A-posteriori error estimation for the finite point method with applications to compressible flow

Ortega, Enrique; Flores, Roberto; Oñate, Eugenio; Idelsohn, Sergio

doi:10.1007/s00466-017-1402-7

Cited by 8 publications

(4 citation statements)

References 68 publications

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“…Meshless methods include SPH, the mesh-free method [147], the finite point method [148,149], and the Galerkin meshless method [150]. The common feature of the meshless methods is that the local approximation of the function that is being searched for is based only on the values of this function at individual selected points in the area.…”

Section: Meshless Methodsmentioning

confidence: 99%

Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

Trzepieciński

Dell’Isola

Lemu

2021

Metals

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The concept of Industry 4.0 is defined as a common term for technology and the concept of new digital tools to optimize the manufacturing process. Within this framework of modular smart factories, cyber-physical systems monitor physical processes creating a virtual copy of the physical world and making decentralized decisions. This article presents a review of the literature on virtual methods of computer-aided manufacturing processes. Numerical modeling is used to predict stress and temperature distribution, springback, material flow, and prediction of phase transformations, as well as for determining forming forces and the locations of potential wrinkling and cracking. The scope of the review has been limited to the last ten years, with an emphasis on the current state of knowledge. Intelligent production driven by the concept of Industry 4.0 and the demand for high-quality equipment in the aerospace and automotive industries forces the development of manufacturing techniques to progress towards intelligent manufacturing and ecological production. Multi-scale approaches that tend to move from macro- to micro- parameters become very important in numerical optimization programs. The software requirements for optimizing a fully coupled thermo-mechanical microstructure then increase rapidly. The highly advanced simulation programs based on our knowledge of physical and mechanical phenomena occurring in non-homogeneous materials allow a significant acceleration of the introduction of new products and the optimization of existing processes.

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Section: Meshless Methodsmentioning

confidence: 99%

Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

Trzepieciński

Dell’Isola

Lemu

2021

Metals

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“…In this work, the local time step approach is used. When handling essentially steady problems, the temporal discretisation can directly follow Equation ( 20) by dropping the first level of discretisation in Equation (19).…”

Section: Implicit Temporal Discretisationmentioning

confidence: 99%

“…For aerodynamic modelling, earlier studies [9][10][11]18,19 have demonstrated the potential of collocation-based mesh-free methods in handling complex geometries and flow conditions. However, to promote these methods within the CFD community and fulfil their potential, significant research and development on algorithms, and on complementary techniques, for example, point cloud generation and adaptation, collocation/stencil search, implicit time marching, and especially the handling of flow conservation, are still necessary.…”

mentioning

confidence: 99%

Assessment of implicit adaptive mesh‐free CFD modelling

Zhang,

Barakos

2024

Numerical Methods in Fluids

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SummaryThis work presents details and assesses implicit and adaptive mesh‐free CFD modelling approaches, to alleviate laborious mesh generation in modern CFD processes. A weighted‐least‐squares‐based, mesh‐free, discretisation scheme was first derived for the compressible RANS equations, and the implicit dual‐time stepping was adopted for improved stability and convergence. A novel weight balancing concept was introduced to improve the mesh‐free modelling on highly irregular point clouds. Automatic point cloud generations based on strand and level‐set points were also discussed. A novel, polar selection approach, was also introduced to establish high‐quality point collocations. The spatial accuracy and convergence properties were validated using 2D and 3D benchmark cases. The impact of irregular point clouds and various point collocation search methods were evaluated in detail. The proposed weight balancing and the polar selection approaches were found capable of improving the mesh‐free modelling on highly irregular point clouds. The mesh‐free flexibility was then exploited for adaptive modelling. Various adaptation strategies were assessed using simulations of an isentropic vortex, combining different point refinement mechanisms and collocation search methods. The mesh‐free modelling was then successfully applied to transonic aerofoil simulations with automated point generation. A weighted pressure gradient metric prioritising high gradient regions with large point sizes was introduced to drive the adaptation. The mesh‐free adaptation was found to effectively improve the shock resolution. The results highlight the potential of mesh‐free methods in alleviating the meshing bottleneck in modern CFD.

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“…Theoretical error estimations for the FPM have been established in References [37][38][39]. Due to these features, the FPM has been applied to many scientific and engineering problems such as fluid mechanics problems [32,40,41], interface problems [42,43], computational finance [39,44], Josephson junctions [45], two-dimensional nonstationary incompressible Boussinesq equations [46] and inverse heat conduction problems [47,48]. In addition, various improvements of the MLS approximation, such as the improved MLS [49], complex variable MLS [50] and interpolating MLS [51] and the corresponding meshless methods have been developed in recent years [24].…”

Section: Introductionmentioning

confidence: 99%

A meshless finite point method for the improved Boussinesq equation using stabilized moving least squares approximation and Richardson extrapolation

2022

Numerical Methods Partial

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A meshless finite point method (FPM) is developed in this paper for the numerical solution of the nonlinear improved Boussinesq equation. A time discrete technique is used to approximate time derivatives, and then a linearized procedure is presented to deal with the nonlinearity. To achieve stable convergence numerical results in space, the stabilized moving least squares approximation is used to obtain the shape function, and then the FPM is adopted to establish the linear system of discrete algebraic equations. To enhance the accuracy and convergence order in time, the Richardson extrapolation is finally incorporated into the FPM. Numerical results show that the FPM is fourth‐order accuracy in both space and time and can obtain highly accurate results in simulating the propagation of a single solitary wave, the interaction of two solitary waves, the solitary wave break‐up and the solution blow‐up phenomena.

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A-posteriori error estimation for the finite point method with applications to compressible flow

Cited by 8 publications

References 68 publications

Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

Assessment of implicit adaptive mesh‐free CFD modelling

A meshless finite point method for the improved Boussinesq equation using stabilized moving least squares approximation and Richardson extrapolation

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