Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems

Ge, Yongbin; Cao, Fujun

doi:10.1016/j.jcp.2011.02.027

Cited by 48 publications

(49 citation statements)

References 42 publications

(100 reference statements)

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“…Once the step sizes on the both x and y directions are equal, then the mesh is uniform and the scheme (2) has fourth order accuracy. For more details about the derivation process, one can refer to [13,14].…”

Section: The Compact Scheme On Nonuniform Meshmentioning

confidence: 99%

“…The numerical results from the HOC scheme on nonuniform mesh and adaptive mesh method are compared with those on uniform and nonuniform mesh by the grid stretching function [13,14].…”

Section: Numerical Examplementioning

confidence: 99%

“…However, the derivation of the high order compact scheme on nonuniform grid is very nontrivial. The high order compact scheme on nonuniform mesh for 2D convection diffusion equation and 3D Poisson equation are presented in [13,14] and [15], respectively. Numerical results show that the HOC scheme on nonuniform grids is very robust and efficient for the convection diffusion problems with boundary layers and local singularities.…”

Section: Introductionmentioning

confidence: 99%

“…A novel adaptive mesh algorithm is proposed to generate orthogonal nonuniform computational mesh for 2D rectangular domain based on the 1D algorithm by [16]. Moreover, in order to accelerate the solving efficiency, the multigrid method in [14] is applied to solve the discrete linear system. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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High Order Compact Scheme and the Moving Mesh Method for Helmholtz Equation with Variable Wave Numbers

Cao¹,

Yuan²,

Ge³

2017

dtcse

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Abstract. High order compact scheme has extensively been used for solving the Helmholtz equation on uniform mesh. Although uniform spacing is computationally advantageous for isotropic problems, the non-uniform mesh will be superior to the problems with the anisotropic properties or boundary layers. In this paper, we proposed a compact scheme on nonuniform mesh which has at least third order accuracy for the 2D Helmholtz equation with variable wave number. A novel adaptive mesh algorithm is also presented to generate the orthogonal nonuniform mesh. The 2D Helmholtz equation is solved by combining the HOC scheme on nonuniform mesh with the moving mesh method. The multigrid method is used to solve the discrete algebraic system. Numerical experiments are executed to verify the accuracy and efficiency of the presented method.

show abstract

Section: The Compact Scheme On Nonuniform Meshmentioning

confidence: 99%

“…The numerical results from the HOC scheme on nonuniform mesh and adaptive mesh method are compared with those on uniform and nonuniform mesh by the grid stretching function [13,14].…”

Section: Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High Order Compact Scheme and the Moving Mesh Method for Helmholtz Equation with Variable Wave Numbers

Cao¹,

Yuan²,

Ge³

2017

dtcse

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“…Under these situations, where points are concentrated in the regions of sharp variation local mesh refinement procedures [8,15,[21][22][23][24] are necessary, thus dramatically reducing the computational time and computer storage. Cao and Ge developed a multigrid method with HOC scheme on non-uniform grids for solving 2D convection diffusion equation [21]. This paper is based on approach that an interpolation operator and a projection operator that are suited for HOC scheme using non-uniform mesh is represented by transformation-free HOC scheme on non-uniform grids.…”

Section: Introductionmentioning

confidence: 99%

Multigrid solution for the cauchy problem associated with helmholtz type equation on non uniform grids

Ghaffar¹,

Badshah²,

Islam³

2017

Matrix sci. math.

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An efficient multiscale‐like multigrid computation for 2D convection‐diffusion equations on nonuniform grids

Zheng

2020

Math Methods in App Sciences

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An efficient multiscale‐like multigrid (MSLMG) method combined with a high‐order compact (HOC) difference scheme on nonuniform grids is presented to solve the two‐dimensional (2D) convection‐diffusion equations. The discrete systems with given appropriate initial solutions on two finest grids are solved to obtain the MSLMG solutions with discretization‐level accuracy by performing fewer multigrid cycles; it is implemented with alternating line Gauss–Seidel smoother, interpolation, and restriction operators on the nonuniform grids. Numerical experiments of boundary layer or local singularity problems are conducted to show that the proposed algorithm with the HOC scheme on nonuniform grids is efficient and effective to decrease the computational cost and time, and the computed approximation on the nonuniform grids has fourth order accuracy.

show abstract

Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems

Cited by 48 publications

References 42 publications

High Order Compact Scheme and the Moving Mesh Method for Helmholtz Equation with Variable Wave Numbers

High Order Compact Scheme and the Moving Mesh Method for Helmholtz Equation with Variable Wave Numbers

Multigrid solution for the cauchy problem associated with helmholtz type equation on non uniform grids

An efficient multiscale‐like multigrid computation for 2D convection‐diffusion equations on nonuniform grids

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