A Third-Order Finite-Volume Residual-Based Scheme on Unstructured Grids

2010 ◽  
pp. 167-180
Author(s):  
Xi Du ◽  
Christophe Corre ◽  
Alain Lerat
Keyword(s):  
Finite Volume ◽  
Unstructured Grids ◽  
Third Order

scholarly journals Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids

2016 ◽  
Vol 14 (2) ◽  
pp. 559-594 ◽  
Author(s):  
Elliot Parramore ◽  
Michael G. Edwards ◽  
Mayur Pal ◽  
Sadok Lamine
Keyword(s):  
Finite Volume ◽  
Unstructured Grids ◽  
Multiscale Finite Volume

Tracing Streamlines on Unstructured Grids From Finite Volume Discretizations

SPE Journal ◽  
2008 ◽  
Vol 13 (04) ◽  
pp. 423-431 ◽  
Author(s):  
Sebastien F. Matringe ◽  
Ruben Juanes ◽  
Hamdi A. Tchelepi
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Finite Difference ◽  
Finite Volume ◽  
Unstructured Grids ◽  
Control Volume ◽  
Next Generation ◽  
Flux Approximation ◽  
Streamline Tracing ◽  
Tracing Method

Summary The accuracy of streamline reservoir simulations depends strongly on the quality of the velocity field and the accuracy of the streamline tracing method. For problems described on complex grids (e.g., corner-point geometry or fully unstructured grids) with full-tensor permeabilities, advanced discretization methods, such as the family of multipoint flux approximation (MPFA) schemes, are necessary to obtain an accurate representation of the fluxes across control volume faces. These fluxes are then interpolated to define the velocity field within each control volume, which is then used to trace the streamlines. Existing methods for the interpolation of the velocity field and integration of the streamlines do not preserve the accuracy of the fluxes computed by MPFA discretizations. Here we propose a method for the reconstruction of the velocity field with high-order accuracy from the fluxes provided by MPFA discretization schemes. This reconstruction relies on a correspondence between the MPFA fluxes and the degrees of freedom of a mixed finite-element method (MFEM) based on the first-order Brezzi-Douglas-Marini space. This link between the finite-volume and finite-element methods allows the use of flux reconstruction and streamline tracing techniques developed previously by the authors for mixed finite elements. After a detailed description of our streamline tracing method, we study its accuracy and efficiency using challenging test cases. Introduction The next-generation reservoir simulators will be unstructured. Several research groups throughout the industry are now developing a new breed of reservoir simulators to replace the current industry standards. One of the main advances offered by these next generation simulators is their ability to support unstructured or, at least, strongly distorted grids populated with full-tensor permeabilities. The constant evolution of reservoir modeling techniques provides an increasingly realistic description of the geological features of petroleum reservoirs. To discretize the complex geometries of geocellular models, unstructured grids seem to be a natural choice. Their inherent flexibility permits the precise description of faults, flow barriers, trapping structures, etc. Obtaining a similar accuracy with more traditional structured grids, if at all possible, would require an overwhelming number of gridblocks. However, the added flexibility of unstructured grids comes with a cost. To accurately resolve the full-tensor permeabilities or the grid distortion, a two-point flux approximation (TPFA) approach, such as that of classical finite difference (FD) methods is not sufficient. The size of the discretization stencil needs to be increased to include more pressure points in the computation of the fluxes through control volume edges. To this end, multipoint flux approximation (MPFA) methods have been developed and applied quite successfully (Aavatsmark et al. 1996; Verma and Aziz 1997; Edwards and Rogers 1998; Aavatsmark et al. 1998b; Aavatsmark et al. 1998c; Aavatsmark et al. 1998a; Edwards 2002; Lee et al. 2002a; Lee et al. 2002b). In this paper, we interpret finite volume discretizations as MFEM for which streamline tracing methods have already been developed (Matringe et al. 2006; Matringe et al. 2007b; Juanes and Matringe In Press). This approach provides a natural way of reconstructing velocity fields from TPFA or MPFA fluxes. For finite difference or TPFA discretizations, the proposed interpretation provides mathematical justification for Pollock's method (Pollock 1988) and some of its extensions to distorted grids (Cordes and Kinzelbach 1992; Prévost et al. 2002; Hægland et al. 2007; Jimenez et al. 2007). For MPFA, our approach provides a high-order streamline tracing algorithm that takes full advantage of the flux information from the MPFA discretization.

Calculation of Flow in Mixing Vessels With Various Turbulence Models

Volume 4 ◽  
2004 ◽  
Author(s):  
Branislav Basara ◽  
Ales Alajbegovic ◽  
Decan Beader
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Turbulence Model ◽  
Unstructured Grids ◽  
Turbulence Models ◽  
Cfd Applications ◽  
Volume Method ◽  
Rushton Impeller

The paper presents calculations of flow in a mixing vessel stirred by a six-blade Rushton impeller. Mathematical model used in computations is based on the ensemble averaged conservation equations. An efficient finite-volume method based on unstructured grids with rotating sliding parts composed of arbitrary polyhedral elements is used together with various turbulence models. Besides the standard k-ε model which served as a reference, k-ε-v2 model (Durbin, 1995) and the recently proposed hybrid EVM/RSM turbulence model (Basara & Jakirlic, 2003) were used in the calculations. The main aim of the paper is to investigate if more advanced turbulence models are needed for this type of CFD applications. The results are compared with the available experimental data.

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