A high-resolution Petrov–Galerkin method for the convection–diffusion–reaction problem. Part II—A multidimensional extension

Nadukandi, Prashanth; Oñate, Eugenio; García, Julio Martínez

doi:10.1016/j.cma.2011.10.003

Cited by 17 publications

(12 citation statements)

References 54 publications

(118 reference statements)

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“…This test is a uniform advection problem on unit square with a constant source term studied in [19]. The problem data is: ϵ = 10 −6 , (b 1 , b 2 ) = (1, 0), σ = 0 and f = 1 which corresponds to Pe = 50,000.…”

Section: Testmentioning

confidence: 99%

A finite difference scheme for multidimensional convection–diffusion–reaction equations

Kaya

2014

Computer Methods in Applied Mechanics and Engineering

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In this paper a finite difference scheme is proposed for multidimensional convection-diffusion-reaction equations, particularly designed to treat the most interesting case of small diffusion. It is based closely on the work Ş endur and Neslitürk (2011). Application of the method to multidimensional convection-diffusion-reaction equation is based on a simple splitting of the convection-diffusion-reaction equation and then joining their approximations obtained with Ş endur and Neslitürk (2011). The method adapts very well to all regimes with continuous transitions from one regime to another. Numerical tests show good performance of the method and superiority with respect to well known stabilized finite element methods.

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Section: Testmentioning

confidence: 99%

A finite difference scheme for multidimensional convection–diffusion–reaction equations

Kaya

2014

Computer Methods in Applied Mechanics and Engineering

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“…In the latter methods, the expression multiplying the reaction coefficient in the stabilization terms introduces a negative advection effect which causes this abnormal behaviour. The FIC-FEM solutions presented in [20,47] and the solution of the SGS-GSGS method [42] successfully control the numerical oscillations for this problem. The solutions obtained by the proposed FIC-FEM method viewed at (120 • , 20 • ) are shown in Fig.…”

Section: Examplesmentioning

confidence: 89%

“…Note the higher accuracy obtained for the structural meshes. [47]) in the solutions obtained using the SUPG method [4], the ASGS method [66] and the CAU method [23]. In the latter methods, the expression multiplying the reaction coefficient in the stabilization terms introduces a negative advection effect which causes this abnormal behaviour.…”

Section: Examplesmentioning

confidence: 99%

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Accurate FIC-FEM formulation for the multidimensional steady-state advection–diffusion–absorption equation

Oñate

Nadukandi

Miquel

2017

Computer Methods in Applied Mechanics and Engineering

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In this paper we present an accurate stabilized FIC-FEM formulation for the multidimensional steady-state advection-diffusionabsorption equation. The stabilized formulation is based on the Galerkin FEM solution of the governing differential equations derived via the Finite Increment Calculus (FIC) method using two stabilization parameters. The value of the two stabilization parameters ensuring an accurate nodal FEM solution using uniform meshes of linear elements is obtained from the optimal values for the 1D problem. The accuracy of the new FIC-FEM formulation is demonstrated in the solution of 2D steady-state advection-diffusionabsorption problems for a range of physical parameters and boundary conditions. c

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“…Next, we consider a test problem with homogeneous Dirichlet boundary conditions which is taken from [30]. We note that the exact solution has exponential layers at the outflow boundary (x = 1, y); characteristic boundary layers at (x, y = 0)…”

Section: Methodsmentioning

confidence: 99%

Finite difference approximations of multidimensional convection–diffusion–reaction problems with small diffusion on a special grid

Kaya

Sendur

2015

Journal of Computational Physics

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A numerical scheme for the convection-diffusion-reaction (CDR) problems is studied herein. We propose a finite difference method on a special grid for solving CDR problems particularly designed to treat the most interesting case of small diffusion. We use the subgrid nodes in the Link-cutting bubble (LCB) strategy [5] to construct a numerical algorithm that can easily be extended to the higher dimensions. The method adapts very well to all regimes with continuous transitions from one regime to another. We also compare the performance of the present method with the Streamline-upwind PetrovGalerkin (SUPG) and the Residual-Free Bubbles (RFB) methods on several benchmark problems. The numerical experiments confirm the good performance of the proposed method.

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A high-resolution Petrov–Galerkin method for the convection–diffusion–reaction problem. Part II—A multidimensional extension

Cited by 17 publications

References 54 publications

A finite difference scheme for multidimensional convection–diffusion–reaction equations

A finite difference scheme for multidimensional convection–diffusion–reaction equations

Accurate FIC-FEM formulation for the multidimensional steady-state advection–diffusion–absorption equation

Finite difference approximations of multidimensional convection–diffusion–reaction problems with small diffusion on a special grid

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