# On meshfree GFDM solvers for the incompressible Navier–Stokes equations

@article{Suchde2017OnMG, title={On meshfree GFDM solvers for the incompressible Navier–Stokes equations}, author={Pratik Suchde and Joerg Kuhnert and Sudarshan Tiwari}, journal={Computers \& Fluids}, year={2017}, volume={165}, pages={1-12} }

## 28 Citations

### A practical finite difference scheme for the Navier-Stokes equation on curved surfaces in R3

- PhysicsJ. Comput. Phys.
- 2020

### A meshfree generalized finite difference method for surface PDEs

- Computer ScienceComput. Math. Appl.
- 2019

### Weighted Moving Square-Based Solver for Unsteady Incompressible Laminar Flow Simulations

- EngineeringApplied Sciences
- 2022

For computational fluid dynamics simulations, grid systems are generally used in the Eulerian frame for both structured and unstructured grids and solvers designed for the chosen grid systems. In…

### High-order simulations of isothermal flows using the local anisotropic basis function method (LABFM)

- PhysicsJ. Comput. Phys.
- 2022

### A meshfree Lagrangian method for flow on manifolds

- Computer ScienceInternational Journal for Numerical Methods in Fluids
- 2021

A new meshfree Lagrangian framework to model flow on surfaces and a strong form meshfree collocation scheme to solve the Navier–Stokes equations posed on manifolds is introduced.

### Meshfree generalized finite difference methods in soil mechanics—part II: numerical results

- GeologyGEM - International Journal on Geomathematics
- 2017

In geotechnical engineering, simulations are of utmost importance. Due to large deformations, meshfree methods are more suitable than classical meshbased methods. Nevertheless, they have to be…

### A meshfree arbitrary Lagrangian-Eulerian method for the BGK model of the Boltzmann equation with moving boundaries

- PhysicsJ. Comput. Phys.
- 2022

### Point cloud movement for fully Lagrangian meshfree methods

- Computer ScienceJ. Comput. Appl. Math.
- 2018

### Parallel Detection of Subsystems in Linear Systems Arising in the MESHFREE Finite Pointset Method

- MathematicsMeshfree Methods for Partial Differential Equations IX
- 2019

The Finite Pointset Method (FPM) is a meshfree method for simulations in the field of fluid dynamics and continuum mechanics (Tiwari and Kuhnert, Finite pointset method based on the projection method…

### Analysis of high Reynolds free surface flows

- Physics, EngineeringJournal of Mechanics
- 2022

In this paper, we will combine an upwind radial basis function-finite element with direct velocity–pressure formulation to study the two-dimensional Navier-Stokes equations with free surface flows.…

## References

SHOWING 1-10 OF 45 REFERENCES

### A flux conserving meshfree method for conservation laws

- Physics, Environmental Science
- 2017

This paper presents a novel modification of classical meshfree GFDMs to include local balances which produce an approximate conservation of numerical fluxes, which is based on locally defined control cells, rather than a globally defined mesh.

### Kinetic meshless method for compressible flows

- Physics
- 2007

We present a grid‐free or meshless approximation called the kinetic meshless method (KMM), for the numerical solution of hyperbolic conservation laws that can be obtained by taking moments of a…

### A Meshfree Method For Incompressible Fluid Flows with Incorporated Surface Tension

- Physics
- 2002

A meshfree particle method is used to simulate free surface flows. This is a Lagrangian method. Flows are modeled by the incompressible Navier-Stokes equations. The particle projection method is used…

### Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions

- Mathematics
- 2013

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of…

### Accurate projection methods for the incompressible Navier—Stokes equations

- Mathematics
- 2001

Abstract This paper considers the accuracy of projection method approximations to the initial–boundary-value problem for the incompressible Navier–Stokes equations. The issue of how to correctly…

### Finite Pointset Method Based on the Projection Method for Simulations of the Incompressible Navier-Stokes Equations

- Engineering, Physics
- 2003

A Lagrangian particle scheme is applied to the projection method for the incompressible Navier-Stokes equations. The approximation of spatial derivatives is obtained by the weighted least squares…

### An implicit monolithic formulation based on finite element formulation for incompressible Navier–Stokes equations

- Computer Science
- 2015

A second-order stable monolithic formulation developed using the finite element method with stabilization and fractional step method for the simulation of three-dimensional laminar incompressible Navier–Stokes problems written in the primitive variables is presented.

### A Numerical Method for the Incompressible Navier-Stokes Equations Based on an Approximate Projection

- Computer ScienceSIAM J. Sci. Comput.
- 1996

In this method we present a fractional step discretization of the time-dependent incompressible Navier--Stokes equations. The method is based on a projection formulation in which we first solve…

### An Upwind Finite Pointset Method (FPM) for Compressible Euler and Navier-Stokes Equations

- Mathematics
- 2003

A Lagrangian scheme for compressible fluid flows is presented. The method can be viewed as a generalized finite difference upwind scheme. The scheme is based on the classical Euler equations in fluid…

### A Generalized (Meshfree) Finite Difference Discretization for Elliptic Interface Problems

- MathematicsNumerical Methods and Application
- 2002

An extension of the second GFDM method is presented, which allows for accounting for internal interfaces, associated with discontinuous coefficients, and results from numerical experiments illustrate the second order convergence of the proposed GFDM for interface problems.