Toward Application of Higher Order Finite Volume Schemes to Porous Media Flow

2013 ◽  
Author(s):  
Rohan Panchadhara ◽  
Laurent White ◽  
Dimitar Trenev
Keyword(s):  
Porous Media ◽  
Finite Volume ◽  
Higher Order ◽  
Porous Media Flow ◽  
Finite Volume Schemes

scholarly journals Convergence of nonlinear finite volume schemes for two-phase porous media flow on general meshes

2020 ◽  
Author(s):  
Léo Agélas ◽  
Martin Schneider ◽  
Guillaume Enchéry ◽  
Bernd Flemisch
Keyword(s):  
Porous Media ◽  
Finite Volume ◽  
A Priori ◽  
Porous Media Flow ◽  
Finite Volume Schemes ◽  
Two Phase ◽  
Finite Volume Discretization ◽  
Flux Approximation ◽  
Specific Scheme ◽  
Flow Through

Abstract In this work we present an abstract finite volume discretization framework for incompressible immiscible two-phase flow through porous media. A priori error estimates are derived that allow us to prove the existence of discrete solutions and to establish the proof of convergence for schemes belonging to this framework. In contrast to existing publications the proof is not restricted to a specific scheme and it assumes neither symmetry nor linearity of the flux approximations. Two nonlinear schemes, namely a nonlinear two-point flux approximation and a nonlinear multipoint flux approximation, are presented, and some properties of these schemes, e.g. saturation bounds, are proven. Furthermore, the numerical behavior of these schemes (e.g. accuracy, coercivity, efficiency or saturation bounds) is investigated for different test cases for which the coercivity is checked numerically.

scholarly journals A Higher-Order Chimera Method for Finite Volume Schemes

2017 ◽  
Vol 25 (3) ◽  
pp. 691-706 ◽  
Author(s):  
Luis Ramírez ◽  
Xesús Nogueira ◽  
Pablo Ouro ◽  
Fermín Navarrina ◽  
Sofiane Khelladi ◽  
...  
Keyword(s):  
Finite Volume ◽  
Higher Order ◽  
Finite Volume Schemes

scholarly journals Higher-Order Accurate Finite Volume Discretization of the Three-Dimensional Poisson Equation Based on An Equation Error Method

2018 ◽  
Vol 6 (6) ◽  
pp. 107-123
Author(s):  
Yaw Kyei
Keyword(s):  
Finite Volume ◽  
Three Dimensional ◽  
Integral Form ◽  
Higher Order ◽  
Finite Volume Schemes ◽  
Finite Volume Discretization ◽  
Equation Error ◽  
Error Expansion ◽  
Control Volumes ◽  
Physical Phenomena

Efficient higher-order accurate finite volume schemes are developed for the threedimensional Poisson’s equation based on optimizations of an equation error expansion on local control volumes. A weighted quadrature of local compact fluxes and the flux integral form of the equation are utilized to formulate the local equation error expansions. Efficient quadrature weights for the schemes are then determined through a minimization of the error expansion for higher-order accurate discretizations of the equation. Consequently, the leading numerical viscosity coefficients are more accurately and completely determined to optimize the weight parameters for uniform higher-order convergence suitable for effective numerical modeling of physical phenomena. Effectiveness of the schemes are evaluated through the solution of the associated eigenvalue problem. Numerical results and analysis of the schemes demonstrate the effectiveness of the methodology.

Error estimates for higher-order finite volume schemes for convection–diffusion problems

2018 ◽  
Vol 26 (1) ◽  
pp. 35-62
Author(s):  
Dietmar Kröner ◽  
Mirko Rokyta
Keyword(s):  
Error Estimates ◽  
Finite Volume ◽  
Original Problem ◽  
A Priori ◽  
Higher Order ◽  
Finite Volume Schemes ◽  
Convection Diffusion ◽  
Type Reconstruction ◽  
Convection Dominated ◽  
Diffusion Problems

AbstractIt is still an open problem to provea priorierror estimates for finite volume schemes of higher order MUSCL type, including limiters, on unstructured meshes, which show some improvement compared to first order schemes. In this paper we use these higher order schemes for the discretization of convection dominated elliptic problems in a convex bounded domainΩin ℝ2and we can prove such kind of ana priorierror estimate. In the part of the estimate, which refers to the discretization of the convective term, we gainh1/2. Although the original problem is linear, the numerical problem becomes nonlinear, due to MUSCL type reconstruction/limiter technique.

scholarly journals New high-resolution-preserving sliding mesh techniques for higher-order finite volume schemes

2015 ◽  
Vol 118 ◽  
pp. 114-130 ◽  
Author(s):  
Luis Ramírez ◽  
Charles Foulquié ◽  
Xesús Nogueira ◽  
Sofiane Khelladi ◽  
Jean-Camille Chassaing ◽  
...  
Keyword(s):  
High Resolution ◽  
Finite Volume ◽  
Higher Order ◽  
Finite Volume Schemes ◽  
Sliding Mesh
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