Investigation of the Oldroyd model as a generalized incompressible Navier-Stokes equation via the interpolating stabilized element free Galerkin technique

DOI10.1016/j.apnum.2019.08.025zbMath1444.76083OpenAlexW2972804654WikidataQ127243478 ScholiaQ127243478MaRDI QIDQ2301294

Mehdi Dehghan, Mostafa Abbaszadeh

Publication date: 24 February 2020

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2019.08.025

zbMATH Keywords

convergenceexistenceuniquenesserror estimatenumerical stabilityBrowder fixed point theorem

Mathematics Subject Classification ID

Finite difference methods applied to problems in fluid mechanics (76M20) Viscoelastic fluids (76A10) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Basic methods in fluid mechanics (76M99)

Related Items (25)

Identification of the air gap thermal resistance in the model of binary alloy solidification including the macrosegregation and the material shrinkage phenomena ⋮ A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh-Stokes problem for a heated generalized second-grade fluid ⋮ A reduced-order variational multiscale interpolating element free Galerkin technique based on proper orthogonal decomposition for solving Navier-Stokes equations coupled with a heat transfer equation: nonstationary incompressible Boussinesq equations ⋮ Investigation of generalized Couette hydromagnetic flow of two-step exothermic chemical reaction in a channel via the direct meshless local Petrov-Galerkin method ⋮ Interior penalty discontinuous Galerkin technique for solving generalized Sobolev equation ⋮ Reduced order modeling of time-dependent incompressible Navier-Stokes equation with variable density based on a local radial basis functions-finite difference (LRBF-FD) technique and the POD/DEIM method ⋮ A three level linearized compact difference scheme for a fourth-order reaction-diffusion equation ⋮ On Romanovski–Jacobi polynomials and their related approximation results ⋮ Application of direct meshless local <scp>Petrov–Galerkin</scp> method for numerical solution of stochastic elliptic interface problems ⋮ Error analysis of interpolating element free Galerkin method to solve non-linear extended Fisher-Kolmogorov equation ⋮ Element-free Galerkin analysis of Stokes problems using the reproducing kernel gradient smoothing integration ⋮ On a three step two‐grid finite element method for the Oldroyd model of order one ⋮ Analysis of Navier-Stokes equations by a BC/GE embedded local meshless method ⋮ Nonlinear vibration analysis of pipeline considering the effects of soft nonlinear clamp ⋮ Compact local integrated radial basis functions (integrated RBF) method for solving system of non-linear advection-diffusion-reaction equations to prevent the groundwater contamination ⋮ Parametric nonlinear model reduction using \(K\)-means clustering for miscible flow simulation ⋮ An efficient dissipation-preserving Legendre-Galerkin spectral method for the Higgs boson equation in the de Sitter spacetime universe ⋮ A divergence-free generalized moving least squares approximation with its application ⋮ The meshless local Petrov-Galerkin method based on moving Taylor polynomial approximation to investigate unsteady diffusion-convection problems of anisotropic functionally graded materials related to incompressible flow ⋮ A meshless technique based on generalized moving least squares combined with the second-order semi-implicit backward differential formula for numerically solving time-dependent phase field models on the spheres ⋮ Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem ⋮ On the static analysis of inhomogeneous magneto-electro-elastic plates in thermal environment via element-free Galerkin method ⋮ High-order compact scheme for the two-dimensional fractional Rayleigh-Stokes problem for a heated generalized second-grade fluid ⋮ Direct meshless local Petrov-Galerkin method to investigate anisotropic potential and plane elastostatic equations of anisotropic functionally graded materials problems ⋮ The element-free Galerkin method for the variational-hemivariational inequality of the dynamic Signorini-Tresca contact problems with friction in elastic materials

Cites Work

• A stabilized Crank-Nicolson mixed finite volume element formulation for the non-stationary incompressible Boussinesq equations
• Error estimates for the interpolating moving least-squares method
• A stabilized mixed finite element formulation for the non-stationary incompressible Boussinesq equations
• Nonlinear model reduction for the Navier-Stokes equations using residual DEIM method
• Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation
• A numerical framework for two-dimensional large deformation of inhomogeneous swelling of gels using the improved complex variable element-free Galerkin method
• Numerical solution of the two-phase incompressible Navier-Stokes equations using a GPU-accelerated meshless method
• Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair
• Proper orthogonal decomposition-based reduced-order stabilized mixed finite volume element extrapolating model for the nonstationary incompressible Boussinesq equations
• On a two-grid finite element scheme for the equations of motion arising in Kelvin-Voigt model
• Parallel computation of unsteady incompressible viscous flows around moving rigid bodies using an immersed object method with overlapping grids
• On error estimates of the penalty method for the viscoelastic flow problem. I: Time discretization
• Complex variable boundary element-free method for two-dimensional elastodynamic problems
• A novel complex variable element-free Galerkin method for two-dimensional large deformation problems
• The interpolating element-free Galerkin method for solving Korteweg-de Vries-Rosenau-regularized long-wave equation with error analysis
• Direct solution of Navier-Stokes equations by radial basis functions
• Solution of magnetohydrodynamic flow problems using the boundary element method
• An advanced meshless LBIE/RBF method for solving two-dimensional incompressible fluid flows
• An error estimate in the EFG method
• Meshless method for the stationary imcompressible Navier-Stokes equations
• Meshless methods: An overview and recent developments
• On the convergence of viscoelastic fluid flows to a steady state
• The dimension split element-free Galerkin method for three-dimensional potential problems
• A novel interpolating element-free Galerkin (IEFG) method for two-dimensional elastoplasticity
• A meshless interpolating Galerkin boundary node method for Stokes flows
• Analysis of two methods based on Galerkin weak form for fractional diffusion-wave: meshless interpolating element free Galerkin (IEFG) and finite element methods
• Analysis of the inherent instability of the interpolating moving least squares method when using improper polynomial bases
• A hybrid improved complex variable element-free Galerkin method for three-dimensional potential problems
• An upwind local radial basis functions-differential quadrature (RBF-DQ) method with proper orthogonal decomposition (POD) approach for solving compressible Euler equation
• Numerical modeling of Stokes flow in a circular cavity by variational multiscale element free Galerkin method
• Error analysis and numerical simulation of magnetohydrodynamics (MHD) equation based on the interpolating element free Galerkin (IEFG) method
• A generalized element-free Galerkin method for Stokes problem
• The fully discrete fractional-step method for the Oldroyd model
• Numerical solution of 2D Navier-Stokes equation discretized via boundary elements method and finite difference approximation
• Boundary element-free methods for exterior acoustic problems with arbitrary and high wavenumbers
• The complex variable reproducing kernel particle method for bending problems of thin plates on elastic foundations
• Analysis of the element-free Galerkin method for Signorini problems
• The boundary element-free method for 2D interior and exterior Helmholtz problems
• The complex variable interpolating moving least-squares method
• Numerical and analytical investigations for neutral delay fractional damped diffusion-wave equation based on the stabilized interpolating element free Galerkin (IEFG) method
• Analysis of the complex moving least squares approximation and the associated element-free Galerkin method
• Three-dimensional complex variable element-free Galerkin method
• Proper orthogonal decomposition variational multiscale element free Galerkin (POD-VMEFG) meshless method for solving incompressible Navier-Stokes equation
• Interpolating stabilized moving least squares (MLS) approximation for 2D elliptic interface problems
• The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation
• A novel vector potential formulation of 3D Navier-Stokes equations with through-flow boundaries by a local meshless method
• A discontinuous Petrov-Galerkin methodology for adaptive solutions to the incompressible Navier-Stokes equations
• On a two-grid finite element scheme combined with Crank-Nicolson method for the equations of motion arising in the Kelvin-Voigt model
• On three steps two-grid finite element methods for the 2D-transient Navier-Stokes equations
• A moving least square reproducing polynomial meshless method
• Meshless schemes for unsteady Navier--Stokes equations in vorticity formulation using radial basis functions
• Parallel-multigrid computation of unsteady incompressible viscous flows using a matrix-free implicit method and high-resolution characteristics-based scheme
• A global meshless collocation particular solution method for solving the two-dimensional Navier-Stokes system of equations
• Non-intrusive reduced order modelling of the Navier-Stokes equations
• AN INTERPOLATING BOUNDARY ELEMENT-FREE METHOD WITH NONSINGULAR WEIGHT FUNCTION FOR TWO-DIMENSIONAL POTENTIAL PROBLEMS
• Optimal error estimates of the penalty method for the linearized viscoelastic flows
• Backward Euler method for the Equations of Motion Arising in Oldroyd Fluids of Order One with Nonsmooth Initial Data
• Steady-state solution of incompressible Navier-Stokes equations using discrete least-squares meshless method
• Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization
• Finite element method for solving mhd flow in a rectangular duct
• Surfaces Generated by Moving Least Squares Methods
• Motion of nonlinear visco-elastic fluid
• Element‐free Galerkin methods
• Boundary element method solution of MHD flow in a rectangular duct
• The two-grid interpolating element free Galerkin (TG-IEFG) method for solving Rosenau-regularized long wave (RRLW) equation with error analysis
• Semidiscrete Galerkin method for equations of motion arising in Kelvin‐Voigt model of viscoelastic fluid flow
• Non‐intrusive reduced‐order modelling of the Navier–Stokes equations based on RBF interpolation
• Radial basis function meshless method for the steady incompressible Navier–Stokes equations
• Semidiscrete finite element Galerkin approximations to the equations of motion arising in the Oldroyd model
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Investigation of the Oldroyd model as a generalized incompressible Navier-Stokes equation via the interpolating stabilized element free Galerkin technique