On the Cancellation Problem in Calculating Compressible Low Mach Number Flows

Sesterhenn, Jörn; Müller, Bernhard; Thomann, H.

doi:10.1006/jcph.1999.6211

Cited by 49 publications

(48 citation statements)

References 11 publications

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“…However, anomalies or computational difficulties with using conservative methods have been reported, such as the low Mach number flow [5][6][7][8][9][10], sonic point glitch [11], carbuncle phenomenon [12], and others [4,[13][14][15][16]. In this paper, we focus on the problems of compressible flows with contact discon-tinuities and/or material interfaces.…”

Section: Introductionmentioning

confidence: 99%

Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities

Zhang

et al. 2015

Journal of Computational Physics

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In simulating compressible flows with contact discontinuities or material interfaces, numerical pressure and velocity oscillations can be induced by point-wise flux vector splitting (FVS) or component-wise nonlinear difference discretization of convection terms. The current analysis showed that the oscillations are due to the incompatibility of the point-wise splitting of eigenvalues in FVS and the inconsistency of component-wise nonlinear difference discretization among equations of mass, momentum, energy, and even fluid composition for multi-material flows. Two practical principles are proposed to prevent these oscillations: (i) convective fluxes must be split by a global FVS, such as the global Lax-Friedrichs FVS, and (ii) consistent discretization between different equations must be guaranteed. The latter, however, is not compatible with component-wise nonlinear difference discretization. Therefore, a consistent discretization method that uses only one set of common weights is proposed for nonlinear weighted essentially non-oscillatory (WENO) schemes. One possible procedure to determine the common weights is presented that provided good results. The analysis and methods stated above are appropriate for both single-(e.g., contact discontinuity) and multi-material (e.g., material interface) discontinuities. For the latter, however, the additional fluid composition equation should be split and discretized consistently for compatibility with the other equations. Numerical tests including several contact discontinuities and multi-material flows confirmed the effectiveness, robustness, and low computation cost of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities

Zhang

et al. 2015

Journal of Computational Physics

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“…It is believed that this is due to the problem of 'cancellation' errors. Sesterhenn et al [9] demonstrated that this is a potential issue even at Ma ≈ 0.02.…”

Section: Numerical Test Casesmentioning

confidence: 96%

Numerical dissipation of upwind schemes in low Mach flow

Thornber

Drikakis

2007

Numerical Methods in Fluids

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SUMMARYThis paper presents a modified Roe scheme for the simulation of multicomponent compressible flows with low Mach features. This modification reduces the excess dissipation of kinetic energy in Godunov-type methods at low Mach. The modification is shown to work effectively to Ma = 0.0002 using a single-mode Kelvin-Helmholtz instability as a test case, and reproduces the correct Ma 2 incompressible pressure scaling. Computational expense is negligible.

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“…The perturbation formulation is employed to minimize cancellation errors when discretizing the Navier-Stokes equations for compressible low Mach number flow (Sesterhenn et al, 1999;Müller, 2008). The conservative form of the 2D compressible Navier-Stokes equations in perturbation formulation can be written as…”

Section: Fluid Flowmentioning

confidence: 99%

Interaction between a simplified soft palate and compressible viscous flow

Khalili

Larsson

Müller

2016

Journal of Fluids and Structures

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Fluid-structure interaction in a simplified 2D model of the upper airways is simulated to study flow-induced oscillation of the soft palate in the pharynx. The goal of our research has been a better understanding of the mechanisms of the Obstructive Sleep Apnea Syndrome and snoring by taking into account compressible viscous flow. The inspiratory airflow is described by the 2D compressible Navier-Stokes equations, and the soft palate is modeled as a flexible plate by the linearized EulerBernoulli thin beam theory. Fluid-structure interaction is handled by the arbitrary LagrangianEulerian formulation. The fluid flow is computed by utilizing 4 th order accurate summation by parts difference operators and the 4 th order accurate classical Runge-Kutta method which lead to very accurate simulation results. The motion of the cantilevered plate is solved numerically by employing the Newmark time integration method. The numerical schemes for the structure are verified by comparing the computed frequencies of plate oscillation with the associated second mode eigenfrequency in vacuum. Vortex dynamics is assessed for the coupled fluid-structure system when both airways are open and when one airway is closed. The effect of mass ratio, rigidity and damping coefficient of the plate on the oscillatory behaviour is investigated. An acoustic analysis is carried out to characterize the acoustic wave propagation induced by the plate oscillation. It is observed that the acoustic wave corresponding to the quarter wave mode along the length of the duct is the dominant frequency. However, the frequency of the plate oscillation is recognizable in the acoustic pressure when reducing the amplitude of the quarter wave mode.

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On the Cancellation Problem in Calculating Compressible Low Mach Number Flows

Cited by 49 publications

References 11 publications

Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities

Preventing numerical oscillations in the flux-split based finite difference method for compressible flows with discontinuities

Numerical dissipation of upwind schemes in low Mach flow

Interaction between a simplified soft palate and compressible viscous flow

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