High‐order Conservative Transport on Yin‐Yang Grids Using the Multi‐moment Constrained Finite Volume Method

2021 ◽  
Author(s):  
Juan Gu ◽  
Xindong Peng ◽  
Jun Chang ◽  
Yuzhang Che
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
High Order ◽  
Yin Yang ◽  
Volume Method

scholarly journals A Multimoment Finite-Volume Shallow-Water Model on the Yin–Yang Overset Spherical Grid

2008 ◽  
Vol 136 (8) ◽  
pp. 3066-3086 ◽  
Author(s):  
Xingliang Li ◽  
Dehui Chen ◽  
Xindong Peng ◽  
Keiko Takahashi ◽  
Feng Xiao
Keyword(s):  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Present Model ◽  
Current Model ◽  
High Order ◽  
Water Model ◽  
Yin Yang ◽  
Volume Method ◽  
High Order Interpolation

Abstract A numerical model for shallow-water equations has been built and tested on the Yin–Yang overset spherical grid. A high-order multimoment finite-volume method is used for the spatial discretization in which two kinds of so-called moments of the physical field [i.e., the volume integrated average (VIA) and the point value (PV)] are treated as the model variables and updated separately in time. In the present model, the PV is computed by the semi-implicit semi-Lagrangian formulation, whereas the VIA is predicted in time via a flux-based finite-volume method and is numerically conserved on each component grid. The concept of including an extra moment (i.e., the volume-integrated value) to enforce the numerical conservativeness provides a general methodology and applies to the existing semi-implicit semi-Lagrangian formulations. Based on both VIA and PV, the high-order interpolation reconstruction can only be done over a single grid cell, which then minimizes the overlapping zone between the Yin and Yang components and effectively reduces the numerical errors introduced in the interpolation required to communicate the data between the two components. The present model completely gets around the singularity and grid convergence in the polar regions of the conventional longitude–latitude grid. Being an issue demanding further investigation, the high-order interpolation across the overlapping region of the Yin–Yang grid in the current model does not rigorously guarantee the numerical conservativeness. Nevertheless, these numerical tests show that the global conservation error in the present model is negligibly small. The model has competitive accuracy and efficiency.

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.

A Hybrid Unstructured/Spectral Method for the Resolution of Navier-Stokes Equations

2009 ◽  
Author(s):  
Roque Corral ◽  
Javier Crespo
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
High Order ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
The Third ◽  
Third Dimension ◽  
Volume Method

A novel high-order finite volume method for the resolution of the Navier-Stokes equations is presented. The approach combines a third order finite volume method in an unstructured two-dimensional grid, with a spectral approximation in the third dimension. The method is suitable for the resolution of complex two-dimensional geometries that require the third dimension to capture three-dimensional non-linear unsteady effects, such as those for instance present in linear cascades with separated bubbles. Its main advantage is the reduction in the computational cost, for a given accuracy, with respect standard finite volume methods due to the inexpensive high-order discretization that may be obtained in the third direction using fast Fourier transforms. The method has been applied to the resolution of transitional bubbles in flat plates with adverse pressure gradients and realistic two-dimensional airfoils.

A high-order Cartesian-grid finite-volume method for aeroacoustics simulations

2014 ◽  
Vol 136 (4) ◽  
pp. 2224-2224
Author(s):  
Mehrdad H. Farahani ◽  
John Mousel ◽  
Sarah Vigmostad
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Cartesian Grid ◽  
High Order ◽  
Volume Method

scholarly journals A framework to perform high‐order deconvolution for finite‐volume method on simplicial meshes

2020 ◽  
Vol 92 (11) ◽  
pp. 1551-1583
Author(s):  
Manuel Bernard ◽  
Ghislain Lartigue ◽  
Guillaume Balarac ◽  
Vincent Moureau ◽  
Guillaume Puigt
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
High Order ◽  
Volume Method
Sign in / Sign up

Export Citation Format

Share Document