Quadratic finite-volume methods for elliptic and parabolic problems on quadrilateral meshes: optimal-order errors based on Barlow points

2013 ◽  
Vol 33 (4) ◽  
pp. 1342-1364 ◽  
Author(s):  
M. Yang ◽  
J. Liu ◽  
Y. Lin
Keyword(s):  
Finite Volume ◽  
Finite Volume Methods ◽  
Parabolic Problems ◽  
Optimal Order ◽  
Quadrilateral Meshes

Cell-Centered Nonlinear Finite-Volume Methods With Improved Robustness

SPE Journal ◽  
2019 ◽  
Vol 25 (01) ◽  
pp. 288-309 ◽  
Author(s):  
Wenjuan Zhang ◽  
Mohammed Al Kobaisi
Keyword(s):  
Finite Volume ◽  
Real Life ◽  
Finite Volume Methods ◽  
Optimal Order ◽  
Test Case ◽  
Correction Algorithm ◽  
Optimal Order Of Convergence ◽  
Industry Standard ◽  
Nonnegative Coefficients ◽  
Volume Method

Summary We present a nonlinear finite-volume method (NFVM) that is either positivity-preserving or extremum-preserving with improved robustness. The key ingredient of the method is the construction of one-sided fluxes, which involves decomposition of conormal vectors by introducing harmonic-averaging points as auxiliary points. The original NFVM using harmonic-averaging points is not robust in the sense that decomposition of conormal vectors with nonnegative coefficients can easily run into difficulties for heterogeneous and anisotropic permeability tensors on general nonorthogonal meshes. To improve NFVM robustness, we first present an alternative derivation of harmonic-averaging points and give a different formula that shows more clearly a point's location. On the basis of the derivation of the new formula, a correction algorithm is proposed to make modifications to those problematic harmonic-averaging points so that all the conormal vectors can be decomposed with nonnegative coefficients successfully. As a result, the resulting NFVM can be applied to more-challenging problems when conormal decomposition with nonnegative coefficients is not possible without correction. The correction algorithm is a compromise between robustness and accuracy. While it improves the robustness of the resulting NFVM, results of numerical convergence tests show that the effect of our correction algorithm on accuracy is problem-dependent. Optimal order of convergence is still maintained for some problems, and the convergence rate is reduced for others. Monotonicity and extremum-preserving properties are verified by numerical experiments. Finally, a field test case is used to demonstrate that the NFVM combined with our correction algorithm can be applied to simulate real-life reservoirs of industry-standard complexity.

Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes

2015 ◽  
Vol 7 (4) ◽  
pp. 454-471
Author(s):  
Yanli Chen ◽  
Yonghai Li
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Equations ◽  
Stiffness Matrix ◽  
Finite Volume Methods ◽  
Matrix Analysis ◽  
Quadrilateral Meshes ◽  
Analysis Technique ◽  
The Stability ◽  
Volume Method

AbstractIn this paper, an optimal bicubic finite volume method is established and analyzed for elliptic equations on quadrilateral meshes. Base on the so-called elementwise stiffness matrix analysis technique, we proceed the stability analysis. It is proved that the new scheme has optimal convergence rate in H1 norm. Additionally, we apply this analysis technique to bilinear finite volume method. Finally, numerical examples are provided to confirm the theoretical analysis of bicubic finite volume method.

Effect of Slit Inclusions in Drag Reduction of Flow over Cylinders

2016 ◽  
Vol 846 ◽  
pp. 18-22
Author(s):  
Rohit Bhattacharya ◽  
Abouzar Moshfegh ◽  
Ahmad Jabbarzadeh
Keyword(s):  
Fluid Flow ◽  
Drag Reduction ◽  
Drag Coefficient ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Circular Cross Section ◽  
Finite Volume Methods ◽  
Turbulent Regime ◽  
Ansys Fluent ◽  
Comparison Of The Results

The flow over bluff bodies is separated compared to the flow over streamlined bodies. The investigation of the fluid flow over a cylinder with a streamwise slit has received little attention in the past, however there is some experimental evidence that show for turbulent regime it reduces the drag coefficient. This work helps in understanding the fluid flow over such cylinders in the laminar regime. As the width of the slit increases the drag coefficient keeps on reducing resulting in a narrower wake as compared to what is expected for flow over a cylinder. In this work we have used two different approaches in modelling a 2D flow for Re=10 to compare the results for CFD using finite volume method (ANSYS FLUENTTM) and Lattice Boltzmann methods. In all cases cylinders of circular cross section have been considered while slit width changing from 10% to 40% of the cylinder diameter. . It will be shown that drag coefficient decreases as the slit ratio increases. The effect of slit size on drag reduction is studied and discussed in detail in the paper. We have also made comparison of the results obtained from Lattice Boltzmann and finite volume methods.

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