Upwind Strategy for Localized Method of Approximate Particular Solutions with Applications to Convection Dominated Diffusion Problems

DOI10.4208/aamm.OA-2019-0103zbMath1488.65528OpenAlexW3116446024MaRDI QIDQ5157051

Luyu Ran, Xue-Ying Zhang

Publication date: 12 October 2021

Published in: Advances in Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/aamm.oa-2019-0103

zbMATH Keywords

radial basis functionsconvection dominated problemsupwind schemeLMAPS

Mathematics Subject Classification ID

Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Initial value problems for first-order hyperbolic equations (35L03) Numerical radial basis function approximation (65D12)

Cites Work

• Radial basis function collocation method for the numerical solution of the two-dimensional transient nonlinear coupled Burgers equations
• A localized approach for the method of approximate particular solutions
• Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion
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• Meshfree explicit local radial basis function collocation method for diffusion problems
• Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier--Stokes equations
• An operator splitting-radial basis function method for the solution of transient nonlinear Poisson problems
• A novel upwind-based local radial basis function differential quadrature method for convection-dominated flows
• Block-marching in time with DQ discretization: An efficient method for time-dependent problems
• Local method of approximate particular solutions for two-dimensional unsteady Burgers' equations
• THE METHOD OF APPROXIMATE PARTICULAR SOLUTIONS FOR SOLVING ELLIPTIC PROBLEMS WITH VARIABLE COEFFICIENTS
• Solution of Incompressible Turbulent Flow by a Mesh-Free Method
• The method of particular solutions for solving scalar wave equations
• Meshless local radial basis function collocation method for convective‐diffusive solid‐liquid phase change problems
• Local RBFs Based Collocation Methods for Unsteady Navier-Stokes Equations

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