A low Mach correction able to deal with low Mach acoustics

Bruel, Pascal; Delmas, Simon; Jung, Jonathan; Perrier, Vincent

doi:10.1016/j.jcp.2018.11.020

Cited by 17 publications

(54 citation statements)

References 46 publications

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“…• The fix of [4] (that we will call LMAAP, for Low Mach Acoustic Accuracy Preserving) which can be seen as an extension of [1] on unstructured meshes…”

Section: Discrete Long Time Behaviour For the Wave Systemmentioning

confidence: 99%

Long time behavior of finite volume discretization of symmetrizable linear hyperbolic systems

Jung

Perrier

2021

IMA Journal of Numerical Analysis

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This article is dedicated to the long time behavior of a finite volume approximation of general symmetrizable linear hyperbolic system on a bounded domain. In the continuous case this problem is very difficult, and the $\omega $–limit set (namely the set of all the possible long time limits) may be large and complicated to depict if no dissipation is introduced. In this article we prove that in general, with a stable finite volume scheme, the discrete solution converges to a steady state when the time goes to infinity. This property is a direct consequence of the numerical dissipation mechanisms used for stabilizing the discretization. We apply this result for determining the long time limit for several stabilizations of the wave system, and perform a formal link with the low Mach number problem of the nonlinear Euler system. Numerical experiments with the wave system are performed for confirming the theoretical results obtained.

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“…• The fix of [4] (that we will call LMAAP, for Low Mach Acoustic Accuracy Preserving) which can be seen as an extension of [1] on unstructured meshes…”

Section: Discrete Long Time Behaviour For the Wave Systemmentioning

confidence: 99%

Long time behavior of finite volume discretization of symmetrizable linear hyperbolic systems

Jung

Perrier

2021

IMA Journal of Numerical Analysis

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“…The all-Mach VFRoe scheme is stable. In fact, as for the constant porosity case, numerical tests seem to show that the all-Mach scheme is stable under a degenerated CFL condition which is exactly the half of the classical one (see [13,5] for more details). This justifies why all numerical results are obtained with CF L = 0.4.…”

Section: Numerical Resultsmentioning

confidence: 91%

“…Indeed, they do not allow to recover the incompressible limit as the Mach number tends to zero. Over the two last decades, a large amount of work has been dedicated to deriving fixes for the uniform porosity case: [23,28,29,13,37,12,15,33,7,24,5]. Some recent works have been done on low Mach fix for non-conservative systems, we refer to [3,2,45] for the Euler equation with gravity or to [35,34] for two-phases flows.…”

Section: Introductionmentioning

confidence: 99%

Construction of a low Mach finite volume scheme for the isentropic Euler system with porosity

Dellacherie

Jung

2021

ESAIM: M2AN

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Classical finite volume schemes for the Euler system are not accurate at low Mach number and some fixes have to be used and were developed in a vast literature over the last two decades. The question we are interested in in this article is: What about if the porosity is no longer uniform? We first show that this problem may be understood on the linear wave equation taking into account porosity. We explain the influence of the cell geometry on the accuracy property at low Mach number. In the triangular case, the stationary space of the Godunov scheme approaches well enough the continuous space of constant pressure and divergence-free velocity, while this is not the case in the Cartesian case. On Cartesian meshes, a fix is proposed and accuracy at low Mach number is proved to be recovered. Based on the linear study, a numerical scheme and a low Mach fix for the non-linear system, with a non-conservative source term due to the porosity variations, is proposed and tested.

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“…Many works over the past years have proposed low Mach corrections for single-fluid flows [13,14,18,45,19]. The fix usually amounts to use a centered pressure evaluation at the cell interfaces in the low Mach regime.…”

Section: Low Mach Regime Accuracy Analysis and Fix For The Bulk Flowmentioning

confidence: 99%

Compressible solver for two-phase flows with sharp interface and capillary effects preserving accuracy in the low Mach regime

Zou

Grenier

Kokh

et al. 2022

Journal of Computational Physics

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We present a sharp interface approach for compressible two-phase flows that preserves its accuracy in the low Mach regime. The interface between both fluids is captured by a Level Set function via the Ghost Fluid method. In the low Mach regime, classic Finite Volume compressible solvers lose accuracy on quadrangle or hexahedral meshes and a low Mach correction is then necessary to reduce the numerical dissipation. The sharp interface that separates both fluids, may induce an important jump in the medium properties that induces additional challenges for the design of a numerical scheme. Indeed, the well-known low Mach fixes in the literature could lead to significant truncation errors when the flow involves large density and sound speed ratios between both phases. To preserve the accuracy of the numerical method, we propose a specific low Mach fix for this interface problem that yields a uniform truncation error with respect to the Mach number. Numerical results show significant evidences of the efficiency and accuracy of the proposed low Mach correction.

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A low Mach correction able to deal with low Mach acoustics

Cited by 17 publications

References 46 publications

Long time behavior of finite volume discretization of symmetrizable linear hyperbolic systems

Long time behavior of finite volume discretization of symmetrizable linear hyperbolic systems

Construction of a low Mach finite volume scheme for the isentropic Euler system with porosity

Compressible solver for two-phase flows with sharp interface and capillary effects preserving accuracy in the low Mach regime

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