolve centered rarefaction waves (CRW). Thus the present scheme is directly Eulerian with easy extension to multi-dimensions and no special treatment is required for sonic cases.…”

Section: Introductionmentioning

confidence: 99%

Implementation of the GRP scheme for computing radially symmetric compressible fluid flows

Liu

Sun

2009

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

Implementation of the GRP scheme for computing radially symmetric compressible fluid flows

Liu

Sun

2009

Journal of Computational Physics

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“…In the Lagrangian onedimensional case, this approximation has been thoroughly described in the monograph [6], we have also recalled it in [23]. We note that a Riemann invariants approach could have been also used, following the methodology developed in [21].…”

Section: The Two-dimensional High-order Extensionmentioning

confidence: 99%

A high-order cell-centered Lagrangian scheme for compressible fluid flows in two-dimensional cylindrical geometry

Maire

2009

Journal of Computational Physics

107

103

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International audienceThe goal of this paper is to present high-order cell-centered schemes for solving the equations of Lagrangian gas dynamics written in cylindrical geometry. A node-based discretization of the numerical fluxes is obtained through the computation of the time rate of change of the cell volume. It allows to derive finite volume numerical schemes that are compatible with the geometric conservation law (GCL). Two discretizations of the momentum equations are proposed depending on the form of the discrete gradient operator. The first one corresponds to the control volume scheme while the second one corresponds to the so-called area weighted scheme. Both formulations share the same discretization for the total energy equation. In both schemes, fluxes are computed using the same nodal solver which can be viewed as a two-dimensional extension of an approximate Riemann solver. The control volume scheme is conservative for momentum, total energy and satisfies a local entropy inequality in its first-order semi-discrete form. However, it does not preserve spherical symmetry. On the other hand, the area weighted scheme is conservative for total energy and preserves spherical symmetry for one-dimensional spherical flow on equiangular polar grid. The two-dimensional high-order extensions of these two schemes are constructed employing the generalized Riemann problem (GRP) in the acoustic approximation. Many numerical tests are presented in order to assess these new schemes. The results obtained for various representative configurations of one and two-dimensional compressible fluid flows show the robustness and the accuracy of our new schemes

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“…The relation of numerical dissipation mechanism and shock instability was analyzed in . A high order GRP treatment is supplied in . A pessimistic remark was even made in that there is no satisfactory solution to attack the oscillation problem in the calculation of slowly moving strong shocks.…”

Section: Introductionmentioning

confidence: 99%

Dissipation matrix and artificial heat conduction for Godunov‐type schemes of compressible fluid flows

Tian

Wang

2016

Numerical Methods in Fluids

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Summary This paper aims to reassess the Riemann solver for compressible fluid flows in Lagrangian frame from the viewpoint of modified equation approach and provides a theoretical insight into dissipation mechanism. It is observed that numerical dissipation vanishes uniformly for the Godunov‐type schemes in the sense that associated dissipation matrix has zero determinant if an exact or approximate Riemann solver is used to construct numerical fluxes in the Lagrangian frame. This fact connects to some numerical defects such as the wall‐heating phenomenon and start‐up errors. To cure these numerical defects, a traditional numerical viscosity is added, as well as the artificial heat conduction is introduced via a simple passage of the Lax–Friedrichs type discretization of internal energy. Copyright © 2016 John Wiley & Sons, Ltd.

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Remark on the generalized Riemann problem method for compressible fluid flows

Cited by 16 publications

References 15 publications

Implementation of the GRP scheme for computing radially symmetric compressible fluid flows

Implementation of the GRP scheme for computing radially symmetric compressible fluid flows

A high-order cell-centered Lagrangian scheme for compressible fluid flows in two-dimensional cylindrical geometry

Dissipation matrix and artificial heat conduction for Godunov‐type schemes of compressible fluid flows

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