A cell-centered multipoint flux approximation method with a diamond stencil coupled with a higher order finite volume method for the simulation of oil–water displacements in heterogeneous and anisotropic petroleum reservoirs

2016 ◽  
Vol 127 ◽  
pp. 1-16 ◽  
Author(s):  
F.R.L. Contreras ◽  
P.R.M. Lyra ◽  
M.R.A. Souza ◽  
D.K.E. Carvalho
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Approximation Method ◽  
Petroleum Reservoirs ◽  
Higher Order ◽  
Flux Approximation ◽  
A Cell ◽  
Oil Water ◽  
Volume Method

scholarly journals A Fitted L-Multi-Point Flux Approximation Method for Pricing Options

2021 ◽  
Author(s):  
Rock Stephane Koffi ◽  
Antoine Tambue
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Approximation Method ◽  
Special Kind ◽  
Diffusion Term ◽  
Pricing Options ◽  
Flux Approximation ◽  
Black Scholes ◽  
Upwind Methods ◽  
Volume Method

AbstractIn this paper, we introduce a special kind of finite volume method called Multi-Point Flux Approximation method (MPFA) to price European and American options in two dimensional domain. We focus on the L-MPFA method for space discretization of the diffusion term of Black–Scholes operator. The degeneracy of the Black-Scholes operator is tackled using the fitted finite volume method. This combination of fitted finite volume method and L-MPFA method coupled to upwind methods gives us a novel scheme, called the fitted L-MPFA method. Numerical experiments show the accuracy of the novel fitted L-MPFA method comparing to well known schemes for pricing options.

Higher Resolution Hybrid-Upwind Spectral Finite-Volume Methods, for Flow in Porous and Fractured Media on Unstructured Grids

2021 ◽  
Author(s):  
Yawei Xie ◽  
Michael G. Edwards
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Unstructured Grids ◽  
Concentration Field ◽  
Convective Transport ◽  
High Order ◽  
Spectral Volume ◽  
Flux Approximation ◽  
Triangular Cell ◽  
Volume Method

Abstract A novel higher resolution spectral volume method coupled with a control-volume distributed multi-Point flux approximation (CVD-MPFA) is presented on unstructured triangular grids for subsurface reservoir simulation. The flow equations involve an essentially hyperbolic convection equation coupled with an elliptic pressure equation resulting from Darcy’s law together with mass conservation. The spectral volume (SV) method is a locally conservative, efficient high-order finite volume method for convective flow. In 2D geometry, the triangular cell is subdivided into sub-cells, and the average state variables in the sub-cells are used to reconstruct a high-order polynomial in the triangular cell. The focus here is on an efficient strategy for reconstruction of both a higher resolution approximation of the convective transport flux and Darcy-flux approximation on sub-cell interfaces, which is also coupled with a discrete fracture model. The strategy involves coupling of the SV method and reconstructed CVD-MPFA fluxes at the faces of the spectral volume, to obtain an efficient finer scale higher resolution finite-volume method which solves for both the saturation and pressure. A limiting procedure based on a Barth-Jespersen type limiter is used to prevent non-physical oscillations on unstructured grids. The fine scale saturation/concentration field is then updated via the reconstructed finite volume approximation over the sub-cell control-volumes. Performance comparisons are presented for two phase flow problems on 2D unstructured meshes including fractures. The results demonstrate that the spectral-volume method achieves further enhanced resolution of flow and fronts in addition to that of achieved by the standard higher resolution method over first order upwind, while improving upon efficiency.

Admissible Regions for Higher-Order Finite Volume Method Grids

2017 ◽  
Vol 7 (2) ◽  
pp. 269-285
Author(s):  
Yuanyuan Zhang ◽  
Zhongying Chen
Keyword(s):  
Boundary Value Problems ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Boundary ◽  
Higher Order ◽  
Elliptic Boundary Value Problems ◽  
Sufficient Condition ◽  
Elliptic Boundary Value ◽  
Admissible Region ◽  
Volume Method

AbstractAdmissible regions for higher-order finite volume method (FVM) grids are considered. A new Hermite quintic FVM and a new hybrid quintic FVM are constructed to solve elliptic boundary value problems, and the corresponding admissible regions are investigated. A sufficient condition for the uniform local-ellipticity of the new hybrid quintic FVM is obtained when its admissible region is known. In addition, the admissible regions for a large number of higher-order FVMs are provided. For the same class of FVM (Lagrange, Hermite or hybrid), the higher order FVM has a smaller admissible region such that stronger geometric restrictions are required to guarantee its uniform local-ellipticity.

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