scholarly journals Coupled finite-volume scheme with adapted Augmented Roe scheme for simulating morphological evolution in arbitrary cross-sections

2018 ◽  
Vol 20 (5) ◽  
pp. 1111-1130 ◽  
Author(s):  
F. Franzini ◽  
S. Soares-Frazao
Keyword(s):  
Finite Volume ◽  
Cross Sections ◽  
Morphological Changes ◽  
Numerical Models ◽  
Morphological Evolution ◽  
Finite Volume Scheme ◽  
Steady Flows ◽  
One Dimensional ◽  
Volume Scheme ◽  
Transient Flows

Abstract A new coupled finite-volume scheme based on the Augmented Roe solver adapted to simulate morphological evolution of arbitrary cross-sections is presented. In pure hydrodynamic conditions, the Augmented Roe scheme has proven to provide accurate results and a constant discharge in steady-flow conditions. Here, this scheme is extended to solve the one-dimensional Saint-Venant–Exner system of equations written for arbitrary cross-sections. Therefore, new eigenvalues and source-term calculations are proposed to account for the irregular shape of the cross-sections. The performances of the proposed scheme are assessed by comparison with three different one-dimensional numerical models aimed at simulating morphological changes, with coupled or uncoupled approaches, and based on HLL or Roe-based flux calculations. Numerous test cases were examined, including water at rest, steady flows and transient flows for which experimental results exist. The results show that the proposed scheme provides stable and accurate results for a wider range of situations than is available with other classical models.

scholarly journals On the use of a cell-centered finite-volume scheme on prismatic meshes in boundary layers

2021 ◽  
pp. 1-44
Author(s):  
Pavel Alexeevisch Bakhvalov
Keyword(s):  
Reynolds Number ◽  
Finite Volume ◽  
High Reynolds Number ◽  
Finite Volume Scheme ◽  
Wall Surface ◽  
One Dimensional ◽  
Volume Scheme ◽  
Dimensional Reconstruction ◽  
A Cell ◽  
High Reynolds

We consider the cell-centered finite-volume scheme with the quasi-one-dimensional reconstruction and generalize it to anisotropic prismatic meshes suitable for high-Reynolds-number problems. We offer a new algorithm of flux computation based on the reconstruction along the wall surface, whereas in the original schemes it was along the tangent to the wall surface. We also study how does the curvature of mesh elements influence the accuracy if taken into account.

scholarly journals Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 635
Author(s):  
Jitraj Saha ◽  
Andreas Bück
Keyword(s):  
Finite Volume ◽  
Three Dimensional ◽  
Test Problems ◽  
Finite Volume Scheme ◽  
Finite Volume Schemes ◽  
One Dimensional ◽  
Volume Scheme ◽  
Multidimensional Problems ◽  
Conservative Form ◽  
Fragmentation Equation

In this article, a new numerical scheme for the solution of the multidimensional fragmentation problem is presented. It is the first that uses the conservative form of the multidimensional problem. The idea to apply the finite volume scheme for solving one-dimensional linear fragmentation problems is extended over a generalized multidimensional setup. The derivation is given in detail for two-dimensional and three-dimensional problems; an outline for the extension to higher dimensions is also presented. Additionally, the existing one-dimensional finite volume scheme for solving conservative one-dimensional multi-fragmentation equation is extended to solve multidimensional problems. The accuracy and efficiency of both proposed schemes is analyzed for several test problems.

scholarly journals Finite volume discretisation for the one-dimensional convection diffusion-dissipation equation

2016 ◽  
Vol 5 (4) ◽  
pp. 206
Author(s):  
Bienvenu ONDAMI
Keyword(s):  
Finite Volume ◽  
Water Table ◽  
Method Of Lines ◽  
Finite Volume Scheme ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Volume Scheme ◽  
The One ◽  
Dissipation Equation

This paper is devoted to analysis of a finite volume scheme for a one-dimensional convection-diffusion-dissipation equation having application in pollution of water table. We analyse a scheme corresponding to a semi-descretization, also called method of lines. Results of umerical experiments using this approach are reported.

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

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