RBF-FD discretization of the Navier-Stokes equations on scattered but staggered nodes

DOI10.1016/j.jcp.2022.111756OpenAlexW4310068874MaRDI QIDQ2112439

Oliver T. Schmidt, Tianyi Chu

Publication date: 11 January 2023

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.06495

zbMATH Keywords

staggered gridNavier-Stokespolyharmonic splinesfractional-stepRBF-FDpolynomial augmentation

Mathematics Subject Classification ID

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)

Uses Software

• rbf_qr

Cites Work

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• A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere
• Stable calculation of Gaussian-based RBF-FD stencils
• Radial basis functions: developments and applications to planetary scale flows
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method
• Analysis of anisotropy of numerical wave solutions by high accuracy finite difference methods
• Stabilization of RBF-generated finite difference methods for convective PDEs
• On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs
• A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions
• On the role of polynomials in RBF-FD approximations. I: Interpolation and accuracy
• Local radial basis function based gridfree scheme for unsteady incompressible viscous flows
• Application of a fractional-step method to incompressible Navier-Stokes equations
• Compact finite difference schemes with spectral-like resolution
• Spatial direct numerical simulation of boundary-layer transition mechanisms: Validation of \(\mathbf{PSE}\) theory
• Preconditioned multigrid methods for unsteady incompressible flows
• Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier--Stokes equations
• A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow.
• Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations
• Bifurcation analysis of incompressible flow in a driven cavity by the Newton-Picard method
• Observations on the behavior of radial basis function approximations near boundaries
• Shape adaptive RBF-FD implicit scheme for incompressible viscous Navier-Stokes equations
• Radial basis functions methods for boundary value problems: performance comparison
• The overlapped radial basis function-finite difference (RBF-FD) method: a generalization of RBF-FD
• Stable computation of multiquadric interpolants for all values of the shape parameter
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
• Numerical investigation on the stability of singular driven cavity flow
• Transition in a 2-D lid-driven cavity flow
• An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
• Hyperviscosity-based stabilization for radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion equations
• A radial basis function (RBF)-finite difference (FD) method for the backward heat conduction problem
• Two dimensional analysis of hybrid spectral/finite difference schemes for linearized compressible Navier-Stokes equations
• A semi-implicit meshless method for incompressible flows in complex geometries
• Transport schemes in spherical geometries using spline-based RBF-FD with polynomials
• A high-order accurate meshless method for solution of incompressible fluid flow problems
• An insight into RBF-FD approximations augmented with polynomials
• On the role of polynomials in RBF-FD approximations. III: Behavior near domain boundaries
• A weighted meshfree collocation method for incompressible flows using radial basis functions
• Rotational transport on a sphere: local node refinement with radial basis functions
• The parameter \(R^ 2\) in multiquadric interpolation
• RBF-LOI: augmenting radial basis functions (RBFs) with least orthogonal interpolation (LOI) for solving PDEs on surfaces
• Comparison of moving least squares and RBF+poly for interpolation and derivative approximation
• Enhancing finite differences with radial basis functions: experiments on the Navier-Stokes equations
• Transport schemes on a sphere using radial basis functions
• On choosing ``optimal shape parameters for RBF approximation
• Numerical computation of three-dimensional incompressible viscous flows in the primitive variable form by local multiquadric differential quadrature method
• The 2D lid-driven cavity problem revisited
• Scattered node compact finite difference-type formulas generated from radial basis functions
• Stable Computation of Differentiation Matrices and Scattered Node Stencils Based on Gaussian Radial Basis Functions
• Fundamentals of Engineering Numerical Analysis
• Stable Computations with Gaussian Radial Basis Functions
• Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
• Direct numerical simulation of decaying compressible turbulence and shocklet statistics
• A radial basis function method for the shallow water equations on a sphere
• A Stable Algorithm for Flat Radial Basis Functions on a Sphere
• Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder
• Scattered Data Interpolation: Tests of Some Method
• Sound generation in a mixing layer
• Shock leakage through an unsteady vortex-laden mixing layer: application to jet screech
• A point interpolation meshless method based on radial basis functions
• Solving PDEs with radial basis functions

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