A unified analysis of fully mixed virtual element method for wormhole propagation arising in the petroleum engineering

Dehghan, Mehdi; Gharibi, Zeinab

doi:10.1016/j.camwa.2022.06.004

Cited by 3 publications

(1 citation statement)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Compared with the incompressible wormhole model, compressible wormhole model is more popular among researchers in recent years. In the last couple of years, researchers have used different methods to simulate compressible wormhole propagation, such as local discontinuous Galerkin (LDG) method [23,24] and fully mixed virtual element method [5]. In 2020, Zhang et al [28] proposed a combined method, namely, for different types of equations, using splitting mixed finite element method, modified mass-conservative characteristic method and traditional finite element method respectively in order to study this phenomenon well.…”

Section: Introductionmentioning

confidence: 99%

A second‐order time discretizing block‐centered finite difference method for compressible wormhole propagation

Sun,

Li,

Rui

2024

Numerical Methods Partial

View full text Add to dashboard Cite

In this paper, a second‐order time discretizing block‐centered finite difference method is introduced to solve the compressible wormhole propagation. The optimal second‐order error estimates for the porosity, pressure, velocity, concentration and its flux are established carefully in different discrete norms on non‐uniform grids. Then by introducing Lagrange multiplier, a novel bound‐preserving scheme for concentration is constructed. Finally, numerical experiments are carried out to demonstrate the correctness of theoretical analysis and capability for simulations of compressible wormhole propagation.

show abstract

Section: Introductionmentioning

confidence: 99%

A second‐order time discretizing block‐centered finite difference method for compressible wormhole propagation

Sun,

Li,

Rui

2024

Numerical Methods Partial

View full text Add to dashboard Cite

show abstract

A high-order time discretizing block-centered finite difference method for compressible wormhole propagation

Sun,

Li,

Rui

2024

Applied Mathematics Letters

View full text Add to dashboard Cite

A Conforming Virtual Element Method for Parabolic Integro-Differential Equations

Yadav,

Suthar,

Kumar

2023

Computational Methods in Applied Mathematics

View full text Add to dashboard Cite

This article develops and analyses a conforming virtual element scheme for the spatial discretization of parabolic integro-differential equations combined with backward Euler’s scheme for temporal discretization. With the help of Ritz–Voltera and L 2 L^{2} projection operators, optimal a priori error estimates are established. Moreover, several numerical experiments are presented to confirm the computational efficiency of the proposed scheme and validate the theoretical findings.

show abstract

A unified analysis of fully mixed virtual element method for wormhole propagation arising in the petroleum engineering

Cited by 3 publications

References 31 publications

A second‐order time discretizing block‐centered finite difference method for compressible wormhole propagation

A second‐order time discretizing block‐centered finite difference method for compressible wormhole propagation

A high-order time discretizing block-centered finite difference method for compressible wormhole propagation

A Conforming Virtual Element Method for Parabolic Integro-Differential Equations

Contact Info

Product

Resources

About