A Comparison of Various Meshless Schemes Within a Unified Algorithm

Jameson, Antony

doi:10.2514/6.2009-596

Cited by 35 publications

(41 citation statements)

References 38 publications

(24 reference statements)

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“…The Jameson's dual-time steeping approach [24] is adopted to integrate in time the semidiscrete equations (11). This procedure allows solving implicitly each physical time increment by means of inner explicit iterations in a fictitious time.…”

Section: Discretization In Timementioning

confidence: 99%

“…(11). Next, for a given increment in physical time t, a modified (unsteady) residual is defined from Eq.…”

Section: Discretization In Timementioning

confidence: 99%

“…[11] for a comparative analysis of popular discretization approaches). Moreover, applications to unsteady problems accounting for body motion have also been explored with success in a meshless context through small perturbation boundary conditions or domain deformation techniques, see for instance [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discretization In Timementioning

confidence: 99%

“…(11). Next, for a given increment in physical time t, a modified (unsteady) residual is defined from Eq.…”

Section: Discretization In Timementioning

confidence: 99%

See 1 more Smart Citation

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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“…By the 1990s [5], it began to be applied to computational fluid dynamics. Large numbers of researches are made by Liu and Su [6], Morinishi [7][8][9], Anandhanarayanan [10,11], and Katz and Jameson [12][13][14] later. The numerical simulation of unsteady flow with moving boundary in meshless method only involves the movement of the discrete points, but not restriction of stretch or distortion of mesh.…”

Section: Introductionmentioning

confidence: 99%

A Meshless Solution Method for Unsteady Flow with Moving Boundary

Zhang

Ren

et al. 2014

Advances in Mechanical Engineering

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Using the concept of overlapping mesh method for reference, a new method called as Overlapping Clouds of Points Method (OCPM) is firstly proposed to simulate unsteady flow with moving boundary problems based on meshless method. Firstly, a set of static background discrete points is generated in the whole calculation zone. Secondly, moving discrete points are created around moving body. According to the initial position of moving object in the flow field, the two sets of discrete points can be overlapped. With the motion of moving objects in the calculation field, moving discrete points around the moving body will inherently move. The exchange of flow field information between static points and moving points is realized by the solution of the clouds of points made up of static and moving discrete points using weighted meshless method nearby overlapping boundary. Four cases including piston problem, NACA0012 airfoil vibration flow around a moving sphere in supersonic and multibody separation are given to verify accuracy and practicability of OCPM. The numerical results agree well with exact solution and experimental results, which shows that the proposed OCPM can be applied to the simulation of unsteady flow problem.

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“…The capabilities of the LSFD-U were further enhanced by including viscous terms (Munikrishna, 2007;Munikrishna & Balakrishnan, 2007;Ninawe, Munikrishna, & Balakrishnan, 2006). Katz and Jameson (2009a, 2009b, 2009c have developed an edge-based meshless Euler solver called the 'meshless volume scheme'. They have demonstrated this method along with a multi-grid convergence acceleration…”

Section: Introductionmentioning

confidence: 99%

Implicit scheme for meshless compressible Euler solver

Singh

Ramesh

Balakrishnan

2015

Engineering Applications of Computational Fluid Mechanics

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In this paper, an implicit scheme is presented for a meshless compressible Euler solver based on the Least Square Kinetic Upwind Method (LSKUM). The Jameson and Yoon's split flux Jacobians formulation is very popular in finite volume methodology, which leads to a scalar diagonal dominant matrix for an efficient implicit procedure . However, this approach leads to a block diagonal matrix when applied to the LSKUM meshless method. The above split flux Jacobian formulation, along with a matrix-free approach, has been adopted to obtain a diagonally dominant, robust and cheap implicit time integration scheme. The efficacy of the scheme is demonstrated by computing 2D flow past a NACA 0012 airfoil under subsonic, transonic and supersonic flow conditions. The results obtained are compared with available experiments and other reliable computational fluid dynamics (CFD) results. The present implicit formulation shows good convergence acceleration over the RK4 explicit procedure. Further, the accuracy and robustness of the scheme in 3D is demonstrated by computing the flow past an ONERA M6 wing and a clipped delta wing with aileron deflection. The computed results show good agreement with wind tunnel experiments and other CFD computations.

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A Comparison of Various Meshless Schemes Within a Unified Algorithm

Cited by 35 publications

References 38 publications

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

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

A Meshless Solution Method for Unsteady Flow with Moving Boundary

Implicit scheme for meshless compressible Euler solver

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