High order finite point method for the solution to the sound propagation problems

Bajko, Jaroslav; Čermák, Libor; Jícha, Miroslav

doi:10.1016/j.cma.2014.07.022

Cited by 8 publications

(14 citation statements)

References 22 publications

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“…The complete (multivariate) polynomial basis of order ν, cf. [3][4][5][6]11] is adopted in this work.…”

Section: Weighted Least Squares Methodsmentioning

confidence: 99%

“…Consequently, the WLSQ with interpolation condition greatly reduces the computation costs and improves stability, cf. [5,6]. The system of ODE (27) is then solved with high order low-dissipation and low-dispersion Runge-Kutta scheme optimized for wave propagation problems, cf.…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…In contrast to the stabilization that is enforced by upwind approximation of derivatives, cf. [3][4][5][6][7][8][9][10], direct central-type approximation and filtering represents another way of obtaining a stable solution. The experimental part of this work is therefore focusing on benchmark problems with respect to stability, robustness and accuracy of the method, which are crucial properties in aeroacoustic applications.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stabilization of a meshless method via weighted least squares filtering

Bajko

Niedoba

Čermák

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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“…The complete (multivariate) polynomial basis of order ν, cf. [3][4][5][6]11] is adopted in this work.…”

Section: Weighted Least Squares Methodsmentioning

confidence: 99%

Section: Spatial Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stabilization of a meshless method via weighted least squares filtering

Bajko

Niedoba

Čermák

et al. 2017

Computer Methods in Applied Mechanics and Engineering

Self Cite

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“…[7,10,11]. The interpolation condition in the WLSQ approach allows to simplify the left side of the equation system (15) avoiding the necessity to solve the system of n linear equations.…”

Section: Spatial Discretization Of Leementioning

confidence: 99%

“…[3,4], have been investigated in this context, but there is also growing interest in meshless methods, cf. [5][6][7][8][9][10][11], due to their potential advantages. Depending on applications, these methods can be superior in accuracy, stability, robustness and can deal with complex geometries, multiphase flow, problems with free boundaries and moving objects.…”

Section: Introductionmentioning

confidence: 99%

Simulation of the acoustic wave propagation using a meshless method

et al. 2017

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Abstract. This paper presents numerical simulations of the acoustic wave propagation phenomenon modelled via Linearized Euler equations. A meshless method based on collocation of the strong form of the equation system is adopted. Moreover, the Weighted least squares method is used for local approximation of derivatives as well as stabilization technique in a form of spatial filtering. The accuracy and robustness of the method is examined on several benchmark problems.

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A study of the role of weights in the spectral properties of the least square finite difference scheme and the least square upwind finite difference scheme

Mungur

2022

Numerical Methods in Fluids

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In this article, we analyze the performance of a family of nonlinear, shock-capturing mesh-free finite-difference schemes in wavenumber space. These finite difference methods are based on the use of a weighted least-square approximation procedure together with a Taylor series expansion of the unknown function. The influence of weights on the spectral properties of these schemes are studied using the approximate dispersion relation. The numerical study evidences that an appropriate choice of the weighting functions reduces dissipation and dispersion inherent to the schemes. The meshless schemes studied in this work, are then used to simulate 2D internal inviscid subsonic and transonic flows respectively in a channel with a bump. The results in 2D corroborate with the 1D analyses and reveal that when the supporting nodes closer to the reference node are assigned a greater weightage value in the computation of the 1st order spatial derivatives, better spectral properties are achieved at low wavenumber. However, the present numerical study shows that weighting function does not shift the frequency of the errors and thus in order to accelerate the convergence of these schemes, methods such as the classic multigrid can be used.

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High order finite point method for the solution to the sound propagation problems

Cited by 8 publications

References 22 publications

Stabilization of a meshless method via weighted least squares filtering

Stabilization of a meshless method via weighted least squares filtering

Simulation of the acoustic wave propagation using a meshless method

A study of the role of weights in the spectral properties of the least square finite difference scheme and the least square upwind finite difference scheme

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