A finite point method for adaptive three‐dimensional compressible flow calculations

Ortega, Enrique; Oñate, Eugenio; Idelsohn, Sergio

doi:10.1002/fld.1892

Cited by 30 publications

(36 citation statements)

References 23 publications

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“…The weighting function φ : R d → R prescribes the contribution of every point to J(α) in the local cloud according the distance to the star point x i 1 , cf. [10]. Solution to the system of normal equations…”

Section: Wlsq Approximationmentioning

confidence: 99%

“…[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%

“…Therefore, using WLSQ with interpolation condition greatly reduces the computation costs and improves stability, cf. [10,11]. The system of ODE (15) is then solved with high order lowdissipation and low-dispersion runge-kutta scheme optimized for wave propagation problems, cf.…”

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%

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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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Section: Wlsq Approximationmentioning

confidence: 99%

“…[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%

Section: Spatial Discretization Of Leementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simulation of the acoustic wave propagation using a meshless method

et al. 2017

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“…In the last two decades, numerous meshless techniques aimed at dealing with steady and unsteady compressible flow problems [3][4][5][6][7][8][9][10] have been developed (cf. [11] for a comparative analysis of popular discretization approaches).…”

Section: Introductionmentioning

confidence: 99%

A meshless finite point method for three‐dimensional analysis of compressible flow problems involving moving boundaries and adaptivity

Ortega

Oñate

Idelsohn

et al. 2013

Numerical Methods in Fluids

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This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.A finite point method for solving compressible flow problems involving moving boundaries and adaptivity is presented. The numerical methodology is based on an upwind-biased discretization of the Euler equations, written in arbitrary Lagrangian–Eulerian form and integrated in time by means of a dual-time steeping technique. In order to exploit the meshless potential of the method, a domain deformation approach based on the spring network analogy is implemented, and h-adaptivity is also employed in the computations. Typical movable boundary problems in transonic flow regime are solved to assess the performance of the proposed technique. In addition, an application to a fluid–structure interaction problem involving static aeroelasticity illustrates the capability of the method to deal with practical engineering analyses. The computational cost and multi-core performance of the proposed technique is also discussed through the examples provided.Peer ReviewedPostprint (author's final draft

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Application of the finite point method to high‐Reynolds number compressible flow problems

Ortega

Oñate

Idelsohn

et al. 2014

Numerical Methods in Fluids

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SUMMARYIn this work, the finite point method is applied to the solution of high‐Reynolds compressible viscous flows. The aim is to explore this important field of applications focusing on two main aspects: the easiness and automation of the meshless discretization of viscous layers and the construction of a robust numerical approximation in the highly stretched clouds of points resulting in such domain areas. The flow solution scheme adopts an upwind‐biased scheme to solve the averaged Navier–Stokes equations in conjunction with an algebraic turbulence model. The numerical applications presented involve different attached boundary layer flows and are intended to show the performance of the numerical technique. The results obtained are satisfactory and indicative of the possibilities to extend the present meshless technique to more complex flow problems. Copyright © 2014 John Wiley & Sons, Ltd.

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A finite point method for adaptive three‐dimensional compressible flow calculations

Cited by 30 publications

References 23 publications

Simulation of the acoustic wave propagation using a meshless method

Simulation of the acoustic wave propagation using a meshless method

A meshless finite point method for three‐dimensional analysis of compressible flow problems involving moving boundaries and adaptivity

Application of the finite point method to high‐Reynolds number compressible flow problems

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