Local Discontinuous Galerkin Method for Incompressible Miscible Displacement Problem in Porous Media

Guo, Hui; Fan, Yu; Yang, Yang

doi:10.1007/s10915-016-0313-7

Cited by 20 publications

(8 citation statements)

References 36 publications

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“…Thanks to the above advantages, the RK-LDG method especially the third-order RK-LDG method has been applied for different problems, such as porous medium equations, 17 incompressible miscible displacement problem, 18 and Keller-Segel chemotaxis model 19 . There are also some work on the theoretical analysis about the third-order RK-LDG method.…”

Section: Introductionmentioning

confidence: 99%

“…22 Our main interest in this work is to investigate the performance of the RK-LDG methods, for solving 1-dimensional nonlinear carburizing model. We will adopt the similar LDG method defined in Guo et al, 18 where one more auxiliary variable was introduced to deal with the nonlinear diffusion, which is a little different from the original LDG method. 9 Meanwhile, we will follow the numerical flux setting in Wang and Zhang 21 and Castillo et al 23 to deal with the Dirichlet boundary condition.…”

Section: Introductionmentioning

confidence: 99%

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Local discontinuous Galerkin methods with explicit Runge‐Kutta time marching for nonlinear carburizing model

Xia

Wang

2018

Math Methods in App Sciences

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A fully discrete local discontinuous Galerkin (LDG) method coupled with 3 total variation diminishing Runge-Kutta time-marching schemes, for solving a nonlinear carburizing model, will be analyzed and implemented in this paper. On the basis of a suitable numerical flux setting in the LDG method, we obtain the optimal error estimate for the Runge-Kutta-LDG schemes by energy analysis, under the condition τ ≤ λh 2 , where h and τ are mesh size and time step, respectively, λ is a positive constant independent of h. Numerical experiments are presented to verify the accuracy and capability of the proposed schemes. For the carburizing diffusion processes of steel and the diffusion simulation for Cu-Ni system, the numerical results show good agreement with the experimental results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Local discontinuous Galerkin methods with explicit Runge‐Kutta time marching for nonlinear carburizing model

Xia

Wang

2018

Math Methods in App Sciences

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“…But the method in [38] is not conservative. Later in [35], LDG was applied to solve incompressible miscible displacements in porous media. Therefore, we continue to develop a conservative local discontinuous Galerkin (LDG) method for the two-dimensional coupled system of the compressible miscible displacement problem.…”

Section: Motivationmentioning

confidence: 99%

“…the optimal error estimates. This approach was proposed in [77,35,46] However, to make the numerical solutions to be physically relevant, we have to add a very large penalty which depends on the numerical approximations of the derivatives of the primary variables [46,36,13].…”

Section: Combine the Convection Terms And Diffusion Terms Together Anmentioning

confidence: 99%

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Discontinuous Galerkin methods for convection-diffusion equations and applications in petroleum engineering

Chuenjarern¹

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A combined hybrid mixed element method for incompressible miscible displacement problem with local discontinuous Galerkin procedure

Zhang

Han

Guo

et al. 2020

Numerical Methods Partial

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In this article, we propose a combined hybrid discontinuous mixed finite element method for miscible displacement problem with local discontinuous Galerkin method. Here, to obtain more accurate approximation and deal with the discontinuous case, we use the hybrid mixed element method to approximate the pressure and velocity, and use the local discontinuous Galerkin finite element method for the concentration. Compared with other combined methods, this method can improve the efficiency of computation, deal with the discontinuous problem well and keep local mass balance. We study the convergence of this method and give the corresponding optimal error estimates in L ∞ (L 2) for velocity and concentration and the super convergence in L ∞ (H 1) for pressure. Finally, we also present some numerical examples to confirm our theoretical analysis.

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Local Discontinuous Galerkin Method for Incompressible Miscible Displacement Problem in Porous Media

Cited by 20 publications

References 36 publications

Local discontinuous Galerkin methods with explicit Runge‐Kutta time marching for nonlinear carburizing model

Local discontinuous Galerkin methods with explicit Runge‐Kutta time marching for nonlinear carburizing model

Discontinuous Galerkin methods for convection-diffusion equations and applications in petroleum engineering

A combined hybrid mixed element method for incompressible miscible displacement problem with local discontinuous Galerkin procedure

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