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AbstractFree vibration and bending behavior of laminated plates are investigated using a combination of Reissner’s mixed variational theorem and the meshless radial point interpolation method. By introducing Reissner’s mixed variational theorem, a refined transverse shear stress field is derived based on three-dimensional (3D) elasticity equations. The efficiency and accuracy of this model are demonstrated through numerical examples. It is found that accurate prediction of shear stresses significantly improves the prediction of natural frequency for composite laminated plates. The difference between shear stresses derived from 3D equilibrium equations and that from constitutive equations is significant. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a Meshfree Variational-Physics-Informed Neural Network. It is a Variational-Physics-Informed Neural Network that does not require the generation of the triangulation of the entire domain and that can be trained with an adaptive set of test functions. In order to generate the test space, we exploit an a posteriori error indicator and add test functions only where the error is higher. Four training strategies are proposed and compared. Numerical results show that the accuracy is higher than the one of a Variational-Physics-Informed Neural Network trained with the same number of test functions but defined on a quasi-uniform mesh. [ABSTRACT FROM AUTHOR]

Geophysical electromagnetic survey methods are particularly effective in locating conductive mineral deposits or mineralization zones in a mineral resource exploration. The forward modelling of the electromagnetic responses over such targets is a fundamental task in quantitatively interpreting the geophysical data into a geological model. Due to the ubiquitous irregular and complex geometries associated with the mineral rock units, it is critical that the numerical modelling approach being used is able to adequately and efficiently incorporate any necessary geometries of the Earth model. To circumvent the difficulties in representing complex but necessary geometry features in an Earth model for the existing mesh-based numerical modelling approaches (e.g., finite element and finite difference methods), I present a meshfree modelling approach that does not require a mesh to solve the Maxwell's equations. The meshfree approach utilizes a set of unconnected points to represent any geometries in the Earth model, allowing for the maximal flexibility to account for irregular surface geometries and topography. In each meshfree subdomain, radial basis functions are used to construct meshfree function approximation in transforming the differential equations in the modelling problem into linear systems of equations. The method solves the potential function equations of the Maxwell's equations in the modelling. The modelling accuracy using the meshfree method is examined and verified using one magnetotelluric model and two frequency-domain controlled-source models. The magnetotelluric model is the well-known Dublin Test Model 2 in which the spherical geometry of the conductor in the shallow subsurface may pose as a challenge for many numerical modelling methods. The first controlled-source model is a simple half-space model with the electric dipole source for which analytical solutions exist for the modelling responses. The second controlled-source model is the volcanic massive sulphide mineral deposit from Voisey's Bay, Labrador, Canada in which the deposit's surface is highly irregular. For all modellings, the calculated electromagnetic responses are found to agree with other independent numerical solutions and the analytical solutions. The advantages of the meshfree method in discretizing the Earth models with complex geometries in the forward modelling of geophysical electromagnetic data is clearly demonstrated. [ABSTRACT FROM AUTHOR]

Particle tracking is a common post processing method in groundwater hydrology. In this paper we describe Ichnos, a particle tracking code able to work with flow simulations obtained from either finite difference, finite element, adaptive mesh, or mesh free methods. Ichnos can trace virtual particles (streamlines) in flow fields of any fluid dynamics context, but its application is here focused on groundwater-based flow fields. The code is written in C++ and the structure of the code allows for it to be easily extended. In this study we describe the main features of the code and present several illustrations.

Subsampling of node sets is useful in contexts such as multilevel methods, computer graphics, and machine learning. On uniform grid-based node sets, the process of subsampling is simple. However, on node sets with high density variation, the process of coarsening a node set through node elimination is more interesting. A novel method for the subsampling of variable density node sets is presented here. Additionally, two novel node set quality measures are presented to determine the ability of a subsampling method to preserve the quality of an initial node set. The new subsampling method is demonstrated on the test problems of solving the Poisson and Laplace equations by multilevel radial basis function-generated finite differences (RBF-FD) iterations. High-order solutions with robust convergence are achieved in linear time with respect to node set size. [ABSTRACT FROM AUTHOR]

Summary: We investigate the transmission of aerosol particles in an airplane cabin with a joint approach using experiments and simulation. Experiments were conducted in a realistic aircraft cabin with heated dummies acting as passengers. A Sheffield head with an aerosol generator was used to emulate an infected passenger and particle numbers were measured at different locations throughout the cabin to quantify the exposure of other passengers. The same setting was simulated with a computational fluid dynamics model consisting of a Lagrange continuous phase for capturing the air flow, coupled with a Lagrange suspended discrete phase to represent the aerosols. Virtual measurements were derived from the simulation and compared with the experiments. Our main results are: the experimental setup provides good measurements well suited for model validation, the simulation does correctly reproduce the fundamental mechanisms of aerosol dispersion and simulations can help to improve the understanding of aerosol transmission for example by visualizing particle distributions. Furthermore, with findings from the simulation it was possible to crucially improve the experimental setup, proving that feedback between the numerical and the hardware world is indeed beneficial. [ABSTRACT FROM AUTHOR]

The concept of oscillator problems finds its indispensable presence in numerous dynamical systems. Machine learning techniques for handling dynamical systems is a challenging and rapidly expanding field of research. In this regard, a machine learning approach, namely Symplectic Artificial Neural Network model, has been used for handling the non-linear systems arising in dusty plasma models. The primary objective of this article is to investigate, the dynamics of Van der Pol-Mathieu-Duffing Oscillator problems for different excitation functions using the meshfree Symplectic Artificial Neural Network algorithm. The numerical simulations and graphical representations are carried out to establish the accuracy of the presented algorithm. Also, the obtained simulation results are compared with the existing numerical solutions. In addition, the statistical assessment studies at various testing points confirm an excellent agreement between the present simulation results and the existing results. [ABSTRACT FROM AUTHOR]

Summary: This 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. [ABSTRACT FROM AUTHOR]

The semi-Lagrangian Reproducing Kernel (SL RK) has been successfully applied to simulations of extreme deformation problems thanks to intensive advancements in meshfree methods in recent decades. The SL RK shape function is constructed centered at a material point with a fixed spatial radius, and therefore it is a time-dependent function. When the SL RK is introduced in the weak form of the equation of motion, the time derivatives of SL RK lead to convective terms in the semi-discrete equation, significantly reducing the computational efficiency and accuracy. This paper presents a novel approximation scheme in which displacement, velocity, and acceleration are approximated by the same SL RK at a time instant. Consequently, the proposed concurrent SL RK formulation avoids the need to compute the convective terms, offering an effective numerical solution for high-strain rate dynamic problems. Furthermore, an eigenvalue analysis is performed on the semi-discrete equation of motion to investigate the temporal stability of the concurrent SL RK formulation. A comprehensive study of the eigenvalue and critical time step is conducted to identify the effective parameters for the stability of the system. Several manufactured dynamic problems are studied to validate the analytical estimate. The estimated analytical eigenvalue and the critical time step are consistent with the numerical result. [ABSTRACT FROM AUTHOR]

In the present paper, the effect of aspect ratio on the initial buckling response of an elastically supported rectangular FGM plate, the thin plate spline radial basis function (RBF) method can be used. This method involves the use of a thin plate spline to interpolate the displacement field of the plate, allowing for accurate analysis of the plate's behavior. The higher-order shear deformation theory (HSDT) is used for the analysis of the FGM rectangular plate resting on two parameters of elastic foundation. The displacement field consists of five unknown variables and approximately parabolic distribution of the transverse stress profile through the plate thickness and tangential stress-free boundary conditions on the plate surface. The governing differential equations (GDEs) of the plate are developed in the framework of Hamilton's principle. The thin plate spline radial basic function-based Meshfree method is used for discretizing the GDEs. To demonstrate the accuracy and efficacy of the present approach, the results obtained by the present approach are compared with the results given in the literature. The effect of various aspect ratios, grading index, span-to-thickness ratio, and two parameters of elastic foundations on the normalized buckling load is proposed. Some new results are also presented, which may be beneficial for future research works. The novelty of the present is the effects of aspect ratio on the elastically supported FGM plates. [ABSTRACT FROM AUTHOR]

Geophysical electromagnetic survey methods are particularly effective in locating conductive mineral deposits or mineralization zones in a mineral resource exploration. The forward modelling of the electromagnetic responses over such targets is a fundamental task in quantitatively interpreting the geophysical data into a geological model. Due to the ubiquitous irregular and complex geometries associated with the mineral rock units, it is critical that the numerical modelling approach being used is able to adequately and efficiently incorporate any necessary geometries of the Earth model. To circumvent the difficulties in representing complex but necessary geometry features in an Earth model for the existing mesh-based numerical modelling approaches (e.g., finite element and finite difference methods), I present a meshfree modelling approach that does not require a mesh to solve the Maxwell’s equations. The meshfree approach utilizes a set of unconnected points to represent any geometries in the Earth model, allowing for the maximal flexibility to account for irregular surface geometries and topography. In each meshfree subdomain, radial basis functions are used to construct meshfree function approximation in transforming the differential equations in the modelling problem into linear systems of equations. The method solves the potential function equations of the Maxwell’s equations in the modelling. The modelling accuracy using the meshfree method is examined and verified using one magnetotelluric model and two frequency-domain controlled-source models. The magnetotelluric model is the well-known Dublin Test Model 2 in which the spherical geometry of the conductor in the shallow subsurface may pose as a challenge for many numerical modelling methods. The first controlled-source model is a simple half-space model with the electric dipole source for which analytical solutions exist for the modelling responses. The second controlled-source model is the volcanic massive sulphide mineral deposit from Voisey’s Bay, Labrador, Canada in which the deposit’s surface is highly irregular. For all modellings, the calculated electromagnetic responses are found to agree with other independent numerical solutions and the analytical solutions. The advantages of the meshfree method in discretizing the Earth models with complex geometries in the forward modelling of geophysical electromagnetic data is clearly demonstrated.

In this paper, we introduce a Meshfree Variational-Physics-Informed Neural Network. It is a Variational-Physics-Informed Neural Network that does not require the generation of the triangulation of the entire domain and that can be trained with an adaptive set of test functions. In order to generate the test space, we exploit an a posteriori error indicator and add test functions only where the error is higher. Four training strategies are proposed and compared. Numerical results show that the accuracy is higher than the one of a Variational-Physics-Informed Neural Network trained with the same number of test functions but defined on a quasi-uniform mesh.

Present work explores quadratic extrapolation (QE) technique for large deformation flexure study of FGM plate with five variables higher-order shear deformation theory (HSDT). Rule of mixtures is utilized in achieving effective material properties across the thickness. Governing differential equations (GDEs) and boundary conditions have been acquired using the principle of virtual work. Quadratic extrapolation (QE) and Newton-Raphson (NR) linearization techniques are considered and compared with respect to computational time. Von-Karman type nonlinearity is used in the present work. Multiquadric radial basis function (RBF) based meshfree technique discretizes GDEs in displacement form. FGM plates with different boundary conditions are investigated under different patch loadings. Present results are validated with some previously published results after a convergence study. Some new results are produced for the flexural response of the FGM plate under patch loads. Effect of types of loads, grading index, patch load location, and boundary conditions are presented. [ABSTRACT FROM AUTHOR]

We present the meshfree mixed collocation method (MCM) for cardiac electrophysiology simulation. Capitalizing on the meshfree property of MCM, we introduce an immersed grid approach for automated generation of meshfree node grids from medical image data. This approach allows us to avoid the time-consuming mesh generation and processing that mesh-based methods like the finite element method (FEM) require. We employ the MCM to solve the cardiac monodomain model considering electrical propagation in 2D tissue sheets, 3D tissue slabs, and a realistic biventricular anatomy. We demonstrate that the solutions obtained by the MCM are in good agreement with the FEM, particularly when immersed grid is used. These findings confirm the suitability of the MCM for cardiac electrophysiology simulation and make the MCM a promising alternative to the FEM for cardiac electrical investigations. [ABSTRACT FROM AUTHOR]

Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD) have been shown to be effective for this task as they can give high orders of accuracy at low computational cost, and they can be applied to surfaces defined only by point clouds. However, there have yet to be any studies that perform a direct comparison of these methods for approximating surface differential operators (SDOs). The first purpose of this work is to fill that gap. For this comparison, we focus on an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly) since they are most closely related to the GMLS method. Additionally, we use a relatively new technique for approximating SDOs with RBF-FD called the tangent plane method since it is simpler than previous techniques and natural to use with PHS+Poly RBF-FD. The second purpose of this work is to relate the tangent plane formulation of SDOs to the local coordinate formulation used in GMLS and to show that they are equivalent when the tangent space to the surface is known exactly. The final purpose is to use ideas from the GMLS SDO formulation to derive a new RBF-FD method for approximating the tangent space for a point cloud surface when it is unknown. For the numerical comparisons of the methods, we examine their convergence rates for approximating the surface gradient, divergence, and Laplacian as the point clouds are refined for various parameter choices. We also compare their efficiency in terms of accuracy per computational cost, both when including and excluding setup costs. • Show the equivalence of the surface differential operators formulation used in MLS methods and a new one based only on the tangent plane. • Develop a new RBF-FD method for approximating the tangent space of surfaces defined only by point clouds. • Perform the first comparison of GMLS and RBF-FD for approximating derivatives on surfaces defined by point clouds. [ABSTRACT FROM AUTHOR]

In this paper, the radial basis collocation method (RBCM) for the free vibration response of elastically supported porous bi-directional functionally graded (BDPFG) plate is investigated in a framework of higher-order shear deformation theory (HSDT). The material properties of BDPFG plates are assumed to be varying continuously in the length and thickness direction. The material properties are evaluated based on Voigt's micro-mechanical model considering power law distribution method with arbitrary power index. Governing differential equations (GDEs) of the porous BFGM plate area achieved utilising Hamilton's principle and multiquadric radial basis function (MQRBF) is used for discretizing the GDEs. To incorporate porosity in the BDPFG plate, five types of porosity distribution models are carried out and analysed. The present results are validated with the available published results in the literature to certify the efficacy and accuracy. The influence of grading index in the length and thickness direction, porosity distribution, porosity index, span to thickness ratio, and elastic foundation over natural frequency of bi-directional BDPFG plate is investigated which is the main contribution. [ABSTRACT FROM AUTHOR]

We develop a new meshfree geometric multilevel (MGM) method for solving linear systems that arise from discretizing elliptic PDEs on surfaces represented by point clouds. The method uses a Poisson disk sampling-type technique for coarsening the point clouds and new meshfree restriction/interpolation operators based on polyharmonic splines for transferring information between the coarsened point clouds. These are then combined with standard smoothing and operator coarsening methods in a V-cycle iteration. MGM is applicable to discretizations of elliptic PDEs based on various localized meshfree methods, including RBF finite differences (RBF-FD) and generalized finite differences (GFD). We test MGM both as a standalone solver and preconditioner for Krylov subspace methods on several test problems using RBF-FD and GFD and numerically analyze convergence rates, efficiency, and scaling with increasing point cloud sizes. We also perform a side-by-side comparison to algebraic multigrid methods for solving the same systems. Finally, we further demonstrate the effectiveness of MGM by applying it to three challenging applications on complicated surfaces: pattern formation, surface harmonics, and geodesic distance. [ABSTRACT FROM AUTHOR]

Traditionally, Biot's formulation is employed to model the behavior of saturated soils. The u - p w (solid displacement–pore water pressure) formulation can be considered as the standard one, since involves a good computational performance together with excellent accuracy for slow and moderate speed phenomena. Dynamic processes can be studied even if the acceleration of the water is neglected, what occurs in the undrained limit. It is well-known that u - p w formulation might display instabilities in the undrained-incompressible limit. Several techniques have been proposed to overcome this issue, principally within an implicit time integration scheme for small strains. In this paper, a robust implementation of the divergence of the momentum equation technique is presented for an explicit u - p w approach within the framework of optimal transportation meshfree scheme at finite strain. Several examples are provided in order to assess the good performance of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, new tangent shape function-based higher-order transverse shear deformation theory (NTHSDT) is proposed to compute the buckling behavior of the elastically supported functionally graded material (FGM) sandwich plates under porous medium. The proposed theory is found to be variationally consistent and fulfills the zero traction boundary conditions on the bottom and top layer without a shear correction factor. The material properties are presumed to be graded in the thickness direction as characterized by a modified power law distribution in terms of volume fraction of constituents. The governing equations are derived using Hamilton's Principle. A strong form of solution discretizes the governing equations by employing a thin plate spline radial basis function-based collocation (TSRBFC) method. The proposed theory is efficient, reliable, and is in close agreement with the results in the literature. Comparison studies show that the NTHSDT is more accurate than other plate theories and is simple in analyzing buckling behavior. A parametric study is done to examine the effects of grading index, porosity index, sandwich schemes, aspect ratio, side-to-length thickness ratio and foundation stiffness. [ABSTRACT FROM AUTHOR]

• Meshfree hybrid discretization of the diffusion operator with discontinuous coefficients. • Formulation of a conservative scheme to enforce Neumann boundary conditions. • Comparison of the introduced methods with respect to convergence and performance depending on jump magnitude. We present a meshfree generalized finite difference method for solving Poisson's equation with a diffusion coefficient that contains jump discontinuities up to several orders of magnitude. To discretize the diffusion operator, we formulate a strong form method that uses a smearing of the discontinuity; and a conservative formulation based on locally computed Voronoi cells. Additionally, we propose a novel conservative formulation for enforcing Neumann boundary conditions that is compatible with the conservative formulation of the diffusion operator. Finally, we introduce a way to switch from the strong form to the conservative formulation to obtain a locally conservative and positivity preserving scheme. The presented numerical methods are benchmarked against four test cases of varying complexity and jump magnitude on point clouds with nodes that are not aligned to the discontinuity. Our results show that the new hybrid method that switches between the two formulations produces better results than the classical generalized finite difference approach for high jumps in diffusivity. [ABSTRACT FROM AUTHOR]

In many applications, domains of interest are geometrically complex containing numerous small features. These features are typically removed in a manual process to facilitate a conventional element-based meshing process. This manual defeaturing process is dependent upon the goals of the simulation and typically involves subjective heuristics. To provide a flexible and easily adaptable discretization process of the governing equations that is independent of the domain discretization, an element-free Galerkin method is proposed in which a fine-scale triangulation is used to first discretize the fully featured domain, but then a coarse-scale element-free discretization is used to approximate the solution of the governing equations. The fine-scale triangulation can be of poor quality and extremely refined since it is not used directly to approximate the solution of the governing equations. The coarse-scale element-free basis has local support and can be adapted through refinement or coarsening without the need to alter the fine-scale triangulation or other geometric considerations. The element-free basis functions are constructed using a conventional moving-least-squares procedure, but the initial weight functions are constructed using manifold geodesics for general applicability to non-convex domains. The weak form of the governing equations is integrated using a secondary coarse-scale element-free basis and a gradient projection technique. The projected-gradient methodology ensures the necessary consistency properties to pass the patch test and obtain optimal rates of convergence. The overall method is termed quasi-meshfree since both meshfree and mesh-based concepts are used. Several verification problems and nonlinear application examples are presented to demonstrate the overall method. [Display omitted] • A quasi-meshfree method is proposed for nonlinear solid mechanics. • A fine-scale triangulation is used to discretize the fully featured domain. • A coarse element-free discretization is used to approximate the PDE. • Basis functions are constructed using conventional moving least squares. • Several verification problems and nonlinear examples are presented. [ABSTRACT FROM AUTHOR]

We present the meshfree mixed collocation method (MCM) for cardiac electrophysiology simulation. Capitalizing on the meshfree property of MCM, we introduce an immersed grid approach for automated generation of meshfree node grids from medical image data. This approach allows us to avoid the time-consuming mesh generation and processing that mesh-based methods like the finite element method (FEM) require. We employ the MCM to solve the cardiac monodomain model considering electrical propagation in 2D tissue sheets, 3D tissue slabs, and a realistic biventricular anatomy. We demonstrate that the solutions obtained by the MCM are in good agreement with the FEM, particularly when immersed grid is used. These findings confirm the suitability of the MCM for cardiac electrophysiology simulation and make the MCM a promising alternative to the FEM for cardiac electrical investigations.

Surface reconstruction from a set of scattered points, or a point cloud, has many applications ranging from computer graphics to remote sensing. We present a new method for this task that produces an implicit surface (zero-level set) approximation for an oriented point cloud using only information about (approximate) normals to the surface. The technique exploits the fundamental result from vector calculus that the normals to an implicit surface are curl-free. By using curl-free radial basis function (RBF) interpolation of the normals, we can extract a potential for the vector field whose zero-level surface approximates the point cloud. We use curl-free RBFs based on polyharmonic splines for this task, since they are free of any shape or support parameters. To make this technique efficient and able to better represent local sharp features, we combine it with a partition of unity method. The result is the curl-free partition of unity (CFPU) method. We show how CFPU can be adapted to enforce exact interpolation of a point cloud and can be regularized to handle noise in both the normals and the point positions. Numerical results are presented that demonstrate how the method converges for a known surface as the sampling density increases, how regularization handles noisy data, and how the method performs on various problems found in the literature. [ABSTRACT FROM AUTHOR]

The present paper deals with the free vibration response of elastically supported porous bidirectional functionally graded soft-core sandwich rectangular plate with proposed new tangent shape function-based higher-order transverse shear deformation theory. The theory is accomplished to uphold the continuity of transverse shear stresses and zero shear stress conditions on both the extreme surfaces of a plate. The bidirectional gradation varies through the thickness (z -axis) and length (x -axis) directions. The effective material properties are calculated via the modified power-law. The governing differential equations (GDEs) of motion are acquired via the Hamilton principle. The inverse multi-quadric radial basis function-based Collocation method is implemented to discretize the GDEs obtained by strong form formulation. The current theory and method's accuracy and efficacy are validated by comparing the present results with existing results in the literature. Studies show that the results of the proposed theory are in close agreement with 3D approach. Numerical results are obtained with a different scheme of sandwich layers for free vibration analysis. Effects of grading index, porosity fraction, two parameters foundation, different scheme, and the span to thickness ratio on free vibration response have been discussed. New results for free vibration response in porous media are presented with different skin materials. [ABSTRACT FROM AUTHOR]

This paper proposes the notion of model adaptivity for fluid flow modelling, where the underlying model (the governing equations) is adaptively changed in space and time. Specifically, this work introduces a hybrid and adaptive coupling of a 3D bulk fluid flow model with a 2D thin film flow model. As a result, this work extends the applicability of existing thin film flow models to complex scenarios where, for example, bulk flow develops into thin films after striking a surface. At each location in space and time, the proposed framework automatically decides whether a 3D model or a 2D model must be applied. Using a meshless approach for both 3D and 2D models, at each particle, the decision to apply a 2D or 3D model is based on the user-prescribed resolution and a local principal component analysis. When a particle needs to be changed from a 3D model to 2D, or vice versa, the discretization is changed, and all relevant data mapping is done on-the-fly. Appropriate two-way coupling conditions and mass conservation considerations between the 3D and 2D models are also developed. Numerical results show that this model adaptive framework shows higher flexibility and compares well against finely resolved 3D simulations. In an actual application scenario, a 3 factor speed up is obtained, while maintaining the accuracy of the solution. • Novel notion of model adaptivity: governing equations are adaptively changed. • Coupling 3D Navier–Stokes and 2D thin film flow. • No a-priori information describing where to use which model. • Model and discretization changed on-the-fly. [ABSTRACT FROM AUTHOR]

At present, there are various image registration algorithms under active development for digital image correlation techniques. These techniques include the meshfree-based (MFree-based) digital image correlation. However, there exists very little study in advancing the method for better computational efficiency in engineering measurement applications. Also, a comparative investigation against the more well-known finite element-based digital image correlation is absent. This paper presents the development of an efficient two-dimensional (2D) MFree-based digital image correlation technique to obtain the strain and displacement of a planar object. In the present method, the speckle pattern in the form of circular adhesive markers is first detected and tracked by employing the Circular-Hough-Transform and Kanade-Lucas-Tomasi algorithms. The element-free Galerkin approach that specifically employs the moving least-square approximation has been adopted as the meshfree method for the strain and displacement determination. A series of tensile tests on pure epoxy samples has then been carried out to verify the applicability of the proposed 2D MFree-based digital image correlation technique, from which a good agreement of the strain and displacement description is found when compared with that obtained by the conventional strain gauge method. Furthermore, the full-field deformations computed from the ABAQUS model have been well captured by the proposed technique. This concludes that the proposed 2D MFree-based digital image correlation technique is greatly applicable and is recommended for use in determining the planar material engineering properties. [ABSTRACT FROM AUTHOR]

• A meshfree method based on a non-boundary-fitted discretization is proposed. • The proposed method is efficient for simulation of complex geometries. • The micro-CT scan images of the cellular materials can be directly employed. • The solution is approximated by library Exponential Basis Functions (EBFs). • The approximation is enriched by the modified singular functions. A meshfree method on fixed grids is devised for simulation of Poisson's equation on 3D image-based cellular materials. The non-boundary fitted discretization of such jagged voxel models of complex geometries is accomplished through embedding the micro-CT scan image in a Cartesian grid of nodes. The computational nodes inside the solid voxels are found by a simple point-in-membership test. Using a set of modified singular functions around the voids, along with the library-rational-exponential basis functions (EBFs) satisfying the governing differential equation, an enriched spatial solution is locally constructed on a generic computational cloud/cell (GCC) of nodes containing the voids. Within each GCC, the boundary conditions are satisfied through a weighted least-squares approximation. Finally, by establishing point-wise compatibility between the solutions of the GCCs a well-conditioned small linear system of equations is resulted. The results are compared with those of the finite element method (FEM) using extremely fine meshes with an excessive number of nodes. [ABSTRACT FROM AUTHOR]

In this two-part paper, a stable and efficient nodally-integrated reproducing kernel particle method (RKPM) is introduced for solving the governing equations of generalized thermomechanical theories. Part I investigates quadrature in the weak form using coupled and uncoupled classical thermoelasticity as model problems. It is first shown that nodal integration of these equations results in spurious oscillations in the solution many orders of magnitude greater than pure elasticity. A naturally stabilized nodal integration is then proposed for the coupled equations. The variational consistency conditions for nth order exactness and convergence in the two-field problem are then derived, and a uniform correction on the test function approximations is proposed to achieve these conditions. Several benchmark problems are solved to demonstrate the effectiveness of the proposed method. In the sequel, these methods are developed for generalized thermoelasticity and generalized finite-strain thermoplasticity theories of the hyperbolic type that are amenable to efficient explicit time integration. [ABSTRACT FROM AUTHOR]

In the present work, new inverse hyperbolic higher-order shear deformation theory (IHHSDT) is proposed and implemented for buckling analysis and free vibration analysis of porous Functionally Graded Material (FGM) plate on the foundation. The proposed theory follows the approximately parabolic distribution of the transverse stresses through the plate thickness and satisfies the conditions of continuity and differentiability. Three different types of porosity distribution considered. Governing differential equations (GDEs) of the plate is developed in the framework of proposed theories by Hamilton’s principle. Multiquadrics radial basis function (MQ-RBF) based Meshfree method used for discretizing the GDEs. The result obtained by the present theory is validated with the three-dimensional elastic theory and other available solutions in the literature to ensure the efficacy and accuracy of the proposed theory. Numerical results obtained for buckling and free vibration for porous FGM plate resting on the foundation. Effect of grading index, porosity fraction, porosity distribution, the effect of foundation, and the span to thickness ratio have discussed. The secured results can consider as a benchmark for future studies.

• A simplified mathematical model to describe combustion inside micro-rotary engines is proposed. • A numerical model based on high-order meshfree RBF-FD discretizations is developed. • Several benchmarks demonstrate the accuracy and effectiveness of our approach. • It aims to be instrumental in providing the needed understanding to produce more reliable micro-combustion systems. New micro-devices, such as unmanned aerial vehicles or micro-robots, have increased the demand of a new generation of small-scale combustion power system that go beyond the energy-density limitations of batteries or fuel cells. The characteristics short residence times and intense heat losses reduce the efficiency of combustion-based devices, a key factor that requires of an acute modelling effort to understand the competing physicochemical phenomena that hamper their efficient operation. With this objective in mind, this paper is devoted to the development of a high-order meshfree method to model combustion inside complex geometries using radial basis functions-generated finite differences (RBF-FD) based on polyharmonic splines (PHS) augmented with multivariate polynomials (PHS+poly). In our model, the combustion chamber of a micro-rotary engine is simulated by a system of unsteady reaction-diffusion equations coupled with a steady flow passing a bidimensional stenotic channel of great slenderness. The conversion efficiency is characterized by identifying the different combustion regimes that emerged as a function of the ignition point. We show that PHS+poly based RBF-FD is able to achieve high-order algebraic convergence on scattered node distributions, enabling for node refinement in key regions of the fluid domain. This feature makes it specially well adapted to integrate problems in irregular geometries with front-like solutions, such as reactive fronts or shock waves. Several numerical tests are carried out to demonstrate the accuracy and effectiveness of our approach. [ABSTRACT FROM AUTHOR]

This paper presents a meshfree collocation method that uses deep learning to determine the basis functions as well as their corresponding weights. This method is shown to be able to approximate elliptic, parabolic, and hyperbolic partial differential equations for both forced and unforced systems, as well as linear and nonlinear partial differential equations. By training a homogeneous network and particular network separately, new forcing functions are able to be approximated quickly without the burden of retraining the full network. The network is demonstrated on several numerical examples including a nonlinear elasticity problem. In addition to providing meshfree approximations to strong form partial differential equations directly, this technique could also provide a foundation for deep learning methods to be used as preconditioners to traditional methods, where the deep learning method will get close to a solution and traditional solvers can finish the solution. [ABSTRACT FROM AUTHOR]

In this article,we present a novelmeshfree framework for fluid flow simulations on arbitrarily curved surfaces. First, we introduce a new meshfree Lagrangian framework to model flow on surfaces. Meshfree points or particles, which are used to discretize the domain, move in a Lagrangian sense along the given surface. This is done without discretizing the bulk around the surface, without parametrizing the surface, and without a background mesh. A key novelty that is introduced is the handling of flow with evolving free boundaries on a curved surface. The use of this framework tomodel flow on moving and deforming surfaces is also introduced. Then, we present the application of this framework to solve fluid flow problems defined on surfaces numerically. In combination with ameshfree generalized finite differencemethod (GFDM), we introduce a strong form meshfree collocation scheme to solve the Navier--Stokes equations posed on manifolds. Benchmark examples are proposed to validate the Lagrangian framework and the surface Navier--Stokes equations with the presence of free boundaries. [ABSTRACT FROM AUTHOR]

A spectrally accurate and very efficient algorithm suitable for prediction of pressure losses in heated grooved channels has been developed. Heating and topography patterns are used to create spatial flow modulations resulting in a pattern interaction problem. Search for combinations of patterns resulting in the reduction of pressure losses requires development of a very accurate and efficient algorithm. The proposed algorithm uses a combination of the Fourier expansions in the horizontal directions and the Chebyshev expansions in the vertical direction to provide a very good resolution of the near wall regions. The immersed boundary conditions (IBC) method is used to enforce flow boundary conditions at the geometrically irregular boundaries. The resulting gridless discretization can be easily adapted to handle a wide range of topography patterns. Various tests demonstrate that the algorithm delivers spectral accuracy and can provide machine level accuracy. Comparisons with the standard open‐source codes based either on the finite volume or on the spectral element discretization demonstrate several orders of magnitude better efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this work, a meshfree Lattice Boltzmann Flux Solver (LBFS) is proposed to resolve compressible flow problems based on scattered points without mesh connections. The new method employs the Least Square‐based Finite Difference (LSFD) scheme to discretize the governing equations. In order to simulate discontinuous problems such as shock wave, the mid‐point between two adjacent nodes is regarded as a discontinuous interface over which the Riemann problem is established. The local fluxes at this interface point are reconstructed by LBFS using the local solution of the Lattice Boltzmann Equation (LBE) as well as its correlations to macroscopic variables and moment relations. The LBFS is constructed based on the non‐free parameter D1Q4 model: the normal component of the particle velocity on the interface is retained, while the tangential component is reconstructed by the macroscopic variables on both sides of the interface. The meshfree LBFS expects some intriguing merits. On one hand, it inherits the physical robustness of the LBFS: the local fluxes are reconstructed from the physical solutions instead of mathematical interpolations. On the other hand, it allows the implementation at arbitrarily distributed nodes, which credits to the flexibility of the method. Representative examples of compressible flows, including Sod shock tube, Osher‐Shu shock tube, flow around NACA0012 airfoil, flow around staggered NACA0012 biplane configuration and shock reflection problem, are simulated by the proposed method for comprehensive evaluation of the meshfree LBFS. [ABSTRACT FROM AUTHOR]