The radial basis function finite collocation approach for capturing sharp fronts in time dependent advection problems

DOI10.1016/j.jcp.2015.05.032zbMath1349.65526OpenAlexW353213632MaRDI QIDQ2374630

Yanyan Li

Publication date: 5 December 2016

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2015.05.032

zbMATH Keywords

radial basis functionsadvectionRichardson extrapolationshock capturingmeshlessfinite collocationRBF local

Mathematics Subject Classification ID

Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (11)

A localized RBF-MLPG method for numerical study of heat and mass transfer equations in elliptic fins ⋮ The Local Singular Boundary Method for Solution of Two-Dimensional Advection–Diffusion Equation ⋮ Extending the Meshless Local Petrov–Galerkin Method to Solve Stabilized Turbulent Fluid Flow Problems ⋮ A novel dual reciprocity boundary element formulation for two-dimensional transient convection-diffusion-reaction problems with variable velocity ⋮ A modified kernel-based collocation method for interface boundary value problems ⋮ Transient Convection-Diffusion-Reaction Problems with Variable Velocity Field by Means of DRBEM with Different Radial Basis Functions ⋮ A Novel B-Spline Method for Modeling Transport Problems in Anisotropic Inhomogeneous Media ⋮ A Novel Method for Solving Time-Dependent 2D Advection-Diffusion-Reaction Equations to Model Transfer in Nonlinear Anisotropic Media ⋮ An adaptive RBF finite collocation approach to track transport processes across moving fronts ⋮ Modified local singular boundary method for solution of two-dimensional diffusion equation ⋮ Local singular boundary method for two-dimensional steady and unsteady potential flow

Uses Software

• rbf_qr

Cites Work

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• An alternative local collocation strategy for high-convergence meshless PDE solutions, using radial basis functions
• A localized collocation meshless method (LCMM) for incompressible flows CFD modeling with applications to transient hemodynamics
• A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere
• Stable calculation of Gaussian-based RBF-FD stencils
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• A numerical study of some radial basis function based solution methods for elliptic PDEs
• Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
• Stabilization of RBF-generated finite difference methods for convective PDEs
• The role of the multiquadric shape parameters in solving elliptic partial differential equations
• The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems
• Improved accuracy of multiquadric interpolation using variable shape parameters
• Analysis of central and upwind compact schemes.
• Improved multiquadric method for elliptic partial differential equations via PDE collocation on the boundary
• Stable computation of multiquadric interpolants for all values of the shape parameter
• An upwind local RBF-DQ method for simulation of inviscid compressible flows
• Computer evaluation of high order numerical schemes to solve advective transport problems
• 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
• Stable Computations with Gaussian Radial Basis Functions
• A Stable Algorithm for Flat Radial Basis Functions on a Sphere
• A note on two upwind strategies for RBF-based grid-free schemes to solve steady convection-diffusion equations
• THE PARTITION OF UNITY METHOD
• Total variation diminishing Runge-Kutta schemes
• Radial point interpolation based finite difference method for mechanics problems
• A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEs
• A Hermite radial basis function collocation approach for the numerical simulation of crystallization processes in a channel

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