arXiv subjects

Pratik Suchde

Publications and source records attributed to Pratik Suchde.

At least 19 recordsLinked to original sources

arXiv2026

Point Cloud Quality for Meshfree Methods

Mesh quality is very well studied and widely used to quantify a good mesh. In contrast, a systematic study of quality of meshfree point clouds is lacking. This gap makes it difficult to substantiate the common claim that generating a good-quality point cloud is easier than generating a good mesh. Various definitions of point cloud quality have been proposed, some of which have theoretical significance for proving convergence and error bounds, while others are used in computational studies. In this work, we compare and contrast existing point cloud quality metrics and introduce a few new ones. We conduct extensive numerical tests with a meshfree collocation method across a wide range of scenarios, including both elliptic and hyperbolic equations, 2D and 3D domains, and variations in parameters of the numerical method. Based on these tests, we assess which quality metrics best correlate with numerical error. Our findings reveal six metrics that consistently serve as reliable indicators of point cloud quality, while also demonstrating that several widely used metrics are poor predictors of accuracy.

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arXiv2026

Meshfree Snow Modelling using a Modified Cam-Clay Approach

Snow is a complex geomaterial whose macroscopic response is governed by density, temperature, and the topology of its evolving microstructure. Its mechanical behavior spans elastic, plastic, viscous, and failure dominated regimes, imposing significant challenges for numerical methods, which intends to simulate large deformations, evolving free surfaces, and complex boundary interactions. This work presents the first integration of a Modified Cam-Clay constitutive formulation for snow into a purely meshfree strong-form collocation framework based on the Generalized Finite Difference Method. The main methodological contribution is a numerical coupling that combines a global implicit mixed formulation for pressure and velocity with a constitutive return-mapping algorithm. The hydrostatic pressure contribution is obtained from a Poisson equation and subsequently corrected through the Modified Cam-Clay return-mapping procedure, while the deviatoric response is treated semi-implicitly using a numerical viscosity formulation. This partitioned treatment of the volumetric and deviatoric stress contributions enables stable simulations with comparatively large time steps while producing smooth spatial pressure fields. As a result, forces on complex boundary geometries can be evaluated accurately. Numerical results of this coupling illustrate the algorithmic stability of the framework, the effective imposition of boundary conditions, and the suitability of local spatial refinement. The feasibility of applying the framework to vehicle-snow interaction through rigid-body coupling is also illustrated. The presented formulation provides a robust basis for future simulations of dynamic snow loading on vehicle structures.

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arXiv2026

Boundary treatment algorithms for meshfree RANS turbulence modeling

In this paper, we propose improved wall-treatment strategies for meshfree methods applied to turbulent flows. The goal is to enhance wall-function handling in simulations of high-Reynolds-number turbulent flows and to understand the performance of turbulence models within these frameworks. While wall-function techniques are well established for mesh-based methods, their implementation in meshfree methods faces unique challenges. The main difficulties arise from scattered point distributions and dynamic point movement in Lagrangian frameworks. To address these issues, we evaluate a baseline closest-neighbor approach alongside two novel techniques: the nearest-band neighbor (NBN) method and the shifted boundary (SB) method. The NBN method enforces wall functions on a band of interior points, helping to maintain uniform point selection. On the other hand, the SB method virtually moves boundary points to a fixed wall-normal distance, eliminating the spatial noise associated with point movement. We evaluate these methods using turbulence closures: Spalart--Allmaras, $k-\varepsilon$, and $k-\omega$ turbulence models. These methods are validated on 1D Couette flow, a turbulent flat plate, and a 3D NACA 0012 airfoil at high Reynolds numbers. Results demonstrate that both novel methods outperform the standard closest-neighbor approach on flat geometries. For flat plates, the SB method provides stability and perfectly smooth $y^+$ distributions. However, when applied to a curved NACA 0012 profile, the NBN method proves to be robust and flexible. In contrast, the SB method exhibits setbacks in numerical diffusion and premature flow separation on curved geometries. This is due to uncorrected normal-vector shifting and adverse pressure gradients. This work establishes the NBN method as a reliable, robust foundation for simulating turbulent flows over practical geometries using meshfree methods.

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arXiv2025

An Overview of Meshfree Collocation Methods

We provide a comprehensive overview of meshfree collocation methods for numerically approximating differential operators on continuously labeled unstructured point clouds. Meshfree collocation methods do not require a computational grid or mesh. Instead, they approximate smooth functions and their derivatives at potentially irregularly distributed collocation points, often called particles, to a desired order of consistency. We review several meshfree collocation methods from the literature, trace the historical development of key concepts, and propose a classification of methods according to their principle of derivation. Although some of the methods reviewed are similar or identical, there are subtle yet important differences between many, which we highlight and discuss. We present a unifying formulation of meshfree collocation methods that renders these differences apparent and show how each method can be derived from this formulation. Finally, we propose a generalized derivation for meshfree collocation methods going forward.

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arXiv2024

An Eulerian Meshless Method for Two-phase Flows with Embedded Geometries

We present a novel Eulerian meshless method for two-phase flows with arbitrary embedded geometries. The spatial derivatives are computed using the meshless generalized finite difference method (GFDM). The sharp phase interface is tracked using a volume fraction function. The volume fraction is advected using a method based on the minimisation of a directional flux-based error. For stability, the advection terms are discretised using upwinding schemes. In the vicinity of the embedded geometries, the signed distance function is used to populate the surface of the geometries to generate a body-conforming point cloud. Consequently, the points on the boundaries participate directly in the discretisation, unlike conventional immersed-boundary methods where they are either used to calculate momentum deficit (for example, continuous forcing) or conservation losses (for example, cut-cell methods). The boundary conditions are, therefore, directly imposed at these points on the embedded geometries, opening up the possibility for a discretisation that is body-conforming and spatially varying in resolution, while retaining the consistency of the scheme. We present benchmark test cases that validate the method for two-phase flows, flows with embedded boundaries and a combination of both.

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arXiv2024

Adaptive coupling of 3D and 2D fluid flow models

Similar to the notion of h-adaptivity, where the discretization resolution is adaptively changed, I propose the notion of model adaptivity, 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.

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arXiv2024

A Lagrangian meshfree model for solidification of liquid thin-films

In this paper, a new method to model solidification of thin liquid films is proposed. \blue{This method is targeted at applications like aircraft icing and tablet coating where the formation of liquid films from impinging droplets on a surface form a critical part of the physics of the process.} The proposed model takes into account the (i) unsteadiness in temperature distribution, (ii) heat transfer at the interface between the solid and the surface, (iii) volumetric expansion/contraction and (iv) the liquid thin-film behaviour, each of which are either partly or fully ignored in existing models. The liquid thin-film, modeled using the Discrete Droplet Method (DDM), is represented as a collection of discrete droplets that are tracked in a Lagrangian sense. The height of the liquid film is estimated as a summation of Gaussian kernel functions associated with each droplet. At each droplet location, a solid height is also computed. The evolution of the solid height is governed by the Stefan problem. The flow of the liquid thin-film is solved just as in the case of DDM, while also taking into consideration the shape of the solidified region lying beneath the droplet. The results presented in this work show the reliability of the proposed model in simulating solidification of thin-films and its applicability to complex problems such as ice-formation on aircraft wings. The model has been verified for canonical problems that have analytical solutions. For the more complex problems of icing, the results of the model are compared with data from literature, without considering a background air flow. The comparison can be improved by coupling this model with suitable air flow solvers, as shown in the final test case.

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arXiv2023

Higher-Order Generalized Finite Differences for Variable Coefficient Diffusion Operators

We present a novel approach of discretizing variable coefficient diffusion operators in the context of meshfree generalized finite difference methods. Our ansatz uses properties of derived operators and combines the discrete Laplace operator with reconstruction functions approximating the diffusion coefficient. Provided that the reconstructions are of a sufficiently high order, we prove that the order of accuracy of the discrete Laplace operator transfers to the derived diffusion operator. We show that the new discrete diffusion operator inherits the diagonal dominance property of the discrete Laplace operator. Finally, we present the possibility of discretizing anisotropic diffusion operators with the help of derived operators. Our numerical results for Poisson's equation and the heat equation show that even low-order reconstructions preserve the order of the underlying discrete Laplace operator for sufficiently smooth diffusion coefficients. In experiments, we demonstrate the applicability of the new discrete diffusion operator to interface problems with point clouds not aligning to the interface and numerically show first-order convergence.

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arXiv2023

Volume and Mass Conservation in Lagrangian Meshfree Methods

Meshfree Lagrangian frameworks for free surface flow simulations do not conserve fluid volume. Meshfree particle methods like SPH are not mimetic, in the sense that discrete mass conservation does not imply discrete volume conservation. On the other hand, meshfree collocation methods typically do not use any notion of mass. As a result, they are neither mass conservative nor volume conservative at the discrete level. In this paper, we give an overview of various sources of conservation errors across different meshfree methods. The present work focuses on one specific issue: unreliable volume and mass definitions. We introduce the concept of representative masses and densities, which are essential for accurate post-processing especially in meshfree collocation methods. Using these, we introduce an artificial compression or expansion in the fluid to rectify errors in volume conservation. Numerical experiments show that the introduced frameworks significantly improve volume conservation behaviour, even for complex industrial test cases such as automotive water crossing.

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arXiv2023

Meshfree One-Fluid Modelling of Liquid-Vapor Phase Transitions

We introduce a meshfree collocation framework to model the phase change from liquid to vapor at or above the boiling point. While typical vaporization or boiling simulations focus on the vaporization from the bulk of the fluid, here we include the possibility of vaporization from the free surface, when a moving fluid comes into contact with a superheated surface. We present a continuum, one-fluid approach in which the liquid and vapor phases are modeled with the same constitutive equations, with different material properties. The novelty here is a monolithic approach without explicit modeling of the interface between the phases, neither in a sharp nor diffuse sense. Furthermore, no interface boundary conditions or source terms are needed between the liquid and vapor phases. Instead, the phase transition is modeled only using material properties varying with temperature. Towards this end, we also present an enrichment of strong form meshfree generalized finite difference methods (GFDM) to accurately capture derivatives in the presence of jumps in density, viscosity, and other physical properties. The numerical results show a good agreement with experimental results, and highlight the ability of our proposed framework to model phase changes with large jumps.

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arXiv2022

Smart cloud collocation: geometry-aware adaptivity directly from CAD

Computer Aided Design (CAD) is widely used in the creation and optimization of various industrial systems and processes. Transforming a CAD geometry into a computational discretization that be used to solve PDEs requires care and a deep knowledge of the selected computational method. In this article, we present a novel integrated collocation scheme based on smart clouds. It allows us to transform a CAD geometry into a complete point collocation model, aware of the base geometry, with minimum effort. For this process, only the geometry of the domain, in the form of a STEP file, and the boundary conditions are needed. We also introduce an adaptive refinement process for the resultant smart cloud using an \textit{a posteriori} error indication. The scheme can be applied to any 2D or 3D geometry, to any PDE and can be applied to most point collocation approaches. We illustrate this with the meshfree Generalized Finite Difference (GFD) method applied to steady linear elasticity problems. We further show that each step of this process, from the initial discretization to the refinement strategy, is connected and is affected by the approach selected in the previous step, thus requiring an integrated scheme where the whole solution process should be considered at once.

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arXiv2022

A Meshfree Point Collocation Method for Elliptic Interface Problems

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.

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arXiv2022

A Discrete Droplet Method for Modelling Thin Film Flows

In this paper, we present a new model to simulate the formation, evolution, and break up of a thin film of fluid flowing over a curved surface. Referred to as the discrete droplet method (DDM), the model captures the evolution of thin fluid films by tracking individual moving fluid droplets. In contrast to existing thin film models that solve a PDE to determine the film height, here, we compute the film height by numerical integration based on the aggregation of droplets. The novelty of this approach in using droplets makes it suitable for simulating the formation of fluid films, and modelling thin film flows on partially wetted surfaces. The DDM is a Lagrangian approach, with a force balance on each droplet governing the motion, and derivatives approximated using a smoothed particle hydrodynamics (SPH) like approach. The proposed model is thoroughly validated by comparing results against analytical solutions, against the results of the shallow-water equations for thin film flow, and also against results from a full 3D resolved Navier Stokes model. We also present the use of the DDM on an industrial test case. The results highlight the effectiveness of the model for simulations of flows with thin films.

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arXiv2020

A Meshfree Generalized Finite Difference Method for Solution Mining Processes

Experimental and field investigations for solution mining processes have improved intensely in recent years. Due to today's computing capacities, three-dimensional simulations of potential salt solution caverns can further enhance the understanding of these processes. They serve as a "virtual prototype" of a projected site and support planning in reasonable time. In this contribution, we present a meshfree Generalized Finite Difference Method (GFDM) based on a cloud of numerical points that is able to simulate solution mining processes on microscopic as well as macroscopic scales, which differ significantly in both the spatial and temporal scale. Focusing on anticipated industrial requirements, Lagrangian and Eulerian formulations including an Arbitrary Lagrangian-Eulerian (ALE) approach are considered.

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arXiv2020

A Meshfree Lagrangian Method for Flow on Manifolds

In this paper, we present a novel meshfree 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 to model 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 a meshfree Generalized Finite Difference Method (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.

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arXiv2019

A Fully Lagrangian Meshfree Framework for PDEs on Evolving Surfaces

We propose a novel framework to solve PDEs on moving manifolds, where the evolving surface is represented by a moving point cloud. This has the advantage of avoiding the need to discretize the bulk volume around the surface, while also avoiding the need to have a global mesh. Distortions in the point cloud as a result of the movement are fixed by local adaptation. We first establish a comprehensive Lagrangian framework for arbitrary movement of curves and surfaces given by point clouds. Collision detection algorithms between point cloud surfaces are introduced, which also allow the handling of evolving manifolds with topological changes. We then couple this Lagrangian framework with a meshfree Generalized Finite Difference Method (GFDM) to approximate surface differential operators, which together give a method to solve PDEs on evolving manifolds. The applicability of this method is illustrated with a range of numerical examples, which include advection-diffusion equations with large deformations of the surface, curvature dependent geometric motion, and wave equations on evolving surfaces.

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arXiv2018

A Meshfree Generalized Finite Difference Method for Surface PDEs

In this paper, we propose a novel meshfree Generalized Finite Difference Method (GFDM) approach to discretize PDEs defined on manifolds. Derivative approximations for the same are done directly on the tangent space, in a manner that mimics the procedure followed in volume-based meshfree GFDMs. As a result, the proposed method not only does not require a mesh, it also does not require an explicit reconstruction of the manifold. In contrast to existing methods, it avoids the complexities of dealing with a manifold metric, while also avoiding the need to solve a PDE in the embedding space. A major advantage of this method is that all developments in usual volume-based numerical methods can be directly ported over to surfaces using this framework. We propose discretizations of the surface gradient operator, the surface Laplacian and surface Diffusion operators. Possibilities to deal with anisotropic and discontinous surface properties (with large jumps) are also introduced, and a few practical applications are presented.

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arXiv2017

Point Cloud Movement For Fully Lagrangian Meshfree Methods

In Lagrangian meshfree methods, the underlying spatial discretization, referred to as a point cloud or a particle cloud, moves with the flow velocity. In this paper, we consider different numerical methods of performing this movement of points or particles. The movement is most commonly done by a first order method, which assumes the velocity to be constant within a time step. We show that this method is very inaccurate and that it introduces volume and mass conservation errors. We further propose new methods for the same which prescribe an additional ODE system that describes the characteristic velocity. Movement is then performed along this characteristic velocity. The first new way of moving points is an extension of mesh-based streamline tracing ideas to meshfree methods. In the second way, the movement is done based on the difference in approximated streamlines between two time levels, which approximates the pathlines in unsteady flow. Numerical comparisons show these method to be vastly superior to the conventionally used first order method.

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