A Novel Multi-Dimensional Limiter for High-Order Finite Volume Methods on Unstructured Grids

2017 ◽  
Vol 22 (5) ◽  
pp. 1385-1412 ◽  
Author(s):  
Yilang Liu ◽  
Weiwei Zhang ◽  
Chunna Li
Keyword(s):  
Finite Volume ◽  
Unstructured Grids ◽  
Finite Volume Methods ◽  
Weighting Coefficient ◽  
Reconstruction Method ◽  
Exact Reconstruction ◽  
Slope Limiters ◽  
Flow Variables ◽  
Volume Method ◽  
Derivatives Of

AbstractThis paper proposes a novel distance derivative weighted ENO (DDWENO) limiter based on fixed reconstruction stencil and applies it to the second- and highorder finite volume method on unstructured grids. We choose the standard deviation coefficients of the flow variables as the smooth indicators by using the k-exact reconstruction method, and obtain the limited derivatives of the flow variables by weighting all derivatives of each cell according to smoothness. Furthermore, an additional weighting coefficient related to distance is introduced to emphasize the contribution of the central cell in smooth regions. The developed limiter, combining the advantages of the slope limiters and WENO-type limiters, can achieve the similar effect of WENO schemes in the fixed stencil with high computational efficiency. The numerical cases demonstrate that the DDWENO limiter can preserve the numerical accuracy in smooth regions, and capture the shock waves clearly and steeply as well.

Finite Volume Methods with Multi-Point Flux Approximation with Unstructured Grids for Diffusion Problems

2010 ◽  
Vol 297-301 ◽  
pp. 670-675
Author(s):  
Jaime Ambrus ◽  
C.R. Maliska ◽  
F.S.V. Hurtado ◽  
A.F.C. da Silva
Keyword(s):  
Finite Volume ◽  
Unstructured Grids ◽  
Control Volume ◽  
Finite Volume Methods ◽  
Porous Media Flow ◽  
Diffusion Operator ◽  
Flux Approximation ◽  
Grid Points ◽  
Volume Method ◽  
Diffusion Problems

This paper addresses the key issue of calculating fluxes at the control-volume interfaces when finite-volumes are employed for the solution of partial differential equations. This calculation becomes even more significant when unstructured grids are used, since the flux approximation involving only two grid points is no longer correct. Two finite volume methods with the ability in dealing with unstructured grids, the EbFVM-Element-based Finite Volume Method and the MPFA-Multi-Point Flux Approximation are presented, pointing out the way the fluxes are numerically evaluated. The methods are applied to a porous media flow with full permeability tensors and non-orthogonal grids and the results are compared with analytical solutions. The results can be extended to any diffusion operator, like heat and mass diffusion, in anisotropic media.

scholarly journals Extending the global-direction stencil with “face-area-weighted centroid” to unstructured finite volume discretization from integral form

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Lingfa Kong ◽  
Yidao Dong ◽  
Wei Liu ◽  
Huaibao Zhang
Keyword(s):  
Convergence Rate ◽  
Finite Volume ◽  
Differential Form ◽  
Integral Form ◽  
Finite Volume Methods ◽  
Reconstruction Method ◽  
Computational Accuracy ◽  
Face Area ◽  
Finite Volume Discretization ◽  
Skewness Reduction

AbstractAccuracy of unstructured finite volume discretization is greatly influenced by the gradient reconstruction. For the commonly used k-exact reconstruction method, the cell centroid is always chosen as the reference point to formulate the reconstructed function. But in some practical problems, such as the boundary layer, cells in this area are always set with high aspect ratio to improve the local field resolution, and if geometric centroid is still utilized for the spatial discretization, the severe grid skewness cannot be avoided, which is adverse to the numerical performance of unstructured finite volume solver. In previous work [Kong, et al. Chin Phys B 29(10):100203, 2020], we explored a novel global-direction stencil and combined it with the face-area-weighted centroid on unstructured finite volume methods from differential form to realize the skewness reduction and a better reflection of flow anisotropy. Greatly inspired by the differential form, in this research, we demonstrate that it is also feasible to extend this novel method to the unstructured finite volume discretization from integral form on both second and third-order finite volume solver. Numerical examples governed by linear convective, Euler and Laplacian equations are utilized to examine the correctness as well as effectiveness of this extension. Compared with traditional vertex-neighbor and face-neighbor stencils based on the geometric centroid, the grid skewness is almost eliminated and computational accuracy as well as convergence rate is greatly improved by the global-direction stencil with face-area-weighted centroid. As a result, on unstructured finite volume discretization from integral form, the method also has superiorities on both computational accuracy and convergence rate.

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.

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.

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